(ignored inputs)COMMENT from Example 3 of \cite{OO03} Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_9)),0,mod(-(0,s(?y_9)),s(?y_9))), 0 = 0, gcd(0,mod(?x_11,0)) = ?x_11, gcd(?y_11,mod(0,?y_11)) = ?y_11, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_9)),0,mod(-(0,s(?y_9)),s(?y_9))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <4, 3> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <9, 8> preceded by [] joinable by a reduction of rules <[([(if,1)],6),([],0)], []> Critical Pair <0, 0> by Rules <10, 8> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <12, 11> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],10),([],13)]> joinable by a reduction of rules <[], [([],13),([],10)]> Critical Pair by Rules <13, 11> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],8),([],12)]> Critical Pair <0, 0> by Rules <13, 12> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 42*42=>42 0 : =>42 < : 42*42=>48 s : 42=>42 if : 48*42*42=>42 gcd : 42*42=>42 mod : 42*42=>42 true : =>48 false : =>48 maximal types: {42,48} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge Try Commutative Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Outside Critical Pair: <0, 0> by Rules <4, 3> develop reducts from lhs term... <{}, 0> develop reducts from rhs term... <{}, 0> Outside Critical Pair: by Rules <9, 8> develop reducts from lhs term... <{4,6,9}, if(true,0,if(<(0,s(?y_9)),0,mod(-(0,s(?y_9)),s(?y_9))))> <{6,9}, if(true,0,if(<(-(0,s(?y_9)),s(?y_9)),-(0,s(?y_9)),mod(-(-(0,s(?y_9)),s(?y_9)),s(?y_9))))> <{4,6}, if(true,0,mod(0,s(?y_9)))> <{6}, if(true,0,mod(-(0,s(?y_9)),s(?y_9)))> <{4,9}, if(<(0,s(?y_9)),0,if(<(0,s(?y_9)),0,mod(-(0,s(?y_9)),s(?y_9))))> <{9}, if(<(0,s(?y_9)),0,if(<(-(0,s(?y_9)),s(?y_9)),-(0,s(?y_9)),mod(-(-(0,s(?y_9)),s(?y_9)),s(?y_9))))> <{4}, if(<(0,s(?y_9)),0,mod(0,s(?y_9)))> <{}, if(<(0,s(?y_9)),0,mod(-(0,s(?y_9)),s(?y_9)))> develop reducts from rhs term... <{}, 0> Outside Critical Pair: <0, 0> by Rules <10, 8> develop reducts from lhs term... <{}, 0> develop reducts from rhs term... <{}, 0> Outside Critical Pair: by Rules <12, 11> develop reducts from lhs term... <{}, ?x_12> develop reducts from rhs term... <{10,13}, ?x_12> <{13}, mod(?x_12,0)> <{10,11}, gcd(?x_12,mod(0,?x_12))> <{11}, gcd(mod(?x_12,0),mod(0,mod(?x_12,0)))> <{10}, gcd(0,?x_12)> <{}, gcd(0,mod(?x_12,0))> Outside Critical Pair: by Rules <13, 11> develop reducts from lhs term... <{}, ?x_13> develop reducts from rhs term... <{8,11}, gcd(0,mod(?x_13,0))> <{11}, gcd(mod(0,?x_13),mod(?x_13,mod(0,?x_13)))> <{8}, gcd(?x_13,0)> <{}, gcd(?x_13,mod(0,?x_13))> Outside Critical Pair: <0, 0> by Rules <13, 12> develop reducts from lhs term... <{}, 0> develop reducts from rhs term... <{}, 0> Try A Minimal Decomposition {8,9}{13,11,12}{0}{1}{2}{3}{4}{5}{6}{7}{10} {8,9} (cm)Rewrite Rules: [ mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_1)),0,mod(-(0,s(?y_1)),s(?y_1))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_1)),0,mod(-(0,s(?y_1)),s(?y_1))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <1, 0> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_1)),0,if(<(-(0,s(?y_1)),s(?y_1)),-(0,s(?y_1)),if(<(-(-(0,s(?y_1)),s(?y_1)),s(?y_1)),-(-(0,s(?y_1)),s(?y_1)),mod(-(-(-(0,s(?y_1)),s(?y_1)),s(?y_1)),s(?y_1)))))> from mod(0,s(?y_1)) Not Confluent Direct Methods: not CR {13,11,12} (cm)Rewrite Rules: [ gcd(0,?x) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ ?x = gcd(?x,mod(0,?x)), 0 = 0, gcd(0,mod(?x_1,0)) = ?x_1 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(0,mod(?x,0)) = ?x, ?x = gcd(0,mod(?x,0)), ?y = gcd(?y,mod(0,?y)), 0 = 0, gcd(?x,mod(0,?x)) = ?x ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <1, 0> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_1,0) Not Confluent Direct Methods: not CR {0} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ ] Overlay, check Innermost Termination... Innermost Terminating (hence Terminating), WCR Knuth&Bendix Direct Methods: CR {1} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ ] Overlay, check Innermost Termination... Innermost Terminating (hence Terminating), WCR Knuth&Bendix Direct Methods: CR {2} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ ] Overlay, check Innermost Termination... Innermost Terminating (hence Terminating), WCR Knuth&Bendix Direct Methods: CR {3} (cm)Rewrite Rules: [ -(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ ] Overlay, check Innermost Termination... Innermost Terminating (hence Terminating), WCR Knuth&Bendix Direct Methods: CR {4} (cm)Rewrite Rules: [ -(0,?x) -> 0 ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ ] Overlay, check Innermost Termination... Innermost Terminating (hence Terminating), WCR Knuth&Bendix Direct Methods: CR {5} (cm)Rewrite Rules: [ <(s(?x),s(?y)) -> <(?x,?y) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ ] Overlay, check Innermost Termination... Innermost Terminating (hence Terminating), WCR Knuth&Bendix Direct Methods: CR {6} (cm)Rewrite Rules: [ <(0,s(?x)) -> true ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ ] Overlay, check Innermost Termination... Innermost Terminating (hence Terminating), WCR Knuth&Bendix Direct Methods: CR {7} (cm)Rewrite Rules: [ <(?x,0) -> false ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ ] Overlay, check Innermost Termination... Innermost Terminating (hence Terminating), WCR Knuth&Bendix Direct Methods: CR {10} (cm)Rewrite Rules: [ mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ ] Overlay, check Innermost Termination... Innermost Terminating (hence Terminating), WCR Knuth&Bendix Direct Methods: CR Try to add other components to {8,9} Add {13,11,12} {8,9,11,12,13} (cm)Rewrite Rules: [ mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_1)),0,mod(-(0,s(?y_1)),s(?y_1))), gcd(0,mod(?x_2,0)) = ?x_2, gcd(?y_2,mod(0,?y_2)) = ?y_2, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_1)),0,mod(-(0,s(?y_1)),s(?y_1))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <1, 0> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_2,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0} {0,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))), gcd(0,mod(?x_3,0)) = ?x_3, gcd(?y_3,mod(0,?y_3)) = ?y_3, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <2, 1> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_3,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1} {0,1,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), gcd(0,mod(?x_4,0)) = ?x_4, gcd(?y_4,mod(0,?y_4)) = ?y_4, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_4,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{2} {0,1,2,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_5,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{2}{3} {0,1,2,3,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{2}{3}{4} {0,1,2,3,4,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <4, 3> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_7,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{2}{3}{4}{5} {0,1,2,3,4,5,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <4, 3> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_8,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{2}{3}{4}{5}{6} {0,1,2,3,4,5,6,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))), gcd(0,mod(?x_9,0)) = ?x_9, gcd(?y_9,mod(0,?y_9)) = ?y_9, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <4, 3> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <8, 7> preceded by [] joinable by a reduction of rules <[([(if,1)],6),([],0)], []> Critical Pair by Rules <10, 9> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_9,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{2}{3}{4}{5}{6}{7} {0,1,2,3,4,5,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_9)),0,mod(-(0,s(?y_9)),s(?y_9))), gcd(0,mod(?x_10,0)) = ?x_10, gcd(?y_10,mod(0,?y_10)) = ?y_10, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_9)),0,mod(-(0,s(?y_9)),s(?y_9))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <4, 3> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <9, 8> preceded by [] joinable by a reduction of rules <[([(if,1)],6),([],0)], []> Critical Pair by Rules <11, 10> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_10,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{2}{3}{4}{5}{6}{10} {0,1,2,3,4,5,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))), 0 = 0, gcd(0,mod(?x_10,0)) = ?x_10, gcd(?y_10,mod(0,?y_10)) = ?y_10, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <4, 3> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <8, 7> preceded by [] joinable by a reduction of rules <[([(if,1)],6),([],0)], []> Critical Pair <0, 0> by Rules <9, 7> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <11, 10> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],9),([],12)]> joinable by a reduction of rules <[], [([],12),([],9)]> Critical Pair by Rules <12, 10> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],7),([],11)]> Critical Pair <0, 0> by Rules <12, 11> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 41*41=>41 0 : =>41 < : 41*41=>47 s : 41=>41 if : 47*41*41=>41 gcd : 41*41=>41 mod : 41*41=>41 true : =>47 false : =>47 maximal types: {41,47} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{1}{2}{3}{4}{5}{7} {0,1,2,3,4,5,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))), gcd(0,mod(?x_9,0)) = ?x_9, gcd(?y_9,mod(0,?y_9)) = ?y_9, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <4, 3> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <8, 7> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_9,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{2}{3}{4}{5}{10} {0,1,2,3,4,5,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), 0 = 0, gcd(0,mod(?x_9,0)) = ?x_9, gcd(?y_9,mod(0,?y_9)) = ?y_9, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <4, 3> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_7)),0,0)> from mod(0,s(?y_7)) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{2}{3}{4}{5}{7}{10} {0,1,2,3,4,5,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))), 0 = 0, gcd(0,mod(?x_10,0)) = ?x_10, gcd(?y_10,mod(0,?y_10)) = ?y_10, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <4, 3> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <8, 7> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_8)),0,0)> from mod(0,s(?y_8)) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{2}{3}{4}{6} {0,1,2,3,4,6,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <4, 3> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],5),([],0)], []> Critical Pair by Rules <9, 8> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_8,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{2}{3}{4}{6}{7} {0,1,2,3,4,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))), gcd(0,mod(?x_9,0)) = ?x_9, gcd(?y_9,mod(0,?y_9)) = ?y_9, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <4, 3> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <8, 7> preceded by [] joinable by a reduction of rules <[([(if,1)],5),([],0)], []> Critical Pair by Rules <10, 9> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_9,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{2}{3}{4}{6}{10} {0,1,2,3,4,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), 0 = 0, gcd(0,mod(?x_9,0)) = ?x_9, gcd(?y_9,mod(0,?y_9)) = ?y_9, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <4, 3> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],5),([],0)], []> Critical Pair <0, 0> by Rules <8, 6> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <10, 9> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],8),([],11)]> joinable by a reduction of rules <[], [([],11),([],8)]> Critical Pair by Rules <11, 9> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],6),([],10)]> Critical Pair <0, 0> by Rules <11, 10> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 39*39=>39 0 : =>39 < : 39*39=>45 s : 39=>39 if : 45*39*39=>39 gcd : 39*39=>39 mod : 39*39=>39 true : =>45 false : =>45 maximal types: {39,45} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{1}{2}{3}{4}{7} {0,1,2,3,4,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <4, 3> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_8,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{2}{3}{4}{10} {0,1,2,3,4,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0, gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <4, 3> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{2}{3}{4}{7}{10} {0,1,2,3,4,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), 0 = 0, gcd(0,mod(?x_9,0)) = ?x_9, gcd(?y_9,mod(0,?y_9)) = ?y_9, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <4, 3> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_7)),0,0)> from mod(0,s(?y_7)) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{2}{3}{4}{6}{7}{10} {0,1,2,3,4,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))), 0 = 0, gcd(0,mod(?x_10,0)) = ?x_10, gcd(?y_10,mod(0,?y_10)) = ?y_10, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <4, 3> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <8, 7> preceded by [] joinable by a reduction of rules <[([(if,1)],5),([],0)], []> Critical Pair <0, 0> by Rules <9, 7> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <11, 10> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],9),([],12)]> joinable by a reduction of rules <[], [([],12),([],9)]> Critical Pair by Rules <12, 10> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],7),([],11)]> Critical Pair <0, 0> by Rules <12, 11> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 40*40=>40 0 : =>40 < : 40*40=>46 s : 40=>40 if : 46*40*40=>40 gcd : 40*40=>40 mod : 40*40=>40 true : =>46 false : =>46 maximal types: {40,46} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{1}{2}{3}{5} {0,1,2,3,5,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_7,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{2}{3}{5}{6} {0,1,2,3,5,6,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],5),([],0)], []> Critical Pair by Rules <9, 8> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_8,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{2}{3}{5}{6}{7} {0,1,2,3,5,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))), gcd(0,mod(?x_9,0)) = ?x_9, gcd(?y_9,mod(0,?y_9)) = ?y_9, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <8, 7> preceded by [] joinable by a reduction of rules <[([(if,1)],5),([],0)], []> Critical Pair by Rules <10, 9> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_9,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{2}{3}{5}{6}{10} {0,1,2,3,5,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), 0 = 0, gcd(0,mod(?x_9,0)) = ?x_9, gcd(?y_9,mod(0,?y_9)) = ?y_9, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],5),([],0)], []> Critical Pair <0, 0> by Rules <8, 6> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <10, 9> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],8),([],11)]> joinable by a reduction of rules <[], [([],11),([],8)]> Critical Pair by Rules <11, 9> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],6),([],10)]> Critical Pair <0, 0> by Rules <11, 10> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 40*40=>40 0 : =>40 < : 40*40=>46 s : 40=>40 if : 46*40*40=>40 gcd : 40*40=>40 mod : 40*40=>40 true : =>46 false : =>46 maximal types: {40,46} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{1}{2}{3}{5}{7} {0,1,2,3,5,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_8,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{2}{3}{5}{10} {0,1,2,3,5,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0, gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 39*39=>39 0 : =>39 < : 39*39=>27 s : 39=>39 if : 27*39*39=>39 gcd : 39*39=>39 mod : 39*39=>39 true : =>27 false : =>27 maximal types: {27,39} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{1}{2}{3}{5}{7}{10} {0,1,2,3,5,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), 0 = 0, gcd(0,mod(?x_9,0)) = ?x_9, gcd(?y_9,mod(0,?y_9)) = ?y_9, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 40*40=>40 0 : =>40 < : 40*40=>46 s : 40=>40 if : 46*40*40=>40 gcd : 40*40=>40 mod : 40*40=>40 true : =>46 false : =>46 maximal types: {40,46} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{1}{2}{3}{6} {0,1,2,3,6,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair by Rules <8, 7> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_7,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{2}{3}{6}{7} {0,1,2,3,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair by Rules <9, 8> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_8,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{2}{3}{6}{10} {0,1,2,3,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0, gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair <0, 0> by Rules <7, 5> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <9, 8> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],7),([],10)]> joinable by a reduction of rules <[], [([],10),([],7)]> Critical Pair by Rules <10, 8> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],5),([],9)]> Critical Pair <0, 0> by Rules <10, 9> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 38*38=>38 0 : =>38 < : 38*38=>44 s : 38=>38 if : 44*38*38=>38 gcd : 38*38=>38 mod : 38*38=>38 true : =>44 false : =>44 maximal types: {38,44} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{1}{2}{3}{7} {0,1,2,3,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_7,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{2}{3}{10} {0,1,2,3,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 37*37=>37 0 : =>37 < : 37*37=>25 s : 37=>37 if : 25*37*37=>37 gcd : 37*37=>37 mod : 37*37=>37 true : =>25 false : =>25 maximal types: {25,37} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{1}{2}{3}{7}{10} {0,1,2,3,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0, gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 38*38=>38 0 : =>38 < : 38*38=>44 s : 38=>38 if : 44*38*38=>38 gcd : 38*38=>38 mod : 38*38=>38 true : =>44 false : =>44 maximal types: {38,44} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{1}{2}{3}{6}{7}{10} {0,1,2,3,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), 0 = 0, gcd(0,mod(?x_9,0)) = ?x_9, gcd(?y_9,mod(0,?y_9)) = ?y_9, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair <0, 0> by Rules <8, 6> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <10, 9> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],8),([],11)]> joinable by a reduction of rules <[], [([],11),([],8)]> Critical Pair by Rules <11, 9> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],6),([],10)]> Critical Pair <0, 0> by Rules <11, 10> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 39*39=>39 0 : =>39 < : 39*39=>45 s : 39=>39 if : 45*39*39=>39 gcd : 39*39=>39 mod : 39*39=>39 true : =>45 false : =>45 maximal types: {39,45} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{1}{2}{3}{5}{6}{7}{10} {0,1,2,3,5,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))), 0 = 0, gcd(0,mod(?x_10,0)) = ?x_10, gcd(?y_10,mod(0,?y_10)) = ?y_10, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <8, 7> preceded by [] joinable by a reduction of rules <[([(if,1)],5),([],0)], []> Critical Pair <0, 0> by Rules <9, 7> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <11, 10> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],9),([],12)]> joinable by a reduction of rules <[], [([],12),([],9)]> Critical Pair by Rules <12, 10> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],7),([],11)]> Critical Pair <0, 0> by Rules <12, 11> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 41*41=>41 0 : =>41 < : 41*41=>47 s : 41=>41 if : 47*41*41=>41 gcd : 41*41=>41 mod : 41*41=>41 true : =>47 false : =>47 maximal types: {41,47} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{1}{2}{4} {0,1,2,4,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{2}{4}{5} {0,1,2,4,5,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_7,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{2}{4}{5}{6} {0,1,2,4,5,6,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],5),([],0)], []> Critical Pair by Rules <9, 8> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_8,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{2}{4}{5}{6}{7} {0,1,2,4,5,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))), gcd(0,mod(?x_9,0)) = ?x_9, gcd(?y_9,mod(0,?y_9)) = ?y_9, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <8, 7> preceded by [] joinable by a reduction of rules <[([(if,1)],5),([],0)], []> Critical Pair by Rules <10, 9> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_9,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{2}{4}{5}{6}{10} {0,1,2,4,5,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), 0 = 0, gcd(0,mod(?x_9,0)) = ?x_9, gcd(?y_9,mod(0,?y_9)) = ?y_9, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],5),([],0)], []> Critical Pair <0, 0> by Rules <8, 6> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <10, 9> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],8),([],11)]> joinable by a reduction of rules <[], [([],11),([],8)]> Critical Pair by Rules <11, 9> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],6),([],10)]> Critical Pair <0, 0> by Rules <11, 10> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 40*40=>40 0 : =>40 < : 40*40=>46 s : 40=>40 if : 46*40*40=>40 gcd : 40*40=>40 mod : 40*40=>40 true : =>46 false : =>46 maximal types: {40,46} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{1}{2}{4}{5}{7} {0,1,2,4,5,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_8,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{2}{4}{5}{10} {0,1,2,4,5,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0, gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{2}{4}{5}{7}{10} {0,1,2,4,5,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), 0 = 0, gcd(0,mod(?x_9,0)) = ?x_9, gcd(?y_9,mod(0,?y_9)) = ?y_9, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_7)),0,0)> from mod(0,s(?y_7)) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{2}{4}{6} {0,1,2,4,6,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair by Rules <8, 7> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_7,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{2}{4}{6}{7} {0,1,2,4,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair by Rules <9, 8> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_8,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{2}{4}{6}{10} {0,1,2,4,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0, gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair <0, 0> by Rules <7, 5> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <9, 8> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],7),([],10)]> joinable by a reduction of rules <[], [([],10),([],7)]> Critical Pair by Rules <10, 8> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],5),([],9)]> Critical Pair <0, 0> by Rules <10, 9> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 38*38=>38 0 : =>38 < : 38*38=>44 s : 38=>38 if : 44*38*38=>38 gcd : 38*38=>38 mod : 38*38=>38 true : =>44 false : =>44 maximal types: {38,44} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{1}{2}{4}{7} {0,1,2,4,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_7,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{2}{4}{10} {0,1,2,4,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{2}{4}{7}{10} {0,1,2,4,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0, gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{2}{4}{6}{7}{10} {0,1,2,4,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), 0 = 0, gcd(0,mod(?x_9,0)) = ?x_9, gcd(?y_9,mod(0,?y_9)) = ?y_9, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair <0, 0> by Rules <8, 6> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <10, 9> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],8),([],11)]> joinable by a reduction of rules <[], [([],11),([],8)]> Critical Pair by Rules <11, 9> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],6),([],10)]> Critical Pair <0, 0> by Rules <11, 10> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 39*39=>39 0 : =>39 < : 39*39=>45 s : 39=>39 if : 45*39*39=>39 gcd : 39*39=>39 mod : 39*39=>39 true : =>45 false : =>45 maximal types: {39,45} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{1}{2}{5} {0,1,2,5,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{2}{5}{6} {0,1,2,5,6,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair by Rules <8, 7> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_7,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{2}{5}{6}{7} {0,1,2,5,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair by Rules <9, 8> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_8,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{2}{5}{6}{10} {0,1,2,5,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0, gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair <0, 0> by Rules <7, 5> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <9, 8> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],7),([],10)]> joinable by a reduction of rules <[], [([],10),([],7)]> Critical Pair by Rules <10, 8> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],5),([],9)]> Critical Pair <0, 0> by Rules <10, 9> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 39*39=>39 0 : =>39 < : 39*39=>45 s : 39=>39 if : 45*39*39=>39 gcd : 39*39=>39 mod : 39*39=>39 true : =>45 false : =>45 maximal types: {39,45} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{1}{2}{5}{7} {0,1,2,5,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_7,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{2}{5}{10} {0,1,2,5,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 38*38=>38 0 : =>38 < : 38*38=>26 s : 38=>38 if : 26*38*38=>38 gcd : 38*38=>38 mod : 38*38=>38 true : =>26 false : =>26 maximal types: {26,38} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{1}{2}{5}{7}{10} {0,1,2,5,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0, gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 39*39=>39 0 : =>39 < : 39*39=>45 s : 39=>39 if : 45*39*39=>39 gcd : 39*39=>39 mod : 39*39=>39 true : =>45 false : =>45 maximal types: {39,45} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{1}{2}{6} {0,1,2,6,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{2}{6}{7} {0,1,2,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair by Rules <8, 7> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_7,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{2}{6}{10} {0,1,2,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair <0, 0> by Rules <6, 4> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <8, 7> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],6),([],9)]> joinable by a reduction of rules <[], [([],9),([],6)]> Critical Pair by Rules <9, 7> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],4),([],8)]> Critical Pair <0, 0> by Rules <9, 8> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 37*37=>37 0 : =>37 < : 37*37=>43 s : 37=>37 if : 43*37*37=>37 gcd : 37*37=>37 mod : 37*37=>37 true : =>43 false : =>43 maximal types: {37,43} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{1}{2}{7} {0,1,2,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{2}{10} {0,1,2,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0, gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 36*36=>36 0 : =>36 < : 36*36=>24 s : 36=>36 if : 24*36*36=>36 gcd : 36*36=>36 mod : 36*36=>36 true : =>24 false : =>24 maximal types: {24,36} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{1}{2}{7}{10} {0,1,2,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 37*37=>37 0 : =>37 < : 37*37=>43 s : 37=>37 if : 43*37*37=>37 gcd : 37*37=>37 mod : 37*37=>37 true : =>43 false : =>43 maximal types: {37,43} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{1}{2}{6}{7}{10} {0,1,2,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0, gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair <0, 0> by Rules <7, 5> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <9, 8> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],7),([],10)]> joinable by a reduction of rules <[], [([],10),([],7)]> Critical Pair by Rules <10, 8> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],5),([],9)]> Critical Pair <0, 0> by Rules <10, 9> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 38*38=>38 0 : =>38 < : 38*38=>44 s : 38=>38 if : 44*38*38=>38 gcd : 38*38=>38 mod : 38*38=>38 true : =>44 false : =>44 maximal types: {38,44} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{1}{2}{5}{6}{7}{10} {0,1,2,5,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), 0 = 0, gcd(0,mod(?x_9,0)) = ?x_9, gcd(?y_9,mod(0,?y_9)) = ?y_9, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair <0, 0> by Rules <8, 6> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <10, 9> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],8),([],11)]> joinable by a reduction of rules <[], [([],11),([],8)]> Critical Pair by Rules <11, 9> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],6),([],10)]> Critical Pair <0, 0> by Rules <11, 10> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 40*40=>40 0 : =>40 < : 40*40=>46 s : 40=>40 if : 46*40*40=>40 gcd : 40*40=>40 mod : 40*40=>40 true : =>46 false : =>46 maximal types: {40,46} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{1}{2}{4}{5}{6}{7}{10} {0,1,2,4,5,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))), 0 = 0, gcd(0,mod(?x_10,0)) = ?x_10, gcd(?y_10,mod(0,?y_10)) = ?y_10, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <8, 7> preceded by [] joinable by a reduction of rules <[([(if,1)],5),([],0)], []> Critical Pair <0, 0> by Rules <9, 7> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <11, 10> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],9),([],12)]> joinable by a reduction of rules <[], [([],12),([],9)]> Critical Pair by Rules <12, 10> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],7),([],11)]> Critical Pair <0, 0> by Rules <12, 11> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 41*41=>41 0 : =>41 < : 41*41=>47 s : 41=>41 if : 47*41*41=>41 gcd : 41*41=>41 mod : 41*41=>41 true : =>47 false : =>47 maximal types: {41,47} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{1}{3} {0,1,3,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_5,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{3}{4} {0,1,3,4,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{3}{4}{5} {0,1,3,4,5,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_7,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{3}{4}{5}{6} {0,1,3,4,5,6,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],5),([],0)], []> Critical Pair by Rules <9, 8> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_8,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{3}{4}{5}{6}{7} {0,1,3,4,5,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))), gcd(0,mod(?x_9,0)) = ?x_9, gcd(?y_9,mod(0,?y_9)) = ?y_9, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <8, 7> preceded by [] joinable by a reduction of rules <[([(if,1)],5),([],0)], []> Critical Pair by Rules <10, 9> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_9,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{3}{4}{5}{6}{10} {0,1,3,4,5,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), 0 = 0, gcd(0,mod(?x_9,0)) = ?x_9, gcd(?y_9,mod(0,?y_9)) = ?y_9, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],5),([],0)], []> Critical Pair <0, 0> by Rules <8, 6> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <10, 9> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],8),([],11)]> joinable by a reduction of rules <[], [([],11),([],8)]> Critical Pair by Rules <11, 9> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],6),([],10)]> Critical Pair <0, 0> by Rules <11, 10> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 39*39=>39 0 : =>39 < : 39*39=>45 s : 39=>39 if : 45*39*39=>39 gcd : 39*39=>39 mod : 39*39=>39 true : =>45 false : =>45 maximal types: {39,45} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{1}{3}{4}{5}{7} {0,1,3,4,5,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_8,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{3}{4}{5}{10} {0,1,3,4,5,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0, gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{3}{4}{5}{7}{10} {0,1,3,4,5,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), 0 = 0, gcd(0,mod(?x_9,0)) = ?x_9, gcd(?y_9,mod(0,?y_9)) = ?y_9, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_7)),0,0)> from mod(0,s(?y_7)) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{3}{4}{6} {0,1,3,4,6,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair by Rules <8, 7> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_7,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{3}{4}{6}{7} {0,1,3,4,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair by Rules <9, 8> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_8,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{3}{4}{6}{10} {0,1,3,4,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0, gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair <0, 0> by Rules <7, 5> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <9, 8> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],7),([],10)]> joinable by a reduction of rules <[], [([],10),([],7)]> Critical Pair by Rules <10, 8> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],5),([],9)]> Critical Pair <0, 0> by Rules <10, 9> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 37*37=>37 0 : =>37 < : 37*37=>43 s : 23=>37 if : 43*37*37=>37 gcd : 37*37=>37 mod : 37*37=>37 true : =>43 false : =>43 maximal types: {23,37,43} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{1}{3}{4}{7} {0,1,3,4,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_7,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{3}{4}{10} {0,1,3,4,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{3}{4}{7}{10} {0,1,3,4,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0, gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{3}{4}{6}{7}{10} {0,1,3,4,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), 0 = 0, gcd(0,mod(?x_9,0)) = ?x_9, gcd(?y_9,mod(0,?y_9)) = ?y_9, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair <0, 0> by Rules <8, 6> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <10, 9> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],8),([],11)]> joinable by a reduction of rules <[], [([],11),([],8)]> Critical Pair by Rules <11, 9> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],6),([],10)]> Critical Pair <0, 0> by Rules <11, 10> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 38*38=>38 0 : =>38 < : 38*38=>44 s : 24=>38 if : 44*38*38=>38 gcd : 38*38=>38 mod : 38*38=>38 true : =>44 false : =>44 maximal types: {24,38,44} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{1}{3}{5} {0,1,3,5,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{3}{5}{6} {0,1,3,5,6,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair by Rules <8, 7> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_7,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{3}{5}{6}{7} {0,1,3,5,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair by Rules <9, 8> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_8,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{3}{5}{6}{10} {0,1,3,5,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0, gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair <0, 0> by Rules <7, 5> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <9, 8> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],7),([],10)]> joinable by a reduction of rules <[], [([],10),([],7)]> Critical Pair by Rules <10, 8> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],5),([],9)]> Critical Pair <0, 0> by Rules <10, 9> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 38*38=>38 0 : =>38 < : 38*38=>44 s : 38=>38 if : 44*38*38=>38 gcd : 38*38=>38 mod : 38*38=>38 true : =>44 false : =>44 maximal types: {38,44} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{1}{3}{5}{7} {0,1,3,5,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_7,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{3}{5}{10} {0,1,3,5,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 37*37=>37 0 : =>37 < : 37*37=>25 s : 37=>37 if : 25*37*37=>37 gcd : 37*37=>37 mod : 37*37=>37 true : =>25 false : =>25 maximal types: {25,37} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{1}{3}{5}{7}{10} {0,1,3,5,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0, gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 38*38=>38 0 : =>38 < : 38*38=>44 s : 38=>38 if : 44*38*38=>38 gcd : 38*38=>38 mod : 38*38=>38 true : =>44 false : =>44 maximal types: {38,44} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{1}{3}{6} {0,1,3,6,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{3}{6}{7} {0,1,3,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair by Rules <8, 7> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_7,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{3}{6}{10} {0,1,3,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair <0, 0> by Rules <6, 4> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <8, 7> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],6),([],9)]> joinable by a reduction of rules <[], [([],9),([],6)]> Critical Pair by Rules <9, 7> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],4),([],8)]> Critical Pair <0, 0> by Rules <9, 8> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 36*36=>36 0 : =>36 < : 36*36=>42 s : 22=>36 if : 42*36*36=>36 gcd : 36*36=>36 mod : 36*36=>36 true : =>42 false : =>42 maximal types: {22,36,42} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{1}{3}{7} {0,1,3,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{3}{10} {0,1,3,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0, gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 35*35=>35 0 : =>35 < : 35*35=>23 s : 21=>35 if : 23*35*35=>35 gcd : 35*35=>35 mod : 35*35=>35 true : =>23 false : =>23 maximal types: {21,23,35} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{1}{3}{7}{10} {0,1,3,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 36*36=>36 0 : =>36 < : 36*36=>42 s : 22=>36 if : 42*36*36=>36 gcd : 36*36=>36 mod : 36*36=>36 true : =>42 false : =>42 maximal types: {22,36,42} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{1}{3}{6}{7}{10} {0,1,3,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0, gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair <0, 0> by Rules <7, 5> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <9, 8> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],7),([],10)]> joinable by a reduction of rules <[], [([],10),([],7)]> Critical Pair by Rules <10, 8> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],5),([],9)]> Critical Pair <0, 0> by Rules <10, 9> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 37*37=>37 0 : =>37 < : 37*37=>43 s : 23=>37 if : 43*37*37=>37 gcd : 37*37=>37 mod : 37*37=>37 true : =>43 false : =>43 maximal types: {23,37,43} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{1}{3}{5}{6}{7}{10} {0,1,3,5,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), 0 = 0, gcd(0,mod(?x_9,0)) = ?x_9, gcd(?y_9,mod(0,?y_9)) = ?y_9, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair <0, 0> by Rules <8, 6> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <10, 9> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],8),([],11)]> joinable by a reduction of rules <[], [([],11),([],8)]> Critical Pair by Rules <11, 9> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],6),([],10)]> Critical Pair <0, 0> by Rules <11, 10> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 39*39=>39 0 : =>39 < : 39*39=>45 s : 39=>39 if : 45*39*39=>39 gcd : 39*39=>39 mod : 39*39=>39 true : =>45 false : =>45 maximal types: {39,45} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{1}{4} {0,1,4,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_5,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{4}{5} {0,1,4,5,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{4}{5}{6} {0,1,4,5,6,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair by Rules <8, 7> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_7,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{4}{5}{6}{7} {0,1,4,5,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair by Rules <9, 8> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_8,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{4}{5}{6}{10} {0,1,4,5,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0, gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair <0, 0> by Rules <7, 5> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <9, 8> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],7),([],10)]> joinable by a reduction of rules <[], [([],10),([],7)]> Critical Pair by Rules <10, 8> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],5),([],9)]> Critical Pair <0, 0> by Rules <10, 9> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 38*38=>38 0 : =>38 < : 38*38=>44 s : 38=>38 if : 44*38*38=>38 gcd : 38*38=>38 mod : 38*38=>38 true : =>44 false : =>44 maximal types: {38,44} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{1}{4}{5}{7} {0,1,4,5,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_7,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{4}{5}{10} {0,1,4,5,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{4}{5}{7}{10} {0,1,4,5,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0, gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{4}{6} {0,1,4,6,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{4}{6}{7} {0,1,4,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair by Rules <8, 7> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_7,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{4}{6}{10} {0,1,4,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair <0, 0> by Rules <6, 4> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <8, 7> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],6),([],9)]> joinable by a reduction of rules <[], [([],9),([],6)]> Critical Pair by Rules <9, 7> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],4),([],8)]> Critical Pair <0, 0> by Rules <9, 8> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 36*36=>36 0 : =>36 < : 36*36=>42 s : 22=>36 if : 42*36*36=>36 gcd : 36*36=>36 mod : 36*36=>36 true : =>42 false : =>42 maximal types: {22,36,42} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{1}{4}{7} {0,1,4,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{4}{10} {0,1,4,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0, gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{4}{7}{10} {0,1,4,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{4}{6}{7}{10} {0,1,4,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0, gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair <0, 0> by Rules <7, 5> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <9, 8> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],7),([],10)]> joinable by a reduction of rules <[], [([],10),([],7)]> Critical Pair by Rules <10, 8> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],5),([],9)]> Critical Pair <0, 0> by Rules <10, 9> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 37*37=>37 0 : =>37 < : 37*37=>43 s : 23=>37 if : 43*37*37=>37 gcd : 37*37=>37 mod : 37*37=>37 true : =>43 false : =>43 maximal types: {23,37,43} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{1}{5} {0,1,5,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_5,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{5}{6} {0,1,5,6,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{5}{6}{7} {0,1,5,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair by Rules <8, 7> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_7,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{5}{6}{10} {0,1,5,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair <0, 0> by Rules <6, 4> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <8, 7> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],6),([],9)]> joinable by a reduction of rules <[], [([],9),([],6)]> Critical Pair by Rules <9, 7> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],4),([],8)]> Critical Pair <0, 0> by Rules <9, 8> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 37*37=>37 0 : =>37 < : 37*37=>43 s : 37=>37 if : 43*37*37=>37 gcd : 37*37=>37 mod : 37*37=>37 true : =>43 false : =>43 maximal types: {37,43} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{1}{5}{7} {0,1,5,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{5}{10} {0,1,5,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0, gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 36*36=>36 0 : =>36 < : 36*36=>24 s : 36=>36 if : 24*36*36=>36 gcd : 36*36=>36 mod : 36*36=>36 true : =>24 false : =>24 maximal types: {24,36} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{1}{5}{7}{10} {0,1,5,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 37*37=>37 0 : =>37 < : 37*37=>43 s : 37=>37 if : 43*37*37=>37 gcd : 37*37=>37 mod : 37*37=>37 true : =>43 false : =>43 maximal types: {37,43} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{1}{6} {0,1,6,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] joinable by a reduction of rules <[([(if,1)],2),([],0)], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_5,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{6}{7} {0,1,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],2),([],0)], []> Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{6}{10} {0,1,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0, gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] joinable by a reduction of rules <[([(if,1)],2),([],0)], []> Critical Pair <0, 0> by Rules <5, 3> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],5),([],8)]> joinable by a reduction of rules <[], [([],8),([],5)]> Critical Pair by Rules <8, 6> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],3),([],7)]> Critical Pair <0, 0> by Rules <8, 7> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 35*35=>35 0 : =>35 < : 35*35=>41 s : 21=>35 if : 41*35*35=>35 gcd : 35*35=>35 mod : 35*35=>35 true : =>41 false : =>41 maximal types: {21,35,41} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{1}{7} {0,1,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_5,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{1}{10} {0,1,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), 0 = 0, gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 34*34=>34 0 : =>34 < : 34*34=>22 s : 20=>34 if : 22*34*34=>34 gcd : 34*34=>34 mod : 34*34=>34 true : =>22 false : =>22 maximal types: {20,22,34} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{1}{7}{10} {0,1,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0, gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 35*35=>35 0 : =>35 < : 35*35=>41 s : 21=>35 if : 41*35*35=>35 gcd : 35*35=>35 mod : 35*35=>35 true : =>41 false : =>41 maximal types: {21,35,41} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{1}{6}{7}{10} {0,1,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],2),([],0)], []> Critical Pair <0, 0> by Rules <6, 4> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <8, 7> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],6),([],9)]> joinable by a reduction of rules <[], [([],9),([],6)]> Critical Pair by Rules <9, 7> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],4),([],8)]> Critical Pair <0, 0> by Rules <9, 8> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 36*36=>36 0 : =>36 < : 36*36=>42 s : 22=>36 if : 42*36*36=>36 gcd : 36*36=>36 mod : 36*36=>36 true : =>42 false : =>42 maximal types: {22,36,42} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{1}{5}{6}{7}{10} {0,1,5,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0, gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair <0, 0> by Rules <7, 5> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <9, 8> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],7),([],10)]> joinable by a reduction of rules <[], [([],10),([],7)]> Critical Pair by Rules <10, 8> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],5),([],9)]> Critical Pair <0, 0> by Rules <10, 9> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 38*38=>38 0 : =>38 < : 38*38=>44 s : 38=>38 if : 44*38*38=>38 gcd : 38*38=>38 mod : 38*38=>38 true : =>44 false : =>44 maximal types: {38,44} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{1}{4}{5}{6}{7}{10} {0,1,4,5,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), 0 = 0, gcd(0,mod(?x_9,0)) = ?x_9, gcd(?y_9,mod(0,?y_9)) = ?y_9, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair <0, 0> by Rules <8, 6> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <10, 9> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],8),([],11)]> joinable by a reduction of rules <[], [([],11),([],8)]> Critical Pair by Rules <11, 9> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],6),([],10)]> Critical Pair <0, 0> by Rules <11, 10> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 39*39=>39 0 : =>39 < : 39*39=>45 s : 39=>39 if : 45*39*39=>39 gcd : 39*39=>39 mod : 39*39=>39 true : =>45 false : =>45 maximal types: {39,45} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{1}{3}{4}{5}{6}{7}{10} {0,1,3,4,5,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))), 0 = 0, gcd(0,mod(?x_10,0)) = ?x_10, gcd(?y_10,mod(0,?y_10)) = ?y_10, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <8, 7> preceded by [] joinable by a reduction of rules <[([(if,1)],5),([],0)], []> Critical Pair <0, 0> by Rules <9, 7> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <11, 10> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],9),([],12)]> joinable by a reduction of rules <[], [([],12),([],9)]> Critical Pair by Rules <12, 10> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],7),([],11)]> Critical Pair <0, 0> by Rules <12, 11> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 40*40=>40 0 : =>40 < : 40*40=>46 s : 40=>40 if : 46*40*40=>40 gcd : 40*40=>40 mod : 40*40=>40 true : =>46 false : =>46 maximal types: {40,46} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{2} {0,2,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), gcd(0,mod(?x_4,0)) = ?x_4, gcd(?y_4,mod(0,?y_4)) = ?y_4, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_4,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{2}{3} {0,2,3,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_5,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{2}{3}{4} {0,2,3,4,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{2}{3}{4}{5} {0,2,3,4,5,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_7,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{2}{3}{4}{5}{6} {0,2,3,4,5,6,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],5),([],0)], []> Critical Pair by Rules <9, 8> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_8,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{2}{3}{4}{5}{6}{7} {0,2,3,4,5,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))), gcd(0,mod(?x_9,0)) = ?x_9, gcd(?y_9,mod(0,?y_9)) = ?y_9, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <8, 7> preceded by [] joinable by a reduction of rules <[([(if,1)],5),([],0)], []> Critical Pair by Rules <10, 9> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_9,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{2}{3}{4}{5}{6}{10} {0,2,3,4,5,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), 0 = 0, gcd(0,mod(?x_9,0)) = ?x_9, gcd(?y_9,mod(0,?y_9)) = ?y_9, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],5),([],0)], []> Critical Pair <0, 0> by Rules <8, 6> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <10, 9> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],8),([],11)]> joinable by a reduction of rules <[], [([],11),([],8)]> Critical Pair by Rules <11, 9> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],6),([],10)]> Critical Pair <0, 0> by Rules <11, 10> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 38*38=>38 0 : =>38 < : 38*38=>44 s : 38=>38 if : 44*38*38=>38 gcd : 38*38=>38 mod : 38*38=>38 true : =>44 maximal types: {38,44} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{2}{3}{4}{5}{7} {0,2,3,4,5,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_8,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{2}{3}{4}{5}{10} {0,2,3,4,5,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0, gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{2}{3}{4}{5}{7}{10} {0,2,3,4,5,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), 0 = 0, gcd(0,mod(?x_9,0)) = ?x_9, gcd(?y_9,mod(0,?y_9)) = ?y_9, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_7)),0,0)> from mod(0,s(?y_7)) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{2}{3}{4}{6} {0,2,3,4,6,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair by Rules <8, 7> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_7,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{2}{3}{4}{6}{7} {0,2,3,4,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair by Rules <9, 8> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_8,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{2}{3}{4}{6}{10} {0,2,3,4,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0, gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair <0, 0> by Rules <7, 5> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <9, 8> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],7),([],10)]> joinable by a reduction of rules <[], [([],10),([],7)]> Critical Pair by Rules <10, 8> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],5),([],9)]> Critical Pair <0, 0> by Rules <10, 9> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 36*36=>36 0 : =>36 < : 36*36=>42 s : 36=>36 if : 42*36*36=>36 gcd : 36*36=>36 mod : 36*36=>36 true : =>42 maximal types: {36,42} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{2}{3}{4}{7} {0,2,3,4,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_7,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{2}{3}{4}{10} {0,2,3,4,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{2}{3}{4}{7}{10} {0,2,3,4,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0, gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{2}{3}{4}{6}{7}{10} {0,2,3,4,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), 0 = 0, gcd(0,mod(?x_9,0)) = ?x_9, gcd(?y_9,mod(0,?y_9)) = ?y_9, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair <0, 0> by Rules <8, 6> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <10, 9> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],8),([],11)]> joinable by a reduction of rules <[], [([],11),([],8)]> Critical Pair by Rules <11, 9> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],6),([],10)]> Critical Pair <0, 0> by Rules <11, 10> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 38*38=>38 0 : =>38 < : 38*38=>44 s : 38=>38 if : 44*38*38=>38 gcd : 38*38=>38 mod : 38*38=>38 true : =>44 false : =>44 maximal types: {38,44} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{2}{3}{5} {0,2,3,5,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{2}{3}{5}{6} {0,2,3,5,6,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair by Rules <8, 7> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_7,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{2}{3}{5}{6}{7} {0,2,3,5,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair by Rules <9, 8> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_8,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{2}{3}{5}{6}{10} {0,2,3,5,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0, gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair <0, 0> by Rules <7, 5> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <9, 8> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],7),([],10)]> joinable by a reduction of rules <[], [([],10),([],7)]> Critical Pair by Rules <10, 8> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],5),([],9)]> Critical Pair <0, 0> by Rules <10, 9> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 37*37=>37 0 : =>37 < : 37*37=>43 s : 37=>37 if : 43*37*37=>37 gcd : 37*37=>37 mod : 37*37=>37 true : =>43 maximal types: {37,43} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{2}{3}{5}{7} {0,2,3,5,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_7,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{2}{3}{5}{10} {0,2,3,5,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 36*36=>36 0 : =>36 < : 36*36=>25 s : 36=>36 if : 25*36*36=>36 gcd : 36*36=>36 mod : 36*36=>36 true : =>25 maximal types: {25,36} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{2}{3}{5}{7}{10} {0,2,3,5,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0, gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 38*38=>38 0 : =>38 < : 38*38=>26 s : 38=>38 if : 26*38*38=>38 gcd : 38*38=>38 mod : 38*38=>38 true : =>26 false : =>26 maximal types: {26,38} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{2}{3}{6} {0,2,3,6,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{2}{3}{6}{7} {0,2,3,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair by Rules <8, 7> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_7,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{2}{3}{6}{10} {0,2,3,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair <0, 0> by Rules <6, 4> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <8, 7> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],6),([],9)]> joinable by a reduction of rules <[], [([],9),([],6)]> Critical Pair by Rules <9, 7> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],4),([],8)]> Critical Pair <0, 0> by Rules <9, 8> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 35*35=>35 0 : =>35 < : 35*35=>41 s : 35=>35 if : 41*35*35=>35 gcd : 35*35=>35 mod : 35*35=>35 true : =>41 maximal types: {35,41} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{2}{3}{7} {0,2,3,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{2}{3}{10} {0,2,3,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0, gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 34*34=>34 0 : =>34 < : 34*34=>23 s : 34=>34 if : 23*34*34=>34 gcd : 34*34=>34 mod : 34*34=>34 true : =>23 maximal types: {23,34} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{2}{3}{7}{10} {0,2,3,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 36*36=>36 0 : =>36 < : 36*36=>24 s : 36=>36 if : 24*36*36=>36 gcd : 36*36=>36 mod : 36*36=>36 true : =>24 false : =>24 maximal types: {24,36} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{2}{3}{6}{7}{10} {0,2,3,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0, gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair <0, 0> by Rules <7, 5> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <9, 8> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],7),([],10)]> joinable by a reduction of rules <[], [([],10),([],7)]> Critical Pair by Rules <10, 8> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],5),([],9)]> Critical Pair <0, 0> by Rules <10, 9> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 37*37=>37 0 : =>37 < : 37*37=>43 s : 37=>37 if : 43*37*37=>37 gcd : 37*37=>37 mod : 37*37=>37 true : =>43 false : =>43 maximal types: {37,43} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{2}{3}{5}{6}{7}{10} {0,2,3,5,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), 0 = 0, gcd(0,mod(?x_9,0)) = ?x_9, gcd(?y_9,mod(0,?y_9)) = ?y_9, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair <0, 0> by Rules <8, 6> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <10, 9> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],8),([],11)]> joinable by a reduction of rules <[], [([],11),([],8)]> Critical Pair by Rules <11, 9> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],6),([],10)]> Critical Pair <0, 0> by Rules <11, 10> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 39*39=>39 0 : =>39 < : 39*39=>45 s : 39=>39 if : 45*39*39=>39 gcd : 39*39=>39 mod : 39*39=>39 true : =>45 false : =>45 maximal types: {39,45} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{2}{4} {0,2,4,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_5,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{2}{4}{5} {0,2,4,5,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{2}{4}{5}{6} {0,2,4,5,6,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair by Rules <8, 7> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_7,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{2}{4}{5}{6}{7} {0,2,4,5,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair by Rules <9, 8> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_8,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{2}{4}{5}{6}{10} {0,2,4,5,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0, gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair <0, 0> by Rules <7, 5> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <9, 8> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],7),([],10)]> joinable by a reduction of rules <[], [([],10),([],7)]> Critical Pair by Rules <10, 8> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],5),([],9)]> Critical Pair <0, 0> by Rules <10, 9> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 37*37=>37 0 : =>37 < : 37*37=>43 s : 37=>37 if : 43*37*37=>37 gcd : 37*37=>37 mod : 37*37=>37 true : =>43 maximal types: {37,43} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{2}{4}{5}{7} {0,2,4,5,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_7,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{2}{4}{5}{10} {0,2,4,5,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{2}{4}{5}{7}{10} {0,2,4,5,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0, gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{2}{4}{6} {0,2,4,6,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{2}{4}{6}{7} {0,2,4,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair by Rules <8, 7> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_7,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{2}{4}{6}{10} {0,2,4,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair <0, 0> by Rules <6, 4> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <8, 7> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],6),([],9)]> joinable by a reduction of rules <[], [([],9),([],6)]> Critical Pair by Rules <9, 7> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],4),([],8)]> Critical Pair <0, 0> by Rules <9, 8> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 35*35=>35 0 : =>35 < : 35*35=>41 s : 35=>35 if : 41*35*35=>35 gcd : 35*35=>35 mod : 35*35=>35 true : =>41 maximal types: {35,41} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{2}{4}{7} {0,2,4,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{2}{4}{10} {0,2,4,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0, gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{2}{4}{7}{10} {0,2,4,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{2}{4}{6}{7}{10} {0,2,4,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0, gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair <0, 0> by Rules <7, 5> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <9, 8> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],7),([],10)]> joinable by a reduction of rules <[], [([],10),([],7)]> Critical Pair by Rules <10, 8> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],5),([],9)]> Critical Pair <0, 0> by Rules <10, 9> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 37*37=>37 0 : =>37 < : 37*37=>43 s : 37=>37 if : 43*37*37=>37 gcd : 37*37=>37 mod : 37*37=>37 true : =>43 false : =>43 maximal types: {37,43} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{2}{5} {0,2,5,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_5,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{2}{5}{6} {0,2,5,6,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{2}{5}{6}{7} {0,2,5,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair by Rules <8, 7> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_7,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{2}{5}{6}{10} {0,2,5,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair <0, 0> by Rules <6, 4> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <8, 7> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],6),([],9)]> joinable by a reduction of rules <[], [([],9),([],6)]> Critical Pair by Rules <9, 7> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],4),([],8)]> Critical Pair <0, 0> by Rules <9, 8> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 36*36=>36 0 : =>36 < : 36*36=>42 s : 36=>36 if : 42*36*36=>36 gcd : 36*36=>36 mod : 36*36=>36 true : =>42 maximal types: {36,42} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{2}{5}{7} {0,2,5,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{2}{5}{10} {0,2,5,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0, gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 35*35=>35 0 : =>35 < : 35*35=>24 s : 35=>35 if : 24*35*35=>35 gcd : 35*35=>35 mod : 35*35=>35 true : =>24 maximal types: {24,35} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{2}{5}{7}{10} {0,2,5,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 37*37=>37 0 : =>37 < : 37*37=>25 s : 37=>37 if : 25*37*37=>37 gcd : 37*37=>37 mod : 37*37=>37 true : =>25 false : =>25 maximal types: {25,37} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{2}{6} {0,2,6,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] joinable by a reduction of rules <[([(if,1)],2),([],0)], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_5,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{2}{6}{7} {0,2,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],2),([],0)], []> Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{2}{6}{10} {0,2,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0, gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] joinable by a reduction of rules <[([(if,1)],2),([],0)], []> Critical Pair <0, 0> by Rules <5, 3> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],5),([],8)]> joinable by a reduction of rules <[], [([],8),([],5)]> Critical Pair by Rules <8, 6> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],3),([],7)]> Critical Pair <0, 0> by Rules <8, 7> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 34*34=>34 0 : =>34 < : 34*34=>40 s : 34=>34 if : 40*34*34=>34 gcd : 34*34=>34 mod : 34*34=>34 true : =>40 maximal types: {34,40} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{2}{7} {0,2,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_5,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{2}{10} {0,2,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), 0 = 0, gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 33*33=>33 0 : =>33 < : 33*33=>22 s : 33=>33 if : 22*33*33=>33 gcd : 33*33=>33 mod : 33*33=>33 true : =>22 maximal types: {22,33} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{2}{7}{10} {0,2,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0, gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 35*35=>35 0 : =>35 < : 35*35=>23 s : 35=>35 if : 23*35*35=>35 gcd : 35*35=>35 mod : 35*35=>35 true : =>23 false : =>23 maximal types: {23,35} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{2}{6}{7}{10} {0,2,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],2),([],0)], []> Critical Pair <0, 0> by Rules <6, 4> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <8, 7> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],6),([],9)]> joinable by a reduction of rules <[], [([],9),([],6)]> Critical Pair by Rules <9, 7> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],4),([],8)]> Critical Pair <0, 0> by Rules <9, 8> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 36*36=>36 0 : =>36 < : 36*36=>42 s : 36=>36 if : 42*36*36=>36 gcd : 36*36=>36 mod : 36*36=>36 true : =>42 false : =>42 maximal types: {36,42} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{2}{5}{6}{7}{10} {0,2,5,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0, gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair <0, 0> by Rules <7, 5> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <9, 8> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],7),([],10)]> joinable by a reduction of rules <[], [([],10),([],7)]> Critical Pair by Rules <10, 8> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],5),([],9)]> Critical Pair <0, 0> by Rules <10, 9> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 38*38=>38 0 : =>38 < : 38*38=>44 s : 38=>38 if : 44*38*38=>38 gcd : 38*38=>38 mod : 38*38=>38 true : =>44 false : =>44 maximal types: {38,44} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{2}{4}{5}{6}{7}{10} {0,2,4,5,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), 0 = 0, gcd(0,mod(?x_9,0)) = ?x_9, gcd(?y_9,mod(0,?y_9)) = ?y_9, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair <0, 0> by Rules <8, 6> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <10, 9> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],8),([],11)]> joinable by a reduction of rules <[], [([],11),([],8)]> Critical Pair by Rules <11, 9> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],6),([],10)]> Critical Pair <0, 0> by Rules <11, 10> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 39*39=>39 0 : =>39 < : 39*39=>45 s : 39=>39 if : 45*39*39=>39 gcd : 39*39=>39 mod : 39*39=>39 true : =>45 false : =>45 maximal types: {39,45} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{3} {0,3,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), gcd(0,mod(?x_4,0)) = ?x_4, gcd(?y_4,mod(0,?y_4)) = ?y_4, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_4,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{3}{4} {0,3,4,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_5,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{3}{4}{5} {0,3,4,5,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{3}{4}{5}{6} {0,3,4,5,6,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair by Rules <8, 7> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_7,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{3}{4}{5}{6}{7} {0,3,4,5,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair by Rules <9, 8> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_8,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{3}{4}{5}{6}{10} {0,3,4,5,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0, gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair <0, 0> by Rules <7, 5> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <9, 8> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],7),([],10)]> joinable by a reduction of rules <[], [([],10),([],7)]> Critical Pair by Rules <10, 8> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],5),([],9)]> Critical Pair <0, 0> by Rules <10, 9> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 36*36=>36 0 : =>36 < : 36*36=>42 s : 36=>36 if : 42*36*36=>36 gcd : 36*36=>36 mod : 36*36=>36 true : =>42 maximal types: {36,42} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{3}{4}{5}{7} {0,3,4,5,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_7,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{3}{4}{5}{10} {0,3,4,5,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{3}{4}{5}{7}{10} {0,3,4,5,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0, gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{3}{4}{6} {0,3,4,6,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{3}{4}{6}{7} {0,3,4,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair by Rules <8, 7> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_7,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{3}{4}{6}{10} {0,3,4,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair <0, 0> by Rules <6, 4> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <8, 7> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],6),([],9)]> joinable by a reduction of rules <[], [([],9),([],6)]> Critical Pair by Rules <9, 7> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],4),([],8)]> Critical Pair <0, 0> by Rules <9, 8> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 34*34=>34 0 : =>34 < : 34*34=>40 s : 21=>34 if : 40*34*34=>34 gcd : 34*34=>34 mod : 34*34=>34 true : =>40 maximal types: {21,34,40} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{3}{4}{7} {0,3,4,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{3}{4}{10} {0,3,4,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0, gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{3}{4}{7}{10} {0,3,4,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{3}{4}{6}{7}{10} {0,3,4,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0, gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair <0, 0> by Rules <7, 5> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <9, 8> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],7),([],10)]> joinable by a reduction of rules <[], [([],10),([],7)]> Critical Pair by Rules <10, 8> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],5),([],9)]> Critical Pair <0, 0> by Rules <10, 9> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 36*36=>36 0 : =>36 < : 36*36=>42 s : 22=>36 if : 42*36*36=>36 gcd : 36*36=>36 mod : 36*36=>36 true : =>42 false : =>42 maximal types: {22,36,42} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{3}{5} {0,3,5,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_5,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{3}{5}{6} {0,3,5,6,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{3}{5}{6}{7} {0,3,5,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair by Rules <8, 7> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_7,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{3}{5}{6}{10} {0,3,5,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair <0, 0> by Rules <6, 4> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <8, 7> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],6),([],9)]> joinable by a reduction of rules <[], [([],9),([],6)]> Critical Pair by Rules <9, 7> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],4),([],8)]> Critical Pair <0, 0> by Rules <9, 8> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 35*35=>35 0 : =>35 < : 35*35=>41 s : 35=>35 if : 41*35*35=>35 gcd : 35*35=>35 mod : 35*35=>35 true : =>41 maximal types: {35,41} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{3}{5}{7} {0,3,5,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{3}{5}{10} {0,3,5,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0, gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 34*34=>34 0 : =>34 < : 34*34=>23 s : 34=>34 if : 23*34*34=>34 gcd : 34*34=>34 mod : 34*34=>34 true : =>23 maximal types: {23,34} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{3}{5}{7}{10} {0,3,5,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 36*36=>36 0 : =>36 < : 36*36=>24 s : 36=>36 if : 24*36*36=>36 gcd : 36*36=>36 mod : 36*36=>36 true : =>24 false : =>24 maximal types: {24,36} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{3}{6} {0,3,6,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] joinable by a reduction of rules <[([(if,1)],2),([],0)], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_5,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{3}{6}{7} {0,3,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],2),([],0)], []> Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{3}{6}{10} {0,3,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0, gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] joinable by a reduction of rules <[([(if,1)],2),([],0)], []> Critical Pair <0, 0> by Rules <5, 3> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],5),([],8)]> joinable by a reduction of rules <[], [([],8),([],5)]> Critical Pair by Rules <8, 6> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],3),([],7)]> Critical Pair <0, 0> by Rules <8, 7> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 33*33=>33 0 : =>33 < : 33*33=>39 s : 20=>33 if : 39*33*33=>33 gcd : 33*33=>33 mod : 33*33=>33 true : =>39 maximal types: {20,33,39} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{3}{7} {0,3,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_5,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{3}{10} {0,3,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), 0 = 0, gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 32*32=>32 0 : =>32 < : 32*32=>21 s : 19=>32 if : 21*32*32=>32 gcd : 32*32=>32 mod : 32*32=>32 true : =>21 maximal types: {19,21,32} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{3}{7}{10} {0,3,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0, gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 34*34=>34 0 : =>34 < : 34*34=>22 s : 20=>34 if : 22*34*34=>34 gcd : 34*34=>34 mod : 34*34=>34 true : =>22 false : =>22 maximal types: {20,22,34} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{3}{6}{7}{10} {0,3,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],2),([],0)], []> Critical Pair <0, 0> by Rules <6, 4> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <8, 7> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],6),([],9)]> joinable by a reduction of rules <[], [([],9),([],6)]> Critical Pair by Rules <9, 7> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],4),([],8)]> Critical Pair <0, 0> by Rules <9, 8> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 35*35=>35 0 : =>35 < : 35*35=>41 s : 21=>35 if : 41*35*35=>35 gcd : 35*35=>35 mod : 35*35=>35 true : =>41 false : =>41 maximal types: {21,35,41} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{3}{5}{6}{7}{10} {0,3,5,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0, gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair <0, 0> by Rules <7, 5> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <9, 8> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],7),([],10)]> joinable by a reduction of rules <[], [([],10),([],7)]> Critical Pair by Rules <10, 8> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],5),([],9)]> Critical Pair <0, 0> by Rules <10, 9> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 37*37=>37 0 : =>37 < : 37*37=>43 s : 37=>37 if : 43*37*37=>37 gcd : 37*37=>37 mod : 37*37=>37 true : =>43 false : =>43 maximal types: {37,43} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{4} {0,4,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), gcd(0,mod(?x_4,0)) = ?x_4, gcd(?y_4,mod(0,?y_4)) = ?y_4, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_4,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{4}{5} {0,4,5,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_5,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{4}{5}{6} {0,4,5,6,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{4}{5}{6}{7} {0,4,5,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair by Rules <8, 7> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_7,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{4}{5}{6}{10} {0,4,5,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair <0, 0> by Rules <6, 4> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <8, 7> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],6),([],9)]> joinable by a reduction of rules <[], [([],9),([],6)]> Critical Pair by Rules <9, 7> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],4),([],8)]> Critical Pair <0, 0> by Rules <9, 8> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 35*35=>35 0 : =>35 < : 35*35=>41 s : 35=>35 if : 41*35*35=>35 gcd : 35*35=>35 mod : 35*35=>35 true : =>41 maximal types: {35,41} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{4}{5}{7} {0,4,5,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{4}{5}{10} {0,4,5,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0, gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{4}{5}{7}{10} {0,4,5,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{4}{6} {0,4,6,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] joinable by a reduction of rules <[([(if,1)],2),([],0)], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_5,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{4}{6}{7} {0,4,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],2),([],0)], []> Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{4}{6}{10} {0,4,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0, gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] joinable by a reduction of rules <[([(if,1)],2),([],0)], []> Critical Pair <0, 0> by Rules <5, 3> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],5),([],8)]> joinable by a reduction of rules <[], [([],8),([],5)]> Critical Pair by Rules <8, 6> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],3),([],7)]> Critical Pair <0, 0> by Rules <8, 7> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 33*33=>33 0 : =>33 < : 33*33=>39 s : 20=>33 if : 39*33*33=>33 gcd : 33*33=>33 mod : 33*33=>33 true : =>39 maximal types: {20,33,39} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{4}{7} {0,4,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_5,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{4}{10} {0,4,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), 0 = 0, gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_3)),0,0)> from mod(0,s(?y_3)) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{4}{7}{10} {0,4,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0, gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{4}{6}{7}{10} {0,4,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],2),([],0)], []> Critical Pair <0, 0> by Rules <6, 4> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <8, 7> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],6),([],9)]> joinable by a reduction of rules <[], [([],9),([],6)]> Critical Pair by Rules <9, 7> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],4),([],8)]> Critical Pair <0, 0> by Rules <9, 8> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 35*35=>35 0 : =>35 < : 35*35=>41 s : 21=>35 if : 41*35*35=>35 gcd : 35*35=>35 mod : 35*35=>35 true : =>41 false : =>41 maximal types: {21,35,41} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{5} {0,5,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), gcd(0,mod(?x_4,0)) = ?x_4, gcd(?y_4,mod(0,?y_4)) = ?y_4, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_4,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{5}{6} {0,5,6,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] joinable by a reduction of rules <[([(if,1)],2),([],0)], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_5,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{5}{6}{7} {0,5,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],2),([],0)], []> Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{5}{6}{10} {0,5,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0, gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] joinable by a reduction of rules <[([(if,1)],2),([],0)], []> Critical Pair <0, 0> by Rules <5, 3> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],5),([],8)]> joinable by a reduction of rules <[], [([],8),([],5)]> Critical Pair by Rules <8, 6> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],3),([],7)]> Critical Pair <0, 0> by Rules <8, 7> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 34*34=>34 0 : =>34 < : 34*34=>40 s : 34=>34 if : 40*34*34=>34 gcd : 34*34=>34 mod : 34*34=>34 true : =>40 maximal types: {34,40} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{5}{7} {0,5,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_5,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{5}{10} {0,5,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), 0 = 0, gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 33*33=>33 0 : =>33 < : 33*33=>22 s : 33=>33 if : 22*33*33=>33 gcd : 33*33=>33 mod : 33*33=>33 true : =>22 maximal types: {22,33} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{5}{7}{10} {0,5,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0, gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 35*35=>35 0 : =>35 < : 35*35=>23 s : 35=>35 if : 23*35*35=>35 gcd : 35*35=>35 mod : 35*35=>35 true : =>23 false : =>23 maximal types: {23,35} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{6} {0,6,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), gcd(0,mod(?x_4,0)) = ?x_4, gcd(?y_4,mod(0,?y_4)) = ?y_4, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] joinable by a reduction of rules <[([(if,1)],1),([],0)], []> Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_4,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{6}{7} {0,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] joinable by a reduction of rules <[([(if,1)],1),([],0)], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_5,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{6}{10} {0,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), 0 = 0, gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] joinable by a reduction of rules <[([(if,1)],1),([],0)], []> Critical Pair <0, 0> by Rules <4, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],4),([],7)]> joinable by a reduction of rules <[], [([],7),([],4)]> Critical Pair by Rules <7, 5> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],2),([],6)]> Critical Pair <0, 0> by Rules <7, 6> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 32*32=>32 0 : =>32 < : 32*32=>38 s : 19=>32 if : 38*32*32=>32 gcd : 32*32=>32 mod : 32*32=>32 true : =>38 maximal types: {19,32,38} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{7} {0,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), gcd(0,mod(?x_4,0)) = ?x_4, gcd(?y_4,mod(0,?y_4)) = ?y_4, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_4,0) Not Confluent Direct Methods: not CR Add {13,11,12}{0}{10} {0,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))), 0 = 0, gcd(0,mod(?x_4,0)) = ?x_4, gcd(?y_4,mod(0,?y_4)) = ?y_4, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <2, 1> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 31*31=>31 0 : =>31 < : 31*31=>20 s : 18=>31 if : 20*31*31=>31 gcd : 31*31=>31 mod : 31*31=>31 true : =>20 maximal types: {18,20,31} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{7}{10} {0,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), 0 = 0, gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 33*33=>33 0 : =>33 < : 33*33=>21 s : 19=>33 if : 21*33*33=>33 gcd : 33*33=>33 mod : 33*33=>33 true : =>21 false : =>21 maximal types: {19,21,33} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{6}{7}{10} {0,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0, gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] joinable by a reduction of rules <[([(if,1)],1),([],0)], []> Critical Pair <0, 0> by Rules <5, 3> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],5),([],8)]> joinable by a reduction of rules <[], [([],8),([],5)]> Critical Pair by Rules <8, 6> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],3),([],7)]> Critical Pair <0, 0> by Rules <8, 7> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 34*34=>34 0 : =>34 < : 34*34=>40 s : 20=>34 if : 40*34*34=>34 gcd : 34*34=>34 mod : 34*34=>34 true : =>40 false : =>40 maximal types: {20,34,40} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{5}{6}{7}{10} {0,5,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],2),([],0)], []> Critical Pair <0, 0> by Rules <6, 4> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <8, 7> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],6),([],9)]> joinable by a reduction of rules <[], [([],9),([],6)]> Critical Pair by Rules <9, 7> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],4),([],8)]> Critical Pair <0, 0> by Rules <9, 8> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 36*36=>36 0 : =>36 < : 36*36=>42 s : 36=>36 if : 42*36*36=>36 gcd : 36*36=>36 mod : 36*36=>36 true : =>42 false : =>42 maximal types: {36,42} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{4}{5}{6}{7}{10} {0,4,5,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0, gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair <0, 0> by Rules <7, 5> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <9, 8> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],7),([],10)]> joinable by a reduction of rules <[], [([],10),([],7)]> Critical Pair by Rules <10, 8> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],5),([],9)]> Critical Pair <0, 0> by Rules <10, 9> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 37*37=>37 0 : =>37 < : 37*37=>43 s : 37=>37 if : 43*37*37=>37 gcd : 37*37=>37 mod : 37*37=>37 true : =>43 false : =>43 maximal types: {37,43} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{3}{4}{5}{6}{7}{10} {0,3,4,5,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), 0 = 0, gcd(0,mod(?x_9,0)) = ?x_9, gcd(?y_9,mod(0,?y_9)) = ?y_9, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair <0, 0> by Rules <8, 6> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <10, 9> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],8),([],11)]> joinable by a reduction of rules <[], [([],11),([],8)]> Critical Pair by Rules <11, 9> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],6),([],10)]> Critical Pair <0, 0> by Rules <11, 10> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 38*38=>38 0 : =>38 < : 38*38=>44 s : 38=>38 if : 44*38*38=>38 gcd : 38*38=>38 mod : 38*38=>38 true : =>44 false : =>44 maximal types: {38,44} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{0}{2}{3}{4}{5}{6}{7}{10} {0,2,3,4,5,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))), 0 = 0, gcd(0,mod(?x_10,0)) = ?x_10, gcd(?y_10,mod(0,?y_10)) = ?y_10, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <8, 7> preceded by [] joinable by a reduction of rules <[([(if,1)],5),([],0)], []> Critical Pair <0, 0> by Rules <9, 7> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <11, 10> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],9),([],12)]> joinable by a reduction of rules <[], [([],12),([],9)]> Critical Pair by Rules <12, 10> preceded by [] joinable by a reduction of rules <[], [([(gcd,2)],7),([],11)]> Critical Pair <0, 0> by Rules <12, 11> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 40*40=>40 0 : =>40 < : 40*40=>46 s : 40=>40 if : 46*40*40=>40 gcd : 40*40=>40 mod : 40*40=>40 true : =>46 false : =>46 maximal types: {40,46} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{1} {1,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))), gcd(0,mod(?x_3,0)) = ?x_3, gcd(?y_3,mod(0,?y_3)) = ?y_3, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <2, 1> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_3,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{2} {1,2,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), gcd(0,mod(?x_4,0)) = ?x_4, gcd(?y_4,mod(0,?y_4)) = ?y_4, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_4,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{2}{3} {1,2,3,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_5,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{2}{3}{4} {1,2,3,4,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{2}{3}{4}{5} {1,2,3,4,5,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_7,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{2}{3}{4}{5}{6} {1,2,3,4,5,6,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_8,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{2}{3}{4}{5}{6}{7} {1,2,3,4,5,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))), gcd(0,mod(?x_9,0)) = ?x_9, gcd(?y_9,mod(0,?y_9)) = ?y_9, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <8, 7> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_9,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{2}{3}{4}{5}{6}{10} {1,2,3,4,5,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), 0 = 0, gcd(0,mod(?x_9,0)) = ?x_9, gcd(?y_9,mod(0,?y_9)) = ?y_9, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_7)),0,0)> from mod(0,s(?y_7)) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{2}{3}{4}{5}{7} {1,2,3,4,5,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_8,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{2}{3}{4}{5}{10} {1,2,3,4,5,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0, gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{2}{3}{4}{5}{7}{10} {1,2,3,4,5,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), 0 = 0, gcd(0,mod(?x_9,0)) = ?x_9, gcd(?y_9,mod(0,?y_9)) = ?y_9, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_7)),0,0)> from mod(0,s(?y_7)) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{2}{3}{4}{6} {1,2,3,4,6,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_7,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{2}{3}{4}{6}{7} {1,2,3,4,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_8,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{2}{3}{4}{6}{10} {1,2,3,4,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0, gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{2}{3}{4}{7} {1,2,3,4,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_7,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{2}{3}{4}{10} {1,2,3,4,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{2}{3}{4}{7}{10} {1,2,3,4,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0, gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{2}{3}{4}{6}{7}{10} {1,2,3,4,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), 0 = 0, gcd(0,mod(?x_9,0)) = ?x_9, gcd(?y_9,mod(0,?y_9)) = ?y_9, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_7)),0,0)> from mod(0,s(?y_7)) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{2}{3}{5} {1,2,3,5,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{2}{3}{5}{6} {1,2,3,5,6,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_7,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{2}{3}{5}{6}{7} {1,2,3,5,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_8,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{2}{3}{5}{6}{10} {1,2,3,5,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0, gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 38*38=>38 0 : =>38 < : 38*38=>26 s : 38=>38 if : 26*38*38=>38 gcd : 38*38=>38 mod : 38*38=>38 true : =>26 false : =>26 maximal types: {26,38} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{1}{2}{3}{5}{7} {1,2,3,5,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_7,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{2}{3}{5}{10} {1,2,3,5,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 36*36=>36 0 : =>36 < : 36*36=>25 s : 36=>36 if : 25*36*36=>36 gcd : 36*36=>36 mod : 36*36=>36 false : =>25 maximal types: {25,36} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{1}{2}{3}{5}{7}{10} {1,2,3,5,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0, gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 37*37=>37 0 : =>37 < : 37*37=>43 s : 37=>37 if : 43*37*37=>37 gcd : 37*37=>37 mod : 37*37=>37 false : =>43 maximal types: {37,43} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{1}{2}{3}{6} {1,2,3,6,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{2}{3}{6}{7} {1,2,3,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_7,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{2}{3}{6}{10} {1,2,3,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 36*36=>36 0 : =>36 < : 36*36=>24 s : 36=>36 if : 24*36*36=>36 gcd : 36*36=>36 mod : 36*36=>36 true : =>24 false : =>24 maximal types: {24,36} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{1}{2}{3}{7} {1,2,3,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{2}{3}{10} {1,2,3,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0, gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 34*34=>34 0 : =>34 < : 34*34=>23 s : 34=>34 if : 23*34*34=>34 gcd : 34*34=>34 mod : 34*34=>34 false : =>23 maximal types: {23,34} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{1}{2}{3}{7}{10} {1,2,3,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 35*35=>35 0 : =>35 < : 35*35=>41 s : 35=>35 if : 41*35*35=>35 gcd : 35*35=>35 mod : 35*35=>35 false : =>41 maximal types: {35,41} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{1}{2}{3}{6}{7}{10} {1,2,3,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0, gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 37*37=>37 0 : =>37 < : 37*37=>43 s : 37=>37 if : 43*37*37=>37 gcd : 37*37=>37 mod : 37*37=>37 true : =>43 false : =>43 maximal types: {37,43} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{1}{2}{3}{5}{6}{7}{10} {1,2,3,5,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), 0 = 0, gcd(0,mod(?x_9,0)) = ?x_9, gcd(?y_9,mod(0,?y_9)) = ?y_9, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 39*39=>39 0 : =>39 < : 39*39=>45 s : 39=>39 if : 45*39*39=>39 gcd : 39*39=>39 mod : 39*39=>39 true : =>45 false : =>45 maximal types: {39,45} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{1}{2}{4} {1,2,4,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_5,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{2}{4}{5} {1,2,4,5,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{2}{4}{5}{6} {1,2,4,5,6,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_7,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{2}{4}{5}{6}{7} {1,2,4,5,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_8,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{2}{4}{5}{6}{10} {1,2,4,5,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0, gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{2}{4}{5}{7} {1,2,4,5,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_7,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{2}{4}{5}{10} {1,2,4,5,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{2}{4}{5}{7}{10} {1,2,4,5,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0, gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{2}{4}{6} {1,2,4,6,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{2}{4}{6}{7} {1,2,4,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_7,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{2}{4}{6}{10} {1,2,4,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{2}{4}{7} {1,2,4,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{2}{4}{10} {1,2,4,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0, gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{2}{4}{7}{10} {1,2,4,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{2}{4}{6}{7}{10} {1,2,4,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0, gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{2}{5} {1,2,5,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_5,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{2}{5}{6} {1,2,5,6,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{2}{5}{6}{7} {1,2,5,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_7,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{2}{5}{6}{10} {1,2,5,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 37*37=>37 0 : =>37 < : 37*37=>25 s : 37=>37 if : 25*37*37=>37 gcd : 37*37=>37 mod : 37*37=>37 true : =>25 false : =>25 maximal types: {25,37} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{1}{2}{5}{7} {1,2,5,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{2}{5}{10} {1,2,5,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0, gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 35*35=>35 0 : =>35 < : 35*35=>24 s : 35=>35 if : 24*35*35=>35 gcd : 35*35=>35 mod : 35*35=>35 false : =>24 maximal types: {24,35} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{1}{2}{5}{7}{10} {1,2,5,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 36*36=>36 0 : =>36 < : 36*36=>42 s : 36=>36 if : 42*36*36=>36 gcd : 36*36=>36 mod : 36*36=>36 false : =>42 maximal types: {36,42} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{1}{2}{6} {1,2,6,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_5,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{2}{6}{7} {1,2,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{2}{6}{10} {1,2,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0, gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 35*35=>35 0 : =>35 < : 35*35=>23 s : 35=>35 if : 23*35*35=>35 gcd : 35*35=>35 mod : 35*35=>35 true : =>23 false : =>23 maximal types: {23,35} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{1}{2}{7} {1,2,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_5,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{2}{10} {1,2,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), 0 = 0, gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 33*33=>33 0 : =>33 < : 33*33=>22 s : 33=>33 if : 22*33*33=>33 gcd : 33*33=>33 mod : 33*33=>33 false : =>22 maximal types: {22,33} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{1}{2}{7}{10} {1,2,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0, gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 34*34=>34 0 : =>34 < : 34*34=>40 s : 34=>34 if : 40*34*34=>34 gcd : 34*34=>34 mod : 34*34=>34 false : =>40 maximal types: {34,40} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{1}{2}{6}{7}{10} {1,2,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 36*36=>36 0 : =>36 < : 36*36=>42 s : 36=>36 if : 42*36*36=>36 gcd : 36*36=>36 mod : 36*36=>36 true : =>42 false : =>42 maximal types: {36,42} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{1}{2}{5}{6}{7}{10} {1,2,5,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0, gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 38*38=>38 0 : =>38 < : 38*38=>44 s : 38=>38 if : 44*38*38=>38 gcd : 38*38=>38 mod : 38*38=>38 true : =>44 false : =>44 maximal types: {38,44} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{1}{2}{4}{5}{6}{7}{10} {1,2,4,5,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), 0 = 0, gcd(0,mod(?x_9,0)) = ?x_9, gcd(?y_9,mod(0,?y_9)) = ?y_9, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_7)),0,0)> from mod(0,s(?y_7)) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{3} {1,3,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), gcd(0,mod(?x_4,0)) = ?x_4, gcd(?y_4,mod(0,?y_4)) = ?y_4, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_4,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{3}{4} {1,3,4,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_5,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{3}{4}{5} {1,3,4,5,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{3}{4}{5}{6} {1,3,4,5,6,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_7,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{3}{4}{5}{6}{7} {1,3,4,5,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_8,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{3}{4}{5}{6}{10} {1,3,4,5,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0, gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{3}{4}{5}{7} {1,3,4,5,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_7,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{3}{4}{5}{10} {1,3,4,5,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{3}{4}{5}{7}{10} {1,3,4,5,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0, gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{3}{4}{6} {1,3,4,6,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{3}{4}{6}{7} {1,3,4,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_7,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{3}{4}{6}{10} {1,3,4,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{3}{4}{7} {1,3,4,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{3}{4}{10} {1,3,4,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0, gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{3}{4}{7}{10} {1,3,4,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{3}{4}{6}{7}{10} {1,3,4,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0, gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{3}{5} {1,3,5,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_5,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{3}{5}{6} {1,3,5,6,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{3}{5}{6}{7} {1,3,5,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_7,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{3}{5}{6}{10} {1,3,5,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 36*36=>36 0 : =>36 < : 36*36=>24 s : 36=>36 if : 24*36*36=>36 gcd : 36*36=>36 mod : 36*36=>36 true : =>24 false : =>24 maximal types: {24,36} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{1}{3}{5}{7} {1,3,5,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{3}{5}{10} {1,3,5,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0, gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 34*34=>34 0 : =>34 < : 34*34=>23 s : 34=>34 if : 23*34*34=>34 gcd : 34*34=>34 mod : 34*34=>34 false : =>23 maximal types: {23,34} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{1}{3}{5}{7}{10} {1,3,5,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 35*35=>35 0 : =>35 < : 35*35=>41 s : 35=>35 if : 41*35*35=>35 gcd : 35*35=>35 mod : 35*35=>35 false : =>41 maximal types: {35,41} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{1}{3}{6} {1,3,6,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_5,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{3}{6}{7} {1,3,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{3}{6}{10} {1,3,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0, gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 34*34=>34 0 : =>34 < : 34*34=>22 s : 20=>34 if : 22*34*34=>34 gcd : 34*34=>34 mod : 34*34=>34 true : =>22 false : =>22 maximal types: {20,22,34} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{1}{3}{7} {1,3,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_5,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{3}{10} {1,3,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), 0 = 0, gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 32*32=>32 0 : =>32 < : 32*32=>21 s : 19=>32 if : 21*32*32=>32 gcd : 32*32=>32 mod : 32*32=>32 false : =>21 maximal types: {19,21,32} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{1}{3}{7}{10} {1,3,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0, gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 33*33=>33 0 : =>33 < : 33*33=>39 s : 20=>33 if : 39*33*33=>33 gcd : 33*33=>33 mod : 33*33=>33 false : =>39 maximal types: {20,33,39} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{1}{3}{6}{7}{10} {1,3,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 35*35=>35 0 : =>35 < : 35*35=>41 s : 21=>35 if : 41*35*35=>35 gcd : 35*35=>35 mod : 35*35=>35 true : =>41 false : =>41 maximal types: {21,35,41} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{1}{3}{5}{6}{7}{10} {1,3,5,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0, gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 37*37=>37 0 : =>37 < : 37*37=>43 s : 37=>37 if : 43*37*37=>37 gcd : 37*37=>37 mod : 37*37=>37 true : =>43 false : =>43 maximal types: {37,43} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{1}{4} {1,4,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), gcd(0,mod(?x_4,0)) = ?x_4, gcd(?y_4,mod(0,?y_4)) = ?y_4, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_4,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{4}{5} {1,4,5,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_5,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{4}{5}{6} {1,4,5,6,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{4}{5}{6}{7} {1,4,5,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_7,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{4}{5}{6}{10} {1,4,5,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{4}{5}{7} {1,4,5,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{4}{5}{10} {1,4,5,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0, gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{4}{5}{7}{10} {1,4,5,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{4}{6} {1,4,6,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_5,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{4}{6}{7} {1,4,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{4}{6}{10} {1,4,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0, gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{4}{7} {1,4,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_5,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{4}{10} {1,4,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), 0 = 0, gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_3)),0,0)> from mod(0,s(?y_3)) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{4}{7}{10} {1,4,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0, gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{4}{6}{7}{10} {1,4,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{5} {1,5,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), gcd(0,mod(?x_4,0)) = ?x_4, gcd(?y_4,mod(0,?y_4)) = ?y_4, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_4,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{5}{6} {1,5,6,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_5,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{5}{6}{7} {1,5,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{5}{6}{10} {1,5,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0, gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 35*35=>35 0 : =>35 < : 35*35=>23 s : 35=>35 if : 23*35*35=>35 gcd : 35*35=>35 mod : 35*35=>35 true : =>23 false : =>23 maximal types: {23,35} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{1}{5}{7} {1,5,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_5,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{5}{10} {1,5,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), 0 = 0, gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 33*33=>33 0 : =>33 < : 33*33=>22 s : 33=>33 if : 22*33*33=>33 gcd : 33*33=>33 mod : 33*33=>33 false : =>22 maximal types: {22,33} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{1}{5}{7}{10} {1,5,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0, gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 34*34=>34 0 : =>34 < : 34*34=>40 s : 34=>34 if : 40*34*34=>34 gcd : 34*34=>34 mod : 34*34=>34 false : =>40 maximal types: {34,40} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{1}{6} {1,6,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), gcd(0,mod(?x_4,0)) = ?x_4, gcd(?y_4,mod(0,?y_4)) = ?y_4, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_4,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{6}{7} {1,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_5,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{6}{10} {1,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), 0 = 0, gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 33*33=>33 0 : =>33 < : 33*33=>21 s : 19=>33 if : 21*33*33=>33 gcd : 33*33=>33 mod : 33*33=>33 true : =>21 false : =>21 maximal types: {19,21,33} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{1}{7} {1,7,8,9,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), gcd(0,mod(?x_4,0)) = ?x_4, gcd(?y_4,mod(0,?y_4)) = ?y_4, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_4,0) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{10} {1,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))), 0 = 0, gcd(0,mod(?x_4,0)) = ?x_4, gcd(?y_4,mod(0,?y_4)) = ?y_4, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <2, 1> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 31*31=>31 0 : =>31 < : 31*31=>20 s : 18=>31 if : 20*31*31=>31 gcd : 31*31=>31 mod : 31*31=>31 false : =>20 maximal types: {18,20,31} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{1}{7}{10} {1,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), 0 = 0, gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 32*32=>32 0 : =>32 < : 32*32=>38 s : 19=>32 if : 38*32*32=>32 gcd : 32*32=>32 mod : 32*32=>32 false : =>38 maximal types: {19,32,38} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{1}{6}{7}{10} {1,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0, gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 34*34=>34 0 : =>34 < : 34*34=>40 s : 20=>34 if : 40*34*34=>34 gcd : 34*34=>34 mod : 34*34=>34 true : =>40 false : =>40 maximal types: {20,34,40} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{1}{5}{6}{7}{10} {1,5,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Sort Assignment: - : 36*36=>36 0 : =>36 < : 36*36=>42 s : 36=>36 if : 42*36*36=>36 gcd : 36*36=>36 mod : 36*36=>36 true : =>42 false : =>42 maximal types: {36,42} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {13,11,12}{1}{4}{5}{6}{7}{10} {1,4,5,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0, gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{3}{4}{5}{6}{7}{10} {1,3,4,5,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), 0 = 0, gcd(0,mod(?x_9,0)) = ?x_9, gcd(?y_9,mod(0,?y_9)) = ?y_9, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_7)),0,0)> from mod(0,s(?y_7)) Not Confluent Direct Methods: not CR Add {13,11,12}{2} {2,8,9,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))), gcd(0,mod(?x_3,0)) = ?x_3, gcd(?y_3,mod(0,?y_3)) = ?y_3, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <2, 1> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_3,0) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{3} {2,3,8,9,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), gcd(0,mod(?x_4,0)) = ?x_4, gcd(?y_4,mod(0,?y_4)) = ?y_4, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_4,0) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{3}{4} {2,3,4,8,9,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_5,0) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{3}{4}{5} {2,3,4,5,8,9,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{3}{4}{5}{6} {2,3,4,5,6,8,9,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_7,0) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{3}{4}{5}{6}{7} {2,3,4,5,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_8,0) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{3}{4}{5}{6}{10} {2,3,4,5,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0, gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{3}{4}{5}{7} {2,3,4,5,7,8,9,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_7,0) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{3}{4}{5}{10} {2,3,4,5,8,9,10,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{3}{4}{5}{7}{10} {2,3,4,5,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0, gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{3}{4}{6} {2,3,4,6,8,9,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{3}{4}{6}{7} {2,3,4,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_7,0) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{3}{4}{6}{10} {2,3,4,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{3}{4}{7} {2,3,4,7,8,9,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{3}{4}{10} {2,3,4,8,9,10,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0, gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{3}{4}{7}{10} {2,3,4,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{3}{4}{6}{7}{10} {2,3,4,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0, gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{3}{5} {2,3,5,8,9,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_5,0) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{3}{5}{6} {2,3,5,6,8,9,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{3}{5}{6}{7} {2,3,5,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_7,0) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{3}{5}{6}{10} {2,3,5,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,if(<(-(0,s(?y_5)),s(?y_5)),-(0,s(?y_5)),if(<(-(-(0,s(?y_5)),s(?y_5)),s(?y_5)),-(-(0,s(?y_5)),s(?y_5)),mod(-(-(-(0,s(?y_5)),s(?y_5)),s(?y_5)),s(?y_5)))))> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{3}{5}{7} {2,3,5,7,8,9,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{3}{5}{10} {2,3,5,8,9,10,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0, gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,if(<(-(0,s(?y_4)),s(?y_4)),-(0,s(?y_4)),if(<(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),-(-(0,s(?y_4)),s(?y_4)),mod(-(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),s(?y_4)))))> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{3}{5}{7}{10} {2,3,5,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,if(<(-(0,s(?y_5)),s(?y_5)),-(0,s(?y_5)),if(<(-(-(0,s(?y_5)),s(?y_5)),s(?y_5)),-(-(0,s(?y_5)),s(?y_5)),mod(-(-(-(0,s(?y_5)),s(?y_5)),s(?y_5)),s(?y_5)))))> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{3}{6} {2,3,6,8,9,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_5,0) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{3}{6}{7} {2,3,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{3}{6}{10} {2,3,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0, gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,if(<(-(0,s(?y_4)),s(?y_4)),-(0,s(?y_4)),if(<(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),-(-(0,s(?y_4)),s(?y_4)),mod(-(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),s(?y_4)))))> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{3}{7} {2,3,7,8,9,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_5,0) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{3}{10} {2,3,8,9,10,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), 0 = 0, gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_3)),0,if(<(-(0,s(?y_3)),s(?y_3)),-(0,s(?y_3)),if(<(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),-(-(0,s(?y_3)),s(?y_3)),mod(-(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),s(?y_3)))))> from mod(0,s(?y_3)) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{3}{7}{10} {2,3,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0, gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,if(<(-(0,s(?y_4)),s(?y_4)),-(0,s(?y_4)),if(<(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),-(-(0,s(?y_4)),s(?y_4)),mod(-(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),s(?y_4)))))> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{3}{6}{7}{10} {2,3,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,if(<(-(0,s(?y_5)),s(?y_5)),-(0,s(?y_5)),if(<(-(-(0,s(?y_5)),s(?y_5)),s(?y_5)),-(-(0,s(?y_5)),s(?y_5)),mod(-(-(-(0,s(?y_5)),s(?y_5)),s(?y_5)),s(?y_5)))))> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{3}{5}{6}{7}{10} {2,3,5,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0, gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,if(<(-(0,s(?y_6)),s(?y_6)),-(0,s(?y_6)),if(<(-(-(0,s(?y_6)),s(?y_6)),s(?y_6)),-(-(0,s(?y_6)),s(?y_6)),mod(-(-(-(0,s(?y_6)),s(?y_6)),s(?y_6)),s(?y_6)))))> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{4} {2,4,8,9,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), gcd(0,mod(?x_4,0)) = ?x_4, gcd(?y_4,mod(0,?y_4)) = ?y_4, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_4,0) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{4}{5} {2,4,5,8,9,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_5,0) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{4}{5}{6} {2,4,5,6,8,9,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{4}{5}{6}{7} {2,4,5,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_7,0) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{4}{5}{6}{10} {2,4,5,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{4}{5}{7} {2,4,5,7,8,9,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{4}{5}{10} {2,4,5,8,9,10,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0, gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{4}{5}{7}{10} {2,4,5,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{4}{6} {2,4,6,8,9,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_5,0) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{4}{6}{7} {2,4,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{4}{6}{10} {2,4,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0, gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{4}{7} {2,4,7,8,9,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_5,0) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{4}{10} {2,4,8,9,10,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), 0 = 0, gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_3)),0,0)> from mod(0,s(?y_3)) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{4}{7}{10} {2,4,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0, gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{4}{6}{7}{10} {2,4,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{5} {2,5,8,9,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), gcd(0,mod(?x_4,0)) = ?x_4, gcd(?y_4,mod(0,?y_4)) = ?y_4, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_4,0) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{5}{6} {2,5,6,8,9,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_5,0) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{5}{6}{7} {2,5,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{5}{6}{10} {2,5,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0, gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,if(<(-(0,s(?y_4)),s(?y_4)),-(0,s(?y_4)),if(<(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),-(-(0,s(?y_4)),s(?y_4)),mod(-(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),s(?y_4)))))> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{5}{7} {2,5,7,8,9,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_5,0) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{5}{10} {2,5,8,9,10,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), 0 = 0, gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_3)),0,if(<(-(0,s(?y_3)),s(?y_3)),-(0,s(?y_3)),if(<(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),-(-(0,s(?y_3)),s(?y_3)),mod(-(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),s(?y_3)))))> from mod(0,s(?y_3)) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{5}{7}{10} {2,5,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0, gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,if(<(-(0,s(?y_4)),s(?y_4)),-(0,s(?y_4)),if(<(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),-(-(0,s(?y_4)),s(?y_4)),mod(-(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),s(?y_4)))))> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{6} {2,6,8,9,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), gcd(0,mod(?x_4,0)) = ?x_4, gcd(?y_4,mod(0,?y_4)) = ?y_4, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_4,0) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{6}{7} {2,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_5,0) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{6}{10} {2,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), 0 = 0, gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_3)),0,if(<(-(0,s(?y_3)),s(?y_3)),-(0,s(?y_3)),if(<(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),-(-(0,s(?y_3)),s(?y_3)),mod(-(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),s(?y_3)))))> from mod(0,s(?y_3)) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{7} {2,7,8,9,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), gcd(0,mod(?x_4,0)) = ?x_4, gcd(?y_4,mod(0,?y_4)) = ?y_4, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_4,0) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{10} {2,8,9,10,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))), 0 = 0, gcd(0,mod(?x_4,0)) = ?x_4, gcd(?y_4,mod(0,?y_4)) = ?y_4, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <2, 1> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_2)),0,if(<(-(0,s(?y_2)),s(?y_2)),-(0,s(?y_2)),if(<(-(-(0,s(?y_2)),s(?y_2)),s(?y_2)),-(-(0,s(?y_2)),s(?y_2)),mod(-(-(-(0,s(?y_2)),s(?y_2)),s(?y_2)),s(?y_2)))))> from mod(0,s(?y_2)) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{7}{10} {2,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), 0 = 0, gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_3)),0,if(<(-(0,s(?y_3)),s(?y_3)),-(0,s(?y_3)),if(<(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),-(-(0,s(?y_3)),s(?y_3)),mod(-(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),s(?y_3)))))> from mod(0,s(?y_3)) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{6}{7}{10} {2,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0, gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,if(<(-(0,s(?y_4)),s(?y_4)),-(0,s(?y_4)),if(<(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),-(-(0,s(?y_4)),s(?y_4)),mod(-(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),s(?y_4)))))> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{5}{6}{7}{10} {2,5,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,if(<(-(0,s(?y_5)),s(?y_5)),-(0,s(?y_5)),if(<(-(-(0,s(?y_5)),s(?y_5)),s(?y_5)),-(-(0,s(?y_5)),s(?y_5)),mod(-(-(-(0,s(?y_5)),s(?y_5)),s(?y_5)),s(?y_5)))))> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{4}{5}{6}{7}{10} {2,4,5,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0, gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {13,11,12}{3} {3,8,9,11,12,13} (cm)Rewrite Rules: [ -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))), gcd(0,mod(?x_3,0)) = ?x_3, gcd(?y_3,mod(0,?y_3)) = ?y_3, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <2, 1> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_3,0) Not Confluent Direct Methods: not CR Add {13,11,12}{3}{4} {3,4,8,9,11,12,13} (cm)Rewrite Rules: [ -(?x,0) -> ?x, -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), gcd(0,mod(?x_4,0)) = ?x_4, gcd(?y_4,mod(0,?y_4)) = ?y_4, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <1, 0> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_4,0) Not Confluent Direct Methods: not CR Add {13,11,12}{3}{4}{5} {3,4,5,8,9,11,12,13} (cm)Rewrite Rules: [ -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <1, 0> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_5,0) Not Confluent Direct Methods: not CR Add {13,11,12}{3}{4}{5}{6} {3,4,5,6,8,9,11,12,13} (cm)Rewrite Rules: [ -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <1, 0> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{3}{4}{5}{6}{7} {3,4,5,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <1, 0> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_7,0) Not Confluent Direct Methods: not CR Add {13,11,12}{3}{4}{5}{6}{10} {3,4,5,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <1, 0> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {13,11,12}{3}{4}{5}{7} {3,4,5,7,8,9,11,12,13} (cm)Rewrite Rules: [ -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <1, 0> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{3}{4}{5}{10} {3,4,5,8,9,10,11,12,13} (cm)Rewrite Rules: [ -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0, gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <1, 0> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {13,11,12}{3}{4}{5}{7}{10} {3,4,5,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <1, 0> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {13,11,12}{3}{4}{6} {3,4,6,8,9,11,12,13} (cm)Rewrite Rules: [ -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <1, 0> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_5,0) Not Confluent Direct Methods: not CR Add {13,11,12}{3}{4}{6}{7} {3,4,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <1, 0> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{3}{4}{6}{10} {3,4,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0, gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <1, 0> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {13,11,12}{3}{4}{7} {3,4,7,8,9,11,12,13} (cm)Rewrite Rules: [ -(?x,0) -> ?x, -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <1, 0> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_5,0) Not Confluent Direct Methods: not CR Add {13,11,12}{3}{4}{10} {3,4,8,9,10,11,12,13} (cm)Rewrite Rules: [ -(?x,0) -> ?x, -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), 0 = 0, gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <1, 0> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_3)),0,0)> from mod(0,s(?y_3)) Not Confluent Direct Methods: not CR Add {13,11,12}{3}{4}{7}{10} {3,4,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ -(?x,0) -> ?x, -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0, gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <1, 0> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {13,11,12}{3}{4}{6}{7}{10} {3,4,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <1, 0> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {13,11,12}{3}{5} {3,5,8,9,11,12,13} (cm)Rewrite Rules: [ -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), gcd(0,mod(?x_4,0)) = ?x_4, gcd(?y_4,mod(0,?y_4)) = ?y_4, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_4,0) Not Confluent Direct Methods: not CR Add {13,11,12}{3}{5}{6} {3,5,6,8,9,11,12,13} (cm)Rewrite Rules: [ -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_5,0) Not Confluent Direct Methods: not CR Add {13,11,12}{3}{5}{6}{7} {3,5,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{3}{5}{6}{10} {3,5,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0, gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,if(<(-(0,s(?y_4)),s(?y_4)),-(0,s(?y_4)),if(<(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),-(-(0,s(?y_4)),s(?y_4)),mod(-(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),s(?y_4)))))> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {13,11,12}{3}{5}{7} {3,5,7,8,9,11,12,13} (cm)Rewrite Rules: [ -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_5,0) Not Confluent Direct Methods: not CR Add {13,11,12}{3}{5}{10} {3,5,8,9,10,11,12,13} (cm)Rewrite Rules: [ -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), 0 = 0, gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_3)),0,if(<(-(0,s(?y_3)),s(?y_3)),-(0,s(?y_3)),if(<(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),-(-(0,s(?y_3)),s(?y_3)),mod(-(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),s(?y_3)))))> from mod(0,s(?y_3)) Not Confluent Direct Methods: not CR Add {13,11,12}{3}{5}{7}{10} {3,5,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0, gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,if(<(-(0,s(?y_4)),s(?y_4)),-(0,s(?y_4)),if(<(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),-(-(0,s(?y_4)),s(?y_4)),mod(-(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),s(?y_4)))))> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {13,11,12}{3}{6} {3,6,8,9,11,12,13} (cm)Rewrite Rules: [ -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), gcd(0,mod(?x_4,0)) = ?x_4, gcd(?y_4,mod(0,?y_4)) = ?y_4, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_4,0) Not Confluent Direct Methods: not CR Add {13,11,12}{3}{6}{7} {3,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_5,0) Not Confluent Direct Methods: not CR Add {13,11,12}{3}{6}{10} {3,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), 0 = 0, gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_3)),0,if(<(-(0,s(?y_3)),s(?y_3)),-(0,s(?y_3)),if(<(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),-(-(0,s(?y_3)),s(?y_3)),mod(-(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),s(?y_3)))))> from mod(0,s(?y_3)) Not Confluent Direct Methods: not CR Add {13,11,12}{3}{7} {3,7,8,9,11,12,13} (cm)Rewrite Rules: [ -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), gcd(0,mod(?x_4,0)) = ?x_4, gcd(?y_4,mod(0,?y_4)) = ?y_4, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_4,0) Not Confluent Direct Methods: not CR Add {13,11,12}{3}{10} {3,8,9,10,11,12,13} (cm)Rewrite Rules: [ -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))), 0 = 0, gcd(0,mod(?x_4,0)) = ?x_4, gcd(?y_4,mod(0,?y_4)) = ?y_4, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <2, 1> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_2)),0,if(<(-(0,s(?y_2)),s(?y_2)),-(0,s(?y_2)),if(<(-(-(0,s(?y_2)),s(?y_2)),s(?y_2)),-(-(0,s(?y_2)),s(?y_2)),mod(-(-(-(0,s(?y_2)),s(?y_2)),s(?y_2)),s(?y_2)))))> from mod(0,s(?y_2)) Not Confluent Direct Methods: not CR Add {13,11,12}{3}{7}{10} {3,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), 0 = 0, gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_3)),0,if(<(-(0,s(?y_3)),s(?y_3)),-(0,s(?y_3)),if(<(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),-(-(0,s(?y_3)),s(?y_3)),mod(-(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),s(?y_3)))))> from mod(0,s(?y_3)) Not Confluent Direct Methods: not CR Add {13,11,12}{3}{6}{7}{10} {3,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0, gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,if(<(-(0,s(?y_4)),s(?y_4)),-(0,s(?y_4)),if(<(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),-(-(0,s(?y_4)),s(?y_4)),mod(-(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),s(?y_4)))))> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {13,11,12}{3}{5}{6}{7}{10} {3,5,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,if(<(-(0,s(?y_5)),s(?y_5)),-(0,s(?y_5)),if(<(-(-(0,s(?y_5)),s(?y_5)),s(?y_5)),-(-(0,s(?y_5)),s(?y_5)),mod(-(-(-(0,s(?y_5)),s(?y_5)),s(?y_5)),s(?y_5)))))> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {13,11,12}{4} {4,8,9,11,12,13} (cm)Rewrite Rules: [ -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))), gcd(0,mod(?x_3,0)) = ?x_3, gcd(?y_3,mod(0,?y_3)) = ?y_3, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <2, 1> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_3,0) Not Confluent Direct Methods: not CR Add {13,11,12}{4}{5} {4,5,8,9,11,12,13} (cm)Rewrite Rules: [ -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), gcd(0,mod(?x_4,0)) = ?x_4, gcd(?y_4,mod(0,?y_4)) = ?y_4, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_4,0) Not Confluent Direct Methods: not CR Add {13,11,12}{4}{5}{6} {4,5,6,8,9,11,12,13} (cm)Rewrite Rules: [ -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_5,0) Not Confluent Direct Methods: not CR Add {13,11,12}{4}{5}{6}{7} {4,5,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_6,0) Not Confluent Direct Methods: not CR Add {13,11,12}{4}{5}{6}{10} {4,5,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0, gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {13,11,12}{4}{5}{7} {4,5,7,8,9,11,12,13} (cm)Rewrite Rules: [ -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_5,0) Not Confluent Direct Methods: not CR Add {13,11,12}{4}{5}{10} {4,5,8,9,10,11,12,13} (cm)Rewrite Rules: [ -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), 0 = 0, gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_3)),0,0)> from mod(0,s(?y_3)) Not Confluent Direct Methods: not CR Add {13,11,12}{4}{5}{7}{10} {4,5,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0, gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {13,11,12}{4}{6} {4,6,8,9,11,12,13} (cm)Rewrite Rules: [ -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), gcd(0,mod(?x_4,0)) = ?x_4, gcd(?y_4,mod(0,?y_4)) = ?y_4, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_4,0) Not Confluent Direct Methods: not CR Add {13,11,12}{4}{6}{7} {4,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_5,0) Not Confluent Direct Methods: not CR Add {13,11,12}{4}{6}{10} {4,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), 0 = 0, gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_3)),0,0)> from mod(0,s(?y_3)) Not Confluent Direct Methods: not CR Add {13,11,12}{4}{7} {4,7,8,9,11,12,13} (cm)Rewrite Rules: [ -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), gcd(0,mod(?x_4,0)) = ?x_4, gcd(?y_4,mod(0,?y_4)) = ?y_4, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_4,0) Not Confluent Direct Methods: not CR Add {13,11,12}{4}{10} {4,8,9,10,11,12,13} (cm)Rewrite Rules: [ -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))), 0 = 0, gcd(0,mod(?x_4,0)) = ?x_4, gcd(?y_4,mod(0,?y_4)) = ?y_4, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <2, 1> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_2)),0,0)> from mod(0,s(?y_2)) Not Confluent Direct Methods: not CR Add {13,11,12}{4}{7}{10} {4,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), 0 = 0, gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_3)),0,0)> from mod(0,s(?y_3)) Not Confluent Direct Methods: not CR Add {13,11,12}{4}{6}{7}{10} {4,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0, gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {13,11,12}{5} {5,8,9,11,12,13} (cm)Rewrite Rules: [ <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))), gcd(0,mod(?x_3,0)) = ?x_3, gcd(?y_3,mod(0,?y_3)) = ?y_3, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <2, 1> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_3,0) Not Confluent Direct Methods: not CR Add {13,11,12}{5}{6} {5,6,8,9,11,12,13} (cm)Rewrite Rules: [ <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), gcd(0,mod(?x_4,0)) = ?x_4, gcd(?y_4,mod(0,?y_4)) = ?y_4, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_4,0) Not Confluent Direct Methods: not CR Add {13,11,12}{5}{6}{7} {5,6,7,8,9,11,12,13} (cm)Rewrite Rules: [ <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_5,0) Not Confluent Direct Methods: not CR Add {13,11,12}{5}{6}{10} {5,6,8,9,10,11,12,13} (cm)Rewrite Rules: [ <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), 0 = 0, gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_3)),0,if(<(-(0,s(?y_3)),s(?y_3)),-(0,s(?y_3)),if(<(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),-(-(0,s(?y_3)),s(?y_3)),mod(-(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),s(?y_3)))))> from mod(0,s(?y_3)) Not Confluent Direct Methods: not CR Add {13,11,12}{5}{7} {5,7,8,9,11,12,13} (cm)Rewrite Rules: [ <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), gcd(0,mod(?x_4,0)) = ?x_4, gcd(?y_4,mod(0,?y_4)) = ?y_4, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_4,0) Not Confluent Direct Methods: not CR Add {13,11,12}{5}{10} {5,8,9,10,11,12,13} (cm)Rewrite Rules: [ <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))), 0 = 0, gcd(0,mod(?x_4,0)) = ?x_4, gcd(?y_4,mod(0,?y_4)) = ?y_4, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <2, 1> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_2)),0,if(<(-(0,s(?y_2)),s(?y_2)),-(0,s(?y_2)),if(<(-(-(0,s(?y_2)),s(?y_2)),s(?y_2)),-(-(0,s(?y_2)),s(?y_2)),mod(-(-(-(0,s(?y_2)),s(?y_2)),s(?y_2)),s(?y_2)))))> from mod(0,s(?y_2)) Not Confluent Direct Methods: not CR Add {13,11,12}{5}{7}{10} {5,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), 0 = 0, gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_3)),0,if(<(-(0,s(?y_3)),s(?y_3)),-(0,s(?y_3)),if(<(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),-(-(0,s(?y_3)),s(?y_3)),mod(-(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),s(?y_3)))))> from mod(0,s(?y_3)) Not Confluent Direct Methods: not CR Add {13,11,12}{6} {6,8,9,11,12,13} (cm)Rewrite Rules: [ <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))), gcd(0,mod(?x_3,0)) = ?x_3, gcd(?y_3,mod(0,?y_3)) = ?y_3, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <2, 1> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_3,0) Not Confluent Direct Methods: not CR Add {13,11,12}{6}{7} {6,7,8,9,11,12,13} (cm)Rewrite Rules: [ <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), gcd(0,mod(?x_4,0)) = ?x_4, gcd(?y_4,mod(0,?y_4)) = ?y_4, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_4,0) Not Confluent Direct Methods: not CR Add {13,11,12}{6}{10} {6,8,9,10,11,12,13} (cm)Rewrite Rules: [ <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))), 0 = 0, gcd(0,mod(?x_4,0)) = ?x_4, gcd(?y_4,mod(0,?y_4)) = ?y_4, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <2, 1> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_2)),0,if(<(-(0,s(?y_2)),s(?y_2)),-(0,s(?y_2)),if(<(-(-(0,s(?y_2)),s(?y_2)),s(?y_2)),-(-(0,s(?y_2)),s(?y_2)),mod(-(-(-(0,s(?y_2)),s(?y_2)),s(?y_2)),s(?y_2)))))> from mod(0,s(?y_2)) Not Confluent Direct Methods: not CR Add {13,11,12}{7} {7,8,9,11,12,13} (cm)Rewrite Rules: [ <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))), gcd(0,mod(?x_3,0)) = ?x_3, gcd(?y_3,mod(0,?y_3)) = ?y_3, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, 0 = 0, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <2, 1> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: from gcd(?x_3,0) Not Confluent Direct Methods: not CR Add {13,11,12}{10} {8,9,10,11,12,13} (cm)Rewrite Rules: [ mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_1)),0,mod(-(0,s(?y_1)),s(?y_1))), 0 = 0, gcd(0,mod(?x_3,0)) = ?x_3, gcd(?y_3,mod(0,?y_3)) = ?y_3, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_1)),0,mod(-(0,s(?y_1)),s(?y_1))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <1, 0> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_1)),0,if(<(-(0,s(?y_1)),s(?y_1)),-(0,s(?y_1)),if(<(-(-(0,s(?y_1)),s(?y_1)),s(?y_1)),-(-(0,s(?y_1)),s(?y_1)),mod(-(-(-(0,s(?y_1)),s(?y_1)),s(?y_1)),s(?y_1)))))> from mod(0,s(?y_1)) Not Confluent Direct Methods: not CR Add {13,11,12}{7}{10} {7,8,9,10,11,12,13} (cm)Rewrite Rules: [ <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))), 0 = 0, gcd(0,mod(?x_4,0)) = ?x_4, gcd(?y_4,mod(0,?y_4)) = ?y_4, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <2, 1> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_2)),0,if(<(-(0,s(?y_2)),s(?y_2)),-(0,s(?y_2)),if(<(-(-(0,s(?y_2)),s(?y_2)),s(?y_2)),-(-(0,s(?y_2)),s(?y_2)),mod(-(-(-(0,s(?y_2)),s(?y_2)),s(?y_2)),s(?y_2)))))> from mod(0,s(?y_2)) Not Confluent Direct Methods: not CR Add {13,11,12}{6}{7}{10} {6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), 0 = 0, gcd(0,mod(?x_5,0)) = ?x_5, gcd(?y_5,mod(0,?y_5)) = ?y_5, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_3)),0,if(<(-(0,s(?y_3)),s(?y_3)),-(0,s(?y_3)),if(<(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),-(-(0,s(?y_3)),s(?y_3)),mod(-(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),s(?y_3)))))> from mod(0,s(?y_3)) Not Confluent Direct Methods: not CR Add {13,11,12}{5}{6}{7}{10} {5,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0, gcd(0,mod(?x_6,0)) = ?x_6, gcd(?y_6,mod(0,?y_6)) = ?y_6, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,if(<(-(0,s(?y_4)),s(?y_4)),-(0,s(?y_4)),if(<(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),-(-(0,s(?y_4)),s(?y_4)),mod(-(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),s(?y_4)))))> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {13,11,12}{4}{5}{6}{7}{10} {4,5,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0, gcd(0,mod(?x_7,0)) = ?x_7, gcd(?y_7,mod(0,?y_7)) = ?y_7, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {13,11,12}{3}{4}{5}{6}{7}{10} {3,4,5,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0, gcd(0,mod(?x_8,0)) = ?x_8, gcd(?y_8,mod(0,?y_8)) = ?y_8, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <1, 0> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {13,11,12}{2}{3}{4}{5}{6}{7}{10} {2,3,4,5,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), 0 = 0, gcd(0,mod(?x_9,0)) = ?x_9, gcd(?y_9,mod(0,?y_9)) = ?y_9, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_7)),0,0)> from mod(0,s(?y_7)) Not Confluent Direct Methods: not CR Add {13,11,12}{1}{2}{3}{4}{5}{6}{7}{10} {1,2,3,4,5,6,7,8,9,10,11,12,13} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x, gcd(?x,?y) -> gcd(?y,mod(?x,?y)), gcd(?x,0) -> ?x, gcd(0,?x) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))), 0 = 0, gcd(0,mod(?x_10,0)) = ?x_10, gcd(?y_10,mod(0,?y_10)) = ?y_10, 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ gcd(?x,mod(0,?x)) = ?x, gcd(0,mod(?x,0)) = ?x, ?y = gcd(?y,mod(0,?y)), ?x = gcd(0,mod(?x,0)), 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <8, 7> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_8)),0,0)> from mod(0,s(?y_8)) Not Confluent Direct Methods: not CR Add {0} {0,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <2, 1> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 6*7=>6 0 : =>6 < : 6*7=>15 s : 13=>7 if : 15*6*6=>6 mod : 6*7=>6 true : =>15 maximal types: {6,7,13,15} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1} {0,1,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 8*9=>8 0 : =>8 < : 8*9=>17 s : 15=>9 if : 17*8*8=>8 mod : 8*9=>8 true : =>17 false : =>17 maximal types: {8,9,15,17} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{2} {0,1,2,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 15*15=>15 0 : =>15 < : 15*15=>19 s : 15=>15 if : 19*15*15=>15 mod : 15*15=>15 true : =>19 false : =>19 maximal types: {15,19} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{2}{3} {0,1,2,3,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 16*16=>16 0 : =>16 < : 16*16=>20 s : 16=>16 if : 20*16*16=>16 mod : 16*16=>16 true : =>20 false : =>20 maximal types: {16,20} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{2}{3}{4} {0,1,2,3,4,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <4, 3> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {0}{1}{2}{3}{4}{5} {0,1,2,3,4,5,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <4, 3> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_7)),0,0)> from mod(0,s(?y_7)) Not Confluent Direct Methods: not CR Add {0}{1}{2}{3}{4}{5}{6} {0,1,2,3,4,5,6,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <4, 3> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <8, 7> preceded by [] joinable by a reduction of rules <[([(if,1)],6),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 29*29=>29 0 : =>29 < : 29*29=>35 s : 29=>29 if : 35*29*29=>29 mod : 29*29=>29 true : =>35 false : =>35 maximal types: {29,35} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{2}{3}{4}{5}{6}{7} {0,1,2,3,4,5,6,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_9)),0,mod(-(0,s(?y_9)),s(?y_9))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_9)),0,mod(-(0,s(?y_9)),s(?y_9))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <4, 3> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <9, 8> preceded by [] joinable by a reduction of rules <[([(if,1)],6),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 30*30=>30 0 : =>30 < : 30*30=>36 s : 30=>30 if : 36*30*30=>30 mod : 30*30=>30 true : =>36 false : =>36 maximal types: {30,36} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{2}{3}{4}{5}{6}{10} {0,1,2,3,4,5,6,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <4, 3> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <8, 7> preceded by [] joinable by a reduction of rules <[([(if,1)],6),([],0)], []> Critical Pair <0, 0> by Rules <9, 7> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 34*34=>34 0 : =>34 < : 34*34=>37 s : 34=>34 if : 37*34*34=>34 mod : 34*34=>34 true : =>37 false : =>37 maximal types: {34,37} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{2}{3}{4}{5}{7} {0,1,2,3,4,5,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <4, 3> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <8, 7> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_8)),0,0)> from mod(0,s(?y_8)) Not Confluent Direct Methods: not CR Add {0}{1}{2}{3}{4}{5}{10} {0,1,2,3,4,5,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <4, 3> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_7)),0,0)> from mod(0,s(?y_7)) Not Confluent Direct Methods: not CR Add {0}{1}{2}{3}{4}{5}{7}{10} {0,1,2,3,4,5,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <4, 3> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <8, 7> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_8)),0,0)> from mod(0,s(?y_8)) Not Confluent Direct Methods: not CR Add {0}{1}{2}{3}{4}{6} {0,1,2,3,4,6,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <4, 3> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],5),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 27*27=>27 0 : =>27 < : 27*27=>33 s : 27=>27 if : 33*27*27=>27 mod : 27*27=>27 true : =>33 false : =>33 maximal types: {27,33} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{2}{3}{4}{6}{7} {0,1,2,3,4,6,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <4, 3> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <8, 7> preceded by [] joinable by a reduction of rules <[([(if,1)],5),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 28*28=>28 0 : =>28 < : 28*28=>34 s : 28=>28 if : 34*28*28=>28 mod : 28*28=>28 true : =>34 false : =>34 maximal types: {28,34} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{2}{3}{4}{6}{10} {0,1,2,3,4,6,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <4, 3> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],5),([],0)], []> Critical Pair <0, 0> by Rules <8, 6> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 32*32=>32 0 : =>32 < : 32*32=>35 s : 32=>32 if : 35*32*32=>32 mod : 32*32=>32 true : =>35 false : =>35 maximal types: {32,35} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{2}{3}{4}{7} {0,1,2,3,4,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <4, 3> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_7)),0,0)> from mod(0,s(?y_7)) Not Confluent Direct Methods: not CR Add {0}{1}{2}{3}{4}{10} {0,1,2,3,4,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <4, 3> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {0}{1}{2}{3}{4}{7}{10} {0,1,2,3,4,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <4, 3> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_7)),0,0)> from mod(0,s(?y_7)) Not Confluent Direct Methods: not CR Add {0}{1}{2}{3}{4}{6}{7}{10} {0,1,2,3,4,6,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <4, 3> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <8, 7> preceded by [] joinable by a reduction of rules <[([(if,1)],5),([],0)], []> Critical Pair <0, 0> by Rules <9, 7> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 33*33=>33 0 : =>33 < : 33*33=>36 s : 33=>33 if : 36*33*33=>33 mod : 33*33=>33 true : =>36 false : =>36 maximal types: {33,36} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{2}{3}{5} {0,1,2,3,5,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 27*27=>27 0 : =>27 < : 27*27=>22 s : 27=>27 if : 22*27*27=>27 mod : 27*27=>27 true : =>22 false : =>22 maximal types: {22,27} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{2}{3}{5}{6} {0,1,2,3,5,6,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],5),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 28*28=>28 0 : =>28 < : 28*28=>34 s : 28=>28 if : 34*28*28=>28 mod : 28*28=>28 true : =>34 false : =>34 maximal types: {28,34} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{2}{3}{5}{6}{7} {0,1,2,3,5,6,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <8, 7> preceded by [] joinable by a reduction of rules <[([(if,1)],5),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 29*29=>29 0 : =>29 < : 29*29=>35 s : 29=>29 if : 35*29*29=>29 mod : 29*29=>29 true : =>35 false : =>35 maximal types: {29,35} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{2}{3}{5}{6}{10} {0,1,2,3,5,6,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],5),([],0)], []> Critical Pair <0, 0> by Rules <8, 6> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 33*33=>33 0 : =>33 < : 33*33=>36 s : 33=>33 if : 36*33*33=>33 mod : 33*33=>33 true : =>36 false : =>36 maximal types: {33,36} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{2}{3}{5}{7} {0,1,2,3,5,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 28*28=>28 0 : =>28 < : 28*28=>34 s : 28=>28 if : 34*28*28=>28 mod : 28*28=>28 true : =>34 false : =>34 maximal types: {28,34} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{2}{3}{5}{10} {0,1,2,3,5,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 32*32=>32 0 : =>32 < : 32*32=>23 s : 32=>32 if : 23*32*32=>32 mod : 32*32=>32 true : =>23 false : =>23 maximal types: {23,32} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{2}{3}{5}{7}{10} {0,1,2,3,5,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 33*33=>33 0 : =>33 < : 33*33=>36 s : 33=>33 if : 36*33*33=>33 mod : 33*33=>33 true : =>36 false : =>36 maximal types: {33,36} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{2}{3}{6} {0,1,2,3,6,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 26*26=>26 0 : =>26 < : 26*26=>32 s : 26=>26 if : 32*26*26=>26 mod : 26*26=>26 true : =>32 false : =>32 maximal types: {26,32} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{2}{3}{6}{7} {0,1,2,3,6,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 27*27=>27 0 : =>27 < : 27*27=>33 s : 27=>27 if : 33*27*27=>27 mod : 27*27=>27 true : =>33 false : =>33 maximal types: {27,33} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{2}{3}{6}{10} {0,1,2,3,6,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair <0, 0> by Rules <7, 5> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 31*31=>31 0 : =>31 < : 31*31=>34 s : 31=>31 if : 34*31*31=>31 mod : 31*31=>31 true : =>34 false : =>34 maximal types: {31,34} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{2}{3}{7} {0,1,2,3,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 16*16=>16 0 : =>16 < : 16*16=>32 s : 16=>16 if : 32*16*16=>16 mod : 16*16=>16 true : =>32 false : =>32 maximal types: {16,32} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{2}{3}{10} {0,1,2,3,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 30*30=>30 0 : =>30 < : 30*30=>21 s : 30=>30 if : 21*30*30=>30 mod : 30*30=>30 true : =>21 false : =>21 maximal types: {21,30} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{2}{3}{7}{10} {0,1,2,3,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 31*31=>31 0 : =>31 < : 31*31=>34 s : 31=>31 if : 34*31*31=>31 mod : 31*31=>31 true : =>34 false : =>34 maximal types: {31,34} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{2}{3}{6}{7}{10} {0,1,2,3,6,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair <0, 0> by Rules <8, 6> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 32*32=>32 0 : =>32 < : 32*32=>35 s : 32=>32 if : 35*32*32=>32 mod : 32*32=>32 true : =>35 false : =>35 maximal types: {32,35} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{2}{3}{5}{6}{7}{10} {0,1,2,3,5,6,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <8, 7> preceded by [] joinable by a reduction of rules <[([(if,1)],5),([],0)], []> Critical Pair <0, 0> by Rules <9, 7> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 34*34=>34 0 : =>34 < : 34*34=>37 s : 34=>34 if : 37*34*34=>34 mod : 34*34=>34 true : =>37 false : =>37 maximal types: {34,37} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{2}{4} {0,1,2,4,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {0}{1}{2}{4}{5} {0,1,2,4,5,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {0}{1}{2}{4}{5}{6} {0,1,2,4,5,6,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],5),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 28*28=>28 0 : =>28 < : 28*28=>34 s : 28=>28 if : 34*28*28=>28 mod : 28*28=>28 true : =>34 false : =>34 maximal types: {28,34} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{2}{4}{5}{6}{7} {0,1,2,4,5,6,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <8, 7> preceded by [] joinable by a reduction of rules <[([(if,1)],5),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 29*29=>29 0 : =>29 < : 29*29=>35 s : 29=>29 if : 35*29*29=>29 mod : 29*29=>29 true : =>35 false : =>35 maximal types: {29,35} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{2}{4}{5}{6}{10} {0,1,2,4,5,6,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],5),([],0)], []> Critical Pair <0, 0> by Rules <8, 6> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 33*33=>33 0 : =>33 < : 33*33=>36 s : 33=>33 if : 36*33*33=>33 mod : 33*33=>33 true : =>36 false : =>36 maximal types: {33,36} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{2}{4}{5}{7} {0,1,2,4,5,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_7)),0,0)> from mod(0,s(?y_7)) Not Confluent Direct Methods: not CR Add {0}{1}{2}{4}{5}{10} {0,1,2,4,5,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {0}{1}{2}{4}{5}{7}{10} {0,1,2,4,5,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_7)),0,0)> from mod(0,s(?y_7)) Not Confluent Direct Methods: not CR Add {0}{1}{2}{4}{6} {0,1,2,4,6,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 26*26=>26 0 : =>26 < : 26*26=>32 s : 26=>26 if : 32*26*26=>26 mod : 26*26=>26 true : =>32 false : =>32 maximal types: {26,32} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{2}{4}{6}{7} {0,1,2,4,6,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 27*27=>27 0 : =>27 < : 27*27=>33 s : 27=>27 if : 33*27*27=>27 mod : 27*27=>27 true : =>33 false : =>33 maximal types: {27,33} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{2}{4}{6}{10} {0,1,2,4,6,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair <0, 0> by Rules <7, 5> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 31*31=>31 0 : =>31 < : 31*31=>34 s : 31=>31 if : 34*31*31=>31 mod : 31*31=>31 true : =>34 false : =>34 maximal types: {31,34} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{2}{4}{7} {0,1,2,4,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {0}{1}{2}{4}{10} {0,1,2,4,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {0}{1}{2}{4}{7}{10} {0,1,2,4,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {0}{1}{2}{4}{6}{7}{10} {0,1,2,4,6,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair <0, 0> by Rules <8, 6> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 32*32=>32 0 : =>32 < : 32*32=>35 s : 32=>32 if : 35*32*32=>32 mod : 32*32=>32 true : =>35 false : =>35 maximal types: {32,35} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{2}{5} {0,1,2,5,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 26*26=>26 0 : =>26 < : 26*26=>21 s : 26=>26 if : 21*26*26=>26 mod : 26*26=>26 true : =>21 false : =>21 maximal types: {21,26} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{2}{5}{6} {0,1,2,5,6,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 27*27=>27 0 : =>27 < : 27*27=>33 s : 27=>27 if : 33*27*27=>27 mod : 27*27=>27 true : =>33 false : =>33 maximal types: {27,33} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{2}{5}{6}{7} {0,1,2,5,6,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 28*28=>28 0 : =>28 < : 28*28=>34 s : 28=>28 if : 34*28*28=>28 mod : 28*28=>28 true : =>34 false : =>34 maximal types: {28,34} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{2}{5}{6}{10} {0,1,2,5,6,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair <0, 0> by Rules <7, 5> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 32*32=>32 0 : =>32 < : 32*32=>35 s : 32=>32 if : 35*32*32=>32 mod : 32*32=>32 true : =>35 false : =>35 maximal types: {32,35} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{2}{5}{7} {0,1,2,5,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 27*27=>27 0 : =>27 < : 27*27=>33 s : 27=>27 if : 33*27*27=>27 mod : 27*27=>27 true : =>33 false : =>33 maximal types: {27,33} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{2}{5}{10} {0,1,2,5,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 31*31=>31 0 : =>31 < : 31*31=>22 s : 31=>31 if : 22*31*31=>31 mod : 31*31=>31 true : =>22 false : =>22 maximal types: {22,31} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{2}{5}{7}{10} {0,1,2,5,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 32*32=>32 0 : =>32 < : 32*32=>35 s : 32=>32 if : 35*32*32=>32 mod : 32*32=>32 true : =>35 false : =>35 maximal types: {32,35} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{2}{6} {0,1,2,6,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 25*25=>25 0 : =>25 < : 25*25=>31 s : 25=>25 if : 31*25*25=>25 mod : 25*25=>25 true : =>31 false : =>31 maximal types: {25,31} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{2}{6}{7} {0,1,2,6,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 26*26=>26 0 : =>26 < : 26*26=>32 s : 26=>26 if : 32*26*26=>26 mod : 26*26=>26 true : =>32 false : =>32 maximal types: {26,32} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{2}{6}{10} {0,1,2,6,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair <0, 0> by Rules <6, 4> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 30*30=>30 0 : =>30 < : 30*30=>33 s : 30=>30 if : 33*30*30=>30 mod : 30*30=>30 true : =>33 false : =>33 maximal types: {30,33} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{2}{7} {0,1,2,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 15*15=>15 0 : =>15 < : 15*15=>31 s : 15=>15 if : 31*15*15=>15 mod : 15*15=>15 true : =>31 false : =>31 maximal types: {15,31} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{2}{10} {0,1,2,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 29*29=>29 0 : =>29 < : 29*29=>20 s : 29=>29 if : 20*29*29=>29 mod : 29*29=>29 true : =>20 false : =>20 maximal types: {20,29} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{2}{7}{10} {0,1,2,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 30*30=>30 0 : =>30 < : 30*30=>33 s : 30=>30 if : 33*30*30=>30 mod : 30*30=>30 true : =>33 false : =>33 maximal types: {30,33} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{2}{6}{7}{10} {0,1,2,6,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair <0, 0> by Rules <7, 5> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 31*31=>31 0 : =>31 < : 31*31=>34 s : 31=>31 if : 34*31*31=>31 mod : 31*31=>31 true : =>34 false : =>34 maximal types: {31,34} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{2}{5}{6}{7}{10} {0,1,2,5,6,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair <0, 0> by Rules <8, 6> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 33*33=>33 0 : =>33 < : 33*33=>36 s : 33=>33 if : 36*33*33=>33 mod : 33*33=>33 true : =>36 false : =>36 maximal types: {33,36} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{2}{4}{5}{6}{7}{10} {0,1,2,4,5,6,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <8, 7> preceded by [] joinable by a reduction of rules <[([(if,1)],5),([],0)], []> Critical Pair <0, 0> by Rules <9, 7> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 34*34=>34 0 : =>34 < : 34*34=>37 s : 34=>34 if : 37*34*34=>34 mod : 34*34=>34 true : =>37 false : =>37 maximal types: {34,37} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{3} {0,1,3,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 13*13=>13 0 : =>13 < : 13*13=>18 s : 16=>13 if : 18*13*13=>13 mod : 13*13=>13 true : =>18 false : =>18 maximal types: {13,16,18} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{3}{4} {0,1,3,4,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {0}{1}{3}{4}{5} {0,1,3,4,5,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {0}{1}{3}{4}{5}{6} {0,1,3,4,5,6,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],5),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 27*27=>27 0 : =>27 < : 27*27=>33 s : 27=>27 if : 33*27*27=>27 mod : 27*27=>27 true : =>33 false : =>33 maximal types: {27,33} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{3}{4}{5}{6}{7} {0,1,3,4,5,6,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <8, 7> preceded by [] joinable by a reduction of rules <[([(if,1)],5),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 28*28=>28 0 : =>28 < : 28*28=>34 s : 28=>28 if : 34*28*28=>28 mod : 28*28=>28 true : =>34 false : =>34 maximal types: {28,34} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{3}{4}{5}{6}{10} {0,1,3,4,5,6,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],5),([],0)], []> Critical Pair <0, 0> by Rules <8, 6> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 32*32=>32 0 : =>32 < : 32*32=>35 s : 32=>32 if : 35*32*32=>32 mod : 32*32=>32 true : =>35 false : =>35 maximal types: {32,35} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{3}{4}{5}{7} {0,1,3,4,5,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_7)),0,0)> from mod(0,s(?y_7)) Not Confluent Direct Methods: not CR Add {0}{1}{3}{4}{5}{10} {0,1,3,4,5,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {0}{1}{3}{4}{5}{7}{10} {0,1,3,4,5,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_7)),0,0)> from mod(0,s(?y_7)) Not Confluent Direct Methods: not CR Add {0}{1}{3}{4}{6} {0,1,3,4,6,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 29*29=>29 0 : =>29 < : 29*29=>31 s : 18=>29 if : 31*29*29=>29 mod : 29*29=>29 true : =>31 false : =>31 maximal types: {18,29,31} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{3}{4}{6}{7} {0,1,3,4,6,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 26*26=>26 0 : =>26 < : 26*26=>32 s : 19=>26 if : 32*26*26=>26 mod : 26*26=>26 true : =>32 false : =>32 maximal types: {19,26,32} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{3}{4}{6}{10} {0,1,3,4,6,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair <0, 0> by Rules <7, 5> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 30*30=>30 0 : =>30 < : 30*30=>33 s : 19=>30 if : 33*30*30=>30 mod : 30*30=>30 true : =>33 false : =>33 maximal types: {19,30,33} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{3}{4}{7} {0,1,3,4,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {0}{1}{3}{4}{10} {0,1,3,4,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {0}{1}{3}{4}{7}{10} {0,1,3,4,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {0}{1}{3}{4}{6}{7}{10} {0,1,3,4,6,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair <0, 0> by Rules <8, 6> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 31*31=>31 0 : =>31 < : 31*31=>34 s : 20=>31 if : 34*31*31=>31 mod : 31*31=>31 true : =>34 false : =>34 maximal types: {20,31,34} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{3}{5} {0,1,3,5,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 25*25=>25 0 : =>25 < : 25*25=>20 s : 25=>25 if : 20*25*25=>25 mod : 25*25=>25 true : =>20 false : =>20 maximal types: {20,25} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{3}{5}{6} {0,1,3,5,6,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 26*26=>26 0 : =>26 < : 26*26=>32 s : 26=>26 if : 32*26*26=>26 mod : 26*26=>26 true : =>32 false : =>32 maximal types: {26,32} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{3}{5}{6}{7} {0,1,3,5,6,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 27*27=>27 0 : =>27 < : 27*27=>33 s : 27=>27 if : 33*27*27=>27 mod : 27*27=>27 true : =>33 false : =>33 maximal types: {27,33} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{3}{5}{6}{10} {0,1,3,5,6,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair <0, 0> by Rules <7, 5> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 31*31=>31 0 : =>31 < : 31*31=>34 s : 31=>31 if : 34*31*31=>31 mod : 31*31=>31 true : =>34 false : =>34 maximal types: {31,34} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{3}{5}{7} {0,1,3,5,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 26*26=>26 0 : =>26 < : 26*26=>32 s : 26=>26 if : 32*26*26=>26 mod : 26*26=>26 true : =>32 false : =>32 maximal types: {26,32} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{3}{5}{10} {0,1,3,5,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 30*30=>30 0 : =>30 < : 30*30=>21 s : 30=>30 if : 21*30*30=>30 mod : 30*30=>30 true : =>21 false : =>21 maximal types: {21,30} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{3}{5}{7}{10} {0,1,3,5,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 31*31=>31 0 : =>31 < : 31*31=>34 s : 31=>31 if : 34*31*31=>31 mod : 31*31=>31 true : =>34 false : =>34 maximal types: {31,34} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{3}{6} {0,1,3,6,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 28*28=>28 0 : =>28 < : 28*28=>30 s : 17=>28 if : 30*28*28=>28 mod : 28*28=>28 true : =>30 false : =>30 maximal types: {17,28,30} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{3}{6}{7} {0,1,3,6,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 25*25=>25 0 : =>25 < : 25*25=>31 s : 18=>25 if : 31*25*25=>25 mod : 25*25=>25 true : =>31 false : =>31 maximal types: {18,25,31} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{3}{6}{10} {0,1,3,6,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair <0, 0> by Rules <6, 4> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 29*29=>29 0 : =>29 < : 29*29=>32 s : 18=>29 if : 32*29*29=>29 mod : 29*29=>29 true : =>32 false : =>32 maximal types: {18,29,32} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{3}{7} {0,1,3,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 14*14=>14 0 : =>14 < : 14*14=>30 s : 17=>14 if : 30*14*14=>14 mod : 14*14=>14 true : =>30 false : =>30 maximal types: {14,17,30} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{3}{10} {0,1,3,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 28*28=>28 0 : =>28 < : 28*28=>19 s : 17=>28 if : 19*28*28=>28 mod : 28*28=>28 true : =>19 false : =>19 maximal types: {17,19,28} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{3}{7}{10} {0,1,3,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 29*29=>29 0 : =>29 < : 29*29=>32 s : 18=>29 if : 32*29*29=>29 mod : 29*29=>29 true : =>32 false : =>32 maximal types: {18,29,32} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{3}{6}{7}{10} {0,1,3,6,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair <0, 0> by Rules <7, 5> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 30*30=>30 0 : =>30 < : 30*30=>33 s : 19=>30 if : 33*30*30=>30 mod : 30*30=>30 true : =>33 false : =>33 maximal types: {19,30,33} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{3}{5}{6}{7}{10} {0,1,3,5,6,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair <0, 0> by Rules <8, 6> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 32*32=>32 0 : =>32 < : 32*32=>35 s : 32=>32 if : 35*32*32=>32 mod : 32*32=>32 true : =>35 false : =>35 maximal types: {32,35} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{4} {0,1,4,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {0}{1}{4}{5} {0,1,4,5,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {0}{1}{4}{5}{6} {0,1,4,5,6,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 13*13=>13 0 : =>13 < : 13*13=>32 s : 13=>13 if : 32*13*13=>13 mod : 13*13=>13 true : =>32 false : =>32 maximal types: {13,32} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{4}{5}{6}{7} {0,1,4,5,6,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 14*14=>14 0 : =>14 < : 14*14=>33 s : 14=>14 if : 33*14*14=>14 mod : 14*14=>14 true : =>33 false : =>33 maximal types: {14,33} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{4}{5}{6}{10} {0,1,4,5,6,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair <0, 0> by Rules <7, 5> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 31*31=>31 0 : =>31 < : 31*31=>34 s : 31=>31 if : 34*31*31=>31 mod : 31*31=>31 true : =>34 false : =>34 maximal types: {31,34} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{4}{5}{7} {0,1,4,5,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {0}{1}{4}{5}{10} {0,1,4,5,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {0}{1}{4}{5}{7}{10} {0,1,4,5,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {0}{1}{4}{6} {0,1,4,6,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 28*11=>28 0 : =>28 < : 28*11=>30 s : 17=>11 if : 30*28*28=>28 mod : 28*11=>28 true : =>30 false : =>30 maximal types: {11,17,28,30} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{4}{6}{7} {0,1,4,6,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 12*12=>12 0 : =>12 < : 12*12=>31 s : 18=>12 if : 31*12*12=>12 mod : 12*12=>12 true : =>31 false : =>31 maximal types: {12,18,31} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{4}{6}{10} {0,1,4,6,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair <0, 0> by Rules <6, 4> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 12*12=>12 0 : =>12 < : 12*12=>32 s : 18=>12 if : 32*12*12=>12 mod : 12*12=>12 true : =>32 false : =>32 maximal types: {12,18,32} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{4}{7} {0,1,4,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {0}{1}{4}{10} {0,1,4,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {0}{1}{4}{7}{10} {0,1,4,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {0}{1}{4}{6}{7}{10} {0,1,4,6,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair <0, 0> by Rules <7, 5> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 30*30=>30 0 : =>30 < : 30*30=>33 s : 19=>30 if : 33*30*30=>30 mod : 30*30=>30 true : =>33 false : =>33 maximal types: {19,30,33} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{5} {0,1,5,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 11*11=>11 0 : =>11 < : 11*11=>19 s : 11=>11 if : 19*11*11=>11 mod : 11*11=>11 true : =>19 false : =>19 maximal types: {11,19} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{5}{6} {0,1,5,6,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 12*12=>12 0 : =>12 < : 12*12=>31 s : 12=>12 if : 31*12*12=>12 mod : 12*12=>12 true : =>31 false : =>31 maximal types: {12,31} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{5}{6}{7} {0,1,5,6,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 13*13=>13 0 : =>13 < : 13*13=>32 s : 13=>13 if : 32*13*13=>13 mod : 13*13=>13 true : =>32 false : =>32 maximal types: {13,32} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{5}{6}{10} {0,1,5,6,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair <0, 0> by Rules <6, 4> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 30*30=>30 0 : =>30 < : 30*30=>33 s : 30=>30 if : 33*30*30=>30 mod : 30*30=>30 true : =>33 false : =>33 maximal types: {30,33} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{5}{7} {0,1,5,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 12*12=>12 0 : =>12 < : 12*12=>31 s : 12=>12 if : 31*12*12=>12 mod : 12*12=>12 true : =>31 false : =>31 maximal types: {12,31} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{5}{10} {0,1,5,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 29*29=>29 0 : =>29 < : 29*29=>20 s : 29=>29 if : 20*29*29=>29 mod : 29*29=>29 true : =>20 false : =>20 maximal types: {20,29} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{5}{7}{10} {0,1,5,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 30*30=>30 0 : =>30 < : 30*30=>33 s : 30=>30 if : 33*30*30=>30 mod : 30*30=>30 true : =>33 false : =>33 maximal types: {30,33} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{6} {0,1,6,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] joinable by a reduction of rules <[([(if,1)],2),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 9*10=>9 0 : =>9 < : 9*10=>29 s : 16=>10 if : 29*9*9=>9 mod : 9*10=>9 true : =>29 false : =>29 maximal types: {9,10,16,29} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{6}{7} {0,1,6,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],2),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 11*11=>11 0 : =>11 < : 11*11=>30 s : 17=>11 if : 30*11*11=>11 mod : 11*11=>11 true : =>30 false : =>30 maximal types: {11,17,30} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{6}{10} {0,1,6,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] joinable by a reduction of rules <[([(if,1)],2),([],0)], []> Critical Pair <0, 0> by Rules <5, 3> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 11*11=>11 0 : =>11 < : 11*11=>31 s : 17=>11 if : 31*11*11=>11 mod : 11*11=>11 true : =>31 false : =>31 maximal types: {11,17,31} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{7} {0,1,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 10*10=>10 0 : =>10 < : 10*10=>29 s : 16=>10 if : 29*10*10=>10 mod : 10*10=>10 true : =>29 false : =>29 maximal types: {10,16,29} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{10} {0,1,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 10*10=>10 0 : =>10 < : 10*10=>18 s : 16=>10 if : 18*10*10=>10 mod : 10*10=>10 true : =>18 false : =>18 maximal types: {10,16,18} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{7}{10} {0,1,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 28*28=>28 0 : =>28 < : 28*28=>31 s : 17=>28 if : 31*28*28=>28 mod : 28*28=>28 true : =>31 false : =>31 maximal types: {17,28,31} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{6}{7}{10} {0,1,6,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],2),([],0)], []> Critical Pair <0, 0> by Rules <6, 4> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 29*29=>29 0 : =>29 < : 29*29=>32 s : 18=>29 if : 32*29*29=>29 mod : 29*29=>29 true : =>32 false : =>32 maximal types: {18,29,32} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{5}{6}{7}{10} {0,1,5,6,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair <0, 0> by Rules <7, 5> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 31*31=>31 0 : =>31 < : 31*31=>34 s : 31=>31 if : 34*31*31=>31 mod : 31*31=>31 true : =>34 false : =>34 maximal types: {31,34} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{4}{5}{6}{7}{10} {0,1,4,5,6,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair <0, 0> by Rules <8, 6> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 32*32=>32 0 : =>32 < : 32*32=>35 s : 32=>32 if : 35*32*32=>32 mod : 32*32=>32 true : =>35 false : =>35 maximal types: {32,35} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{1}{3}{4}{5}{6}{7}{10} {0,1,3,4,5,6,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <8, 7> preceded by [] joinable by a reduction of rules <[([(if,1)],5),([],0)], []> Critical Pair <0, 0> by Rules <9, 7> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 33*33=>33 0 : =>33 < : 33*33=>36 s : 33=>33 if : 36*33*33=>33 mod : 33*33=>33 true : =>36 false : =>36 maximal types: {33,36} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{2} {0,2,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 13*13=>13 0 : =>13 < : 13*13=>17 s : 13=>13 if : 17*13*13=>13 mod : 13*13=>13 true : =>17 maximal types: {13,17} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{2}{3} {0,2,3,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 20*20=>20 0 : =>20 < : 20*20=>18 s : 20=>20 if : 18*20*20=>20 mod : 20*20=>20 true : =>18 maximal types: {18,20} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{2}{3}{4} {0,2,3,4,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {0}{2}{3}{4}{5} {0,2,3,4,5,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {0}{2}{3}{4}{5}{6} {0,2,3,4,5,6,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],5),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 24*24=>24 0 : =>24 < : 24*24=>32 s : 24=>24 if : 32*24*24=>24 mod : 24*24=>24 true : =>32 maximal types: {24,32} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{2}{3}{4}{5}{6}{7} {0,2,3,4,5,6,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <8, 7> preceded by [] joinable by a reduction of rules <[([(if,1)],5),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 25*25=>25 0 : =>25 < : 25*25=>34 s : 25=>25 if : 34*25*25=>25 mod : 25*25=>25 true : =>34 false : =>34 maximal types: {25,34} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{2}{3}{4}{5}{6}{10} {0,2,3,4,5,6,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],5),([],0)], []> Critical Pair <0, 0> by Rules <8, 6> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 31*31=>31 0 : =>31 < : 31*31=>34 s : 31=>31 if : 34*31*31=>31 mod : 31*31=>31 true : =>34 maximal types: {31,34} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{2}{3}{4}{5}{7} {0,2,3,4,5,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_7)),0,0)> from mod(0,s(?y_7)) Not Confluent Direct Methods: not CR Add {0}{2}{3}{4}{5}{10} {0,2,3,4,5,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {0}{2}{3}{4}{5}{7}{10} {0,2,3,4,5,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_7)),0,0)> from mod(0,s(?y_7)) Not Confluent Direct Methods: not CR Add {0}{2}{3}{4}{6} {0,2,3,4,6,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 22*22=>22 0 : =>22 < : 22*22=>30 s : 22=>22 if : 30*22*22=>22 mod : 22*22=>22 true : =>30 maximal types: {22,30} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{2}{3}{4}{6}{7} {0,2,3,4,6,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 23*23=>23 0 : =>23 < : 23*23=>32 s : 23=>23 if : 32*23*23=>23 mod : 23*23=>23 true : =>32 false : =>32 maximal types: {23,32} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{2}{3}{4}{6}{10} {0,2,3,4,6,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair <0, 0> by Rules <7, 5> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 29*29=>29 0 : =>29 < : 29*29=>32 s : 29=>29 if : 32*29*29=>29 mod : 29*29=>29 true : =>32 maximal types: {29,32} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{2}{3}{4}{7} {0,2,3,4,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {0}{2}{3}{4}{10} {0,2,3,4,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {0}{2}{3}{4}{7}{10} {0,2,3,4,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {0}{2}{3}{4}{6}{7}{10} {0,2,3,4,6,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair <0, 0> by Rules <8, 6> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 31*31=>31 0 : =>31 < : 31*31=>34 s : 31=>31 if : 34*31*31=>31 mod : 31*31=>31 true : =>34 false : =>34 maximal types: {31,34} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{2}{3}{5} {0,2,3,5,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 22*22=>22 0 : =>22 < : 22*22=>20 s : 22=>22 if : 20*22*22=>22 mod : 22*22=>22 true : =>20 maximal types: {20,22} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{2}{3}{5}{6} {0,2,3,5,6,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 23*23=>23 0 : =>23 < : 23*23=>31 s : 23=>23 if : 31*23*23=>23 mod : 23*23=>23 true : =>31 maximal types: {23,31} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{2}{3}{5}{6}{7} {0,2,3,5,6,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 24*24=>24 0 : =>24 < : 24*24=>33 s : 24=>24 if : 33*24*24=>24 mod : 24*24=>24 true : =>33 false : =>33 maximal types: {24,33} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{2}{3}{5}{6}{10} {0,2,3,5,6,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair <0, 0> by Rules <7, 5> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 30*30=>30 0 : =>30 < : 30*30=>33 s : 30=>30 if : 33*30*30=>30 mod : 30*30=>30 true : =>33 maximal types: {30,33} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{2}{3}{5}{7} {0,2,3,5,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 23*23=>23 0 : =>23 < : 23*23=>21 s : 23=>23 if : 21*23*23=>23 mod : 23*23=>23 true : =>21 false : =>21 maximal types: {21,23} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{2}{3}{5}{10} {0,2,3,5,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 29*29=>29 0 : =>29 < : 29*29=>21 s : 29=>29 if : 21*29*29=>29 mod : 29*29=>29 true : =>21 maximal types: {21,29} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{2}{3}{5}{7}{10} {0,2,3,5,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 31*31=>31 0 : =>31 < : 31*31=>22 s : 31=>31 if : 22*31*31=>31 mod : 31*31=>31 true : =>22 false : =>22 maximal types: {22,31} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{2}{3}{6} {0,2,3,6,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 21*21=>21 0 : =>21 < : 21*21=>29 s : 21=>21 if : 29*21*21=>21 mod : 21*21=>21 true : =>29 maximal types: {21,29} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{2}{3}{6}{7} {0,2,3,6,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 22*22=>22 0 : =>22 < : 22*22=>31 s : 22=>22 if : 31*22*22=>22 mod : 22*22=>22 true : =>31 false : =>31 maximal types: {22,31} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{2}{3}{6}{10} {0,2,3,6,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair <0, 0> by Rules <6, 4> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 28*28=>28 0 : =>28 < : 28*28=>31 s : 28=>28 if : 31*28*28=>28 mod : 28*28=>28 true : =>31 maximal types: {28,31} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{2}{3}{7} {0,2,3,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 21*21=>21 0 : =>21 < : 21*21=>19 s : 21=>21 if : 19*21*21=>21 mod : 21*21=>21 true : =>19 false : =>19 maximal types: {19,21} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{2}{3}{10} {0,2,3,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 27*27=>27 0 : =>27 < : 27*27=>19 s : 27=>27 if : 19*27*27=>27 mod : 27*27=>27 true : =>19 maximal types: {19,27} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{2}{3}{7}{10} {0,2,3,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 29*29=>29 0 : =>29 < : 29*29=>20 s : 29=>29 if : 20*29*29=>29 mod : 29*29=>29 true : =>20 false : =>20 maximal types: {20,29} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{2}{3}{6}{7}{10} {0,2,3,6,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair <0, 0> by Rules <7, 5> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 30*30=>30 0 : =>30 < : 30*30=>33 s : 30=>30 if : 33*30*30=>30 mod : 30*30=>30 true : =>33 false : =>33 maximal types: {30,33} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{2}{3}{5}{6}{7}{10} {0,2,3,5,6,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair <0, 0> by Rules <8, 6> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 32*32=>32 0 : =>32 < : 32*32=>35 s : 32=>32 if : 35*32*32=>32 mod : 32*32=>32 true : =>35 false : =>35 maximal types: {32,35} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{2}{4} {0,2,4,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {0}{2}{4}{5} {0,2,4,5,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {0}{2}{4}{5}{6} {0,2,4,5,6,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 23*23=>23 0 : =>23 < : 23*23=>31 s : 23=>23 if : 31*23*23=>23 mod : 23*23=>23 true : =>31 maximal types: {23,31} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{2}{4}{5}{6}{7} {0,2,4,5,6,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 24*24=>24 0 : =>24 < : 24*24=>33 s : 24=>24 if : 33*24*24=>24 mod : 24*24=>24 true : =>33 false : =>33 maximal types: {24,33} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{2}{4}{5}{6}{10} {0,2,4,5,6,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair <0, 0> by Rules <7, 5> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 30*30=>30 0 : =>30 < : 30*30=>33 s : 30=>30 if : 33*30*30=>30 mod : 30*30=>30 true : =>33 maximal types: {30,33} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{2}{4}{5}{7} {0,2,4,5,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {0}{2}{4}{5}{10} {0,2,4,5,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {0}{2}{4}{5}{7}{10} {0,2,4,5,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {0}{2}{4}{6} {0,2,4,6,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 21*21=>21 0 : =>21 < : 21*21=>29 s : 21=>21 if : 29*21*21=>21 mod : 21*21=>21 true : =>29 maximal types: {21,29} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{2}{4}{6}{7} {0,2,4,6,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 22*22=>22 0 : =>22 < : 22*22=>31 s : 22=>22 if : 31*22*22=>22 mod : 22*22=>22 true : =>31 false : =>31 maximal types: {22,31} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{2}{4}{6}{10} {0,2,4,6,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair <0, 0> by Rules <6, 4> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 28*28=>28 0 : =>28 < : 28*28=>31 s : 28=>28 if : 31*28*28=>28 mod : 28*28=>28 true : =>31 maximal types: {28,31} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{2}{4}{7} {0,2,4,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {0}{2}{4}{10} {0,2,4,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {0}{2}{4}{7}{10} {0,2,4,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {0}{2}{4}{6}{7}{10} {0,2,4,6,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair <0, 0> by Rules <7, 5> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 30*30=>30 0 : =>30 < : 30*30=>33 s : 30=>30 if : 33*30*30=>30 mod : 30*30=>30 true : =>33 false : =>33 maximal types: {30,33} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{2}{5} {0,2,5,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 21*21=>21 0 : =>21 < : 21*21=>19 s : 21=>21 if : 19*21*21=>21 mod : 21*21=>21 true : =>19 maximal types: {19,21} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{2}{5}{6} {0,2,5,6,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 22*22=>22 0 : =>22 < : 22*22=>30 s : 22=>22 if : 30*22*22=>22 mod : 22*22=>22 true : =>30 maximal types: {22,30} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{2}{5}{6}{7} {0,2,5,6,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 23*23=>23 0 : =>23 < : 23*23=>32 s : 23=>23 if : 32*23*23=>23 mod : 23*23=>23 true : =>32 false : =>32 maximal types: {23,32} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{2}{5}{6}{10} {0,2,5,6,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair <0, 0> by Rules <6, 4> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 29*29=>29 0 : =>29 < : 29*29=>32 s : 29=>29 if : 32*29*29=>29 mod : 29*29=>29 true : =>32 maximal types: {29,32} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{2}{5}{7} {0,2,5,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 22*22=>22 0 : =>22 < : 22*22=>20 s : 22=>22 if : 20*22*22=>22 mod : 22*22=>22 true : =>20 false : =>20 maximal types: {20,22} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{2}{5}{10} {0,2,5,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 28*28=>28 0 : =>28 < : 28*28=>20 s : 28=>28 if : 20*28*28=>28 mod : 28*28=>28 true : =>20 maximal types: {20,28} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{2}{5}{7}{10} {0,2,5,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 30*30=>30 0 : =>30 < : 30*30=>21 s : 30=>30 if : 21*30*30=>30 mod : 30*30=>30 true : =>21 false : =>21 maximal types: {21,30} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{2}{6} {0,2,6,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] joinable by a reduction of rules <[([(if,1)],2),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 23*23=>23 0 : =>23 < : 23*23=>28 s : 23=>23 if : 28*23*23=>23 mod : 23*23=>23 true : =>28 maximal types: {23,28} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{2}{6}{7} {0,2,6,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],2),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 21*21=>21 0 : =>21 < : 21*21=>30 s : 21=>21 if : 30*21*21=>21 mod : 21*21=>21 true : =>30 false : =>30 maximal types: {21,30} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{2}{6}{10} {0,2,6,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] joinable by a reduction of rules <[([(if,1)],2),([],0)], []> Critical Pair <0, 0> by Rules <5, 3> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 27*27=>27 0 : =>27 < : 27*27=>30 s : 27=>27 if : 30*27*27=>27 mod : 27*27=>27 true : =>30 maximal types: {27,30} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{2}{7} {0,2,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 20*20=>20 0 : =>20 < : 20*20=>18 s : 20=>20 if : 18*20*20=>20 mod : 20*20=>20 true : =>18 false : =>18 maximal types: {18,20} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{2}{10} {0,2,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 26*26=>26 0 : =>26 < : 26*26=>18 s : 26=>26 if : 18*26*26=>26 mod : 26*26=>26 true : =>18 maximal types: {18,26} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{2}{7}{10} {0,2,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 28*28=>28 0 : =>28 < : 28*28=>19 s : 28=>28 if : 19*28*28=>28 mod : 28*28=>28 true : =>19 false : =>19 maximal types: {19,28} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{2}{6}{7}{10} {0,2,6,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],2),([],0)], []> Critical Pair <0, 0> by Rules <6, 4> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 29*29=>29 0 : =>29 < : 29*29=>32 s : 29=>29 if : 32*29*29=>29 mod : 29*29=>29 true : =>32 false : =>32 maximal types: {29,32} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{2}{5}{6}{7}{10} {0,2,5,6,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair <0, 0> by Rules <7, 5> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 31*31=>31 0 : =>31 < : 31*31=>34 s : 31=>31 if : 34*31*31=>31 mod : 31*31=>31 true : =>34 false : =>34 maximal types: {31,34} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{2}{4}{5}{6}{7}{10} {0,2,4,5,6,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair <0, 0> by Rules <8, 6> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 32*32=>32 0 : =>32 < : 32*32=>35 s : 32=>32 if : 35*32*32=>32 mod : 32*32=>32 true : =>35 false : =>35 maximal types: {32,35} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{3} {0,3,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 18*18=>18 0 : =>18 < : 18*18=>16 s : 14=>18 if : 16*18*18=>18 mod : 18*18=>18 true : =>16 maximal types: {14,16,18} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{3}{4} {0,3,4,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {0}{3}{4}{5} {0,3,4,5,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {0}{3}{4}{5}{6} {0,3,4,5,6,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 22*22=>22 0 : =>22 < : 22*22=>30 s : 22=>22 if : 30*22*22=>22 mod : 22*22=>22 true : =>30 maximal types: {22,30} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{3}{4}{5}{6}{7} {0,3,4,5,6,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 23*23=>23 0 : =>23 < : 23*23=>32 s : 23=>23 if : 32*23*23=>23 mod : 23*23=>23 true : =>32 false : =>32 maximal types: {23,32} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{3}{4}{5}{6}{10} {0,3,4,5,6,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair <0, 0> by Rules <7, 5> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 29*29=>29 0 : =>29 < : 29*29=>32 s : 29=>29 if : 32*29*29=>29 mod : 29*29=>29 true : =>32 maximal types: {29,32} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{3}{4}{5}{7} {0,3,4,5,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {0}{3}{4}{5}{10} {0,3,4,5,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {0}{3}{4}{5}{7}{10} {0,3,4,5,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {0}{3}{4}{6} {0,3,4,6,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 20*20=>20 0 : =>20 < : 20*20=>28 s : 16=>20 if : 28*20*20=>20 mod : 20*20=>20 true : =>28 maximal types: {16,20,28} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{3}{4}{6}{7} {0,3,4,6,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 21*21=>21 0 : =>21 < : 21*21=>30 s : 17=>21 if : 30*21*21=>21 mod : 21*21=>21 true : =>30 false : =>30 maximal types: {17,21,30} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{3}{4}{6}{10} {0,3,4,6,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair <0, 0> by Rules <6, 4> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 27*27=>27 0 : =>27 < : 27*27=>30 s : 17=>27 if : 30*27*27=>27 mod : 27*27=>27 true : =>30 maximal types: {17,27,30} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{3}{4}{7} {0,3,4,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {0}{3}{4}{10} {0,3,4,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {0}{3}{4}{7}{10} {0,3,4,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {0}{3}{4}{6}{7}{10} {0,3,4,6,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair <0, 0> by Rules <7, 5> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 29*29=>29 0 : =>29 < : 29*29=>32 s : 18=>29 if : 32*29*29=>29 mod : 29*29=>29 true : =>32 false : =>32 maximal types: {18,29,32} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{3}{5} {0,3,5,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 20*20=>20 0 : =>20 < : 20*20=>18 s : 20=>20 if : 18*20*20=>20 mod : 20*20=>20 true : =>18 maximal types: {18,20} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{3}{5}{6} {0,3,5,6,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 21*21=>21 0 : =>21 < : 21*21=>29 s : 21=>21 if : 29*21*21=>21 mod : 21*21=>21 true : =>29 maximal types: {21,29} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{3}{5}{6}{7} {0,3,5,6,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 22*22=>22 0 : =>22 < : 22*22=>31 s : 22=>22 if : 31*22*22=>22 mod : 22*22=>22 true : =>31 false : =>31 maximal types: {22,31} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{3}{5}{6}{10} {0,3,5,6,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair <0, 0> by Rules <6, 4> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 28*28=>28 0 : =>28 < : 28*28=>31 s : 28=>28 if : 31*28*28=>28 mod : 28*28=>28 true : =>31 maximal types: {28,31} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{3}{5}{7} {0,3,5,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 21*21=>21 0 : =>21 < : 21*21=>19 s : 21=>21 if : 19*21*21=>21 mod : 21*21=>21 true : =>19 false : =>19 maximal types: {19,21} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{3}{5}{10} {0,3,5,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 27*27=>27 0 : =>27 < : 27*27=>19 s : 27=>27 if : 19*27*27=>27 mod : 27*27=>27 true : =>19 maximal types: {19,27} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{3}{5}{7}{10} {0,3,5,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 29*29=>29 0 : =>29 < : 29*29=>20 s : 29=>29 if : 20*29*29=>29 mod : 29*29=>29 true : =>20 false : =>20 maximal types: {20,29} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{3}{6} {0,3,6,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] joinable by a reduction of rules <[([(if,1)],2),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 19*19=>19 0 : =>19 < : 19*19=>27 s : 15=>19 if : 27*19*19=>19 mod : 19*19=>19 true : =>27 maximal types: {15,19,27} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{3}{6}{7} {0,3,6,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],2),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 20*20=>20 0 : =>20 < : 20*20=>29 s : 16=>20 if : 29*20*20=>20 mod : 20*20=>20 true : =>29 false : =>29 maximal types: {16,20,29} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{3}{6}{10} {0,3,6,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] joinable by a reduction of rules <[([(if,1)],2),([],0)], []> Critical Pair <0, 0> by Rules <5, 3> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 26*26=>26 0 : =>26 < : 26*26=>29 s : 16=>26 if : 29*26*26=>26 mod : 26*26=>26 true : =>29 maximal types: {16,26,29} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{3}{7} {0,3,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 19*19=>19 0 : =>19 < : 19*19=>17 s : 15=>19 if : 17*19*19=>19 mod : 19*19=>19 true : =>17 false : =>17 maximal types: {15,17,19} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{3}{10} {0,3,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 25*25=>25 0 : =>25 < : 25*25=>17 s : 15=>25 if : 17*25*25=>25 mod : 25*25=>25 true : =>17 maximal types: {15,17,25} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{3}{7}{10} {0,3,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 27*27=>27 0 : =>27 < : 27*27=>18 s : 16=>27 if : 18*27*27=>27 mod : 27*27=>27 true : =>18 false : =>18 maximal types: {16,18,27} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{3}{6}{7}{10} {0,3,6,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],2),([],0)], []> Critical Pair <0, 0> by Rules <6, 4> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 28*28=>28 0 : =>28 < : 28*28=>31 s : 17=>28 if : 31*28*28=>28 mod : 28*28=>28 true : =>31 false : =>31 maximal types: {17,28,31} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{3}{5}{6}{7}{10} {0,3,5,6,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair <0, 0> by Rules <7, 5> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 30*30=>30 0 : =>30 < : 30*30=>33 s : 30=>30 if : 33*30*30=>30 mod : 30*30=>30 true : =>33 false : =>33 maximal types: {30,33} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{4} {0,4,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_3)),0,0)> from mod(0,s(?y_3)) Not Confluent Direct Methods: not CR Add {0}{4}{5} {0,4,5,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {0}{4}{5}{6} {0,4,5,6,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 11*11=>11 0 : =>11 < : 11*11=>29 s : 11=>11 if : 29*11*11=>11 mod : 11*11=>11 true : =>29 maximal types: {11,29} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{4}{5}{6}{7} {0,4,5,6,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 12*12=>12 0 : =>12 < : 12*12=>31 s : 12=>12 if : 31*12*12=>12 mod : 12*12=>12 true : =>31 false : =>31 maximal types: {12,31} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{4}{5}{6}{10} {0,4,5,6,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair <0, 0> by Rules <6, 4> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 28*28=>28 0 : =>28 < : 28*28=>31 s : 28=>28 if : 31*28*28=>28 mod : 28*28=>28 true : =>31 maximal types: {28,31} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{4}{5}{7} {0,4,5,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {0}{4}{5}{10} {0,4,5,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {0}{4}{5}{7}{10} {0,4,5,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {0}{4}{6} {0,4,6,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] joinable by a reduction of rules <[([(if,1)],2),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 19*9=>19 0 : =>19 < : 19*9=>27 s : 15=>9 if : 27*19*19=>19 mod : 19*9=>19 true : =>27 maximal types: {9,15,19,27} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{4}{6}{7} {0,4,6,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],2),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 10*10=>10 0 : =>10 < : 10*10=>29 s : 16=>10 if : 29*10*10=>10 mod : 10*10=>10 true : =>29 false : =>29 maximal types: {10,16,29} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{4}{6}{10} {0,4,6,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] joinable by a reduction of rules <[([(if,1)],2),([],0)], []> Critical Pair <0, 0> by Rules <5, 3> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 10*10=>10 0 : =>10 < : 10*10=>29 s : 16=>10 if : 29*10*10=>10 mod : 10*10=>10 true : =>29 maximal types: {10,16,29} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{4}{7} {0,4,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {0}{4}{10} {0,4,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_3)),0,0)> from mod(0,s(?y_3)) Not Confluent Direct Methods: not CR Add {0}{4}{7}{10} {0,4,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {0}{4}{6}{7}{10} {0,4,6,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],2),([],0)], []> Critical Pair <0, 0> by Rules <6, 4> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 28*28=>28 0 : =>28 < : 28*28=>31 s : 17=>28 if : 31*28*28=>28 mod : 28*28=>28 true : =>31 false : =>31 maximal types: {17,28,31} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{5} {0,5,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 9*9=>9 0 : =>9 < : 9*9=>17 s : 9=>9 if : 17*9*9=>9 mod : 9*9=>9 true : =>17 maximal types: {9,17} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{5}{6} {0,5,6,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] joinable by a reduction of rules <[([(if,1)],2),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 10*10=>10 0 : =>10 < : 10*10=>28 s : 10=>10 if : 28*10*10=>10 mod : 10*10=>10 true : =>28 maximal types: {10,28} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{5}{6}{7} {0,5,6,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],2),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 11*11=>11 0 : =>11 < : 11*11=>30 s : 11=>11 if : 30*11*11=>11 mod : 11*11=>11 true : =>30 false : =>30 maximal types: {11,30} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{5}{6}{10} {0,5,6,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] joinable by a reduction of rules <[([(if,1)],2),([],0)], []> Critical Pair <0, 0> by Rules <5, 3> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 27*27=>27 0 : =>27 < : 27*27=>30 s : 27=>27 if : 30*27*27=>27 mod : 27*27=>27 true : =>30 maximal types: {27,30} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{5}{7} {0,5,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 10*10=>10 0 : =>10 < : 10*10=>18 s : 10=>10 if : 18*10*10=>10 mod : 10*10=>10 true : =>18 false : =>18 maximal types: {10,18} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{5}{10} {0,5,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 26*26=>26 0 : =>26 < : 26*26=>18 s : 26=>26 if : 18*26*26=>26 mod : 26*26=>26 true : =>18 maximal types: {18,26} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{5}{7}{10} {0,5,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 28*28=>28 0 : =>28 < : 28*28=>19 s : 28=>28 if : 19*28*28=>28 mod : 28*28=>28 true : =>19 false : =>19 maximal types: {19,28} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{6} {0,6,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] joinable by a reduction of rules <[([(if,1)],1),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 7*8=>7 0 : =>7 < : 7*8=>26 s : 14=>8 if : 26*7*7=>7 mod : 7*8=>7 true : =>26 maximal types: {7,8,14,26} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{6}{7} {0,6,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] joinable by a reduction of rules <[([(if,1)],1),([],0)], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 9*9=>9 0 : =>9 < : 9*9=>28 s : 15=>9 if : 28*9*9=>9 mod : 9*9=>9 true : =>28 false : =>28 maximal types: {9,15,28} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{6}{10} {0,6,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] joinable by a reduction of rules <[([(if,1)],1),([],0)], []> Critical Pair <0, 0> by Rules <4, 2> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 9*9=>9 0 : =>9 < : 9*9=>28 s : 15=>9 if : 28*9*9=>9 mod : 9*9=>9 true : =>28 maximal types: {9,15,28} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{7} {0,7,8,9} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 8*8=>8 0 : =>8 < : 8*8=>16 s : 14=>8 if : 16*8*8=>8 mod : 8*8=>8 true : =>16 false : =>16 maximal types: {8,14,16} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{10} {0,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <2, 1> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 8*8=>8 0 : =>8 < : 8*8=>16 s : 14=>8 if : 16*8*8=>8 mod : 8*8=>8 true : =>16 maximal types: {8,14,16} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{7}{10} {0,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 26*26=>26 0 : =>26 < : 26*26=>17 s : 15=>26 if : 17*26*26=>26 mod : 26*26=>26 true : =>17 false : =>17 maximal types: {15,17,26} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{6}{7}{10} {0,6,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] joinable by a reduction of rules <[([(if,1)],1),([],0)], []> Critical Pair <0, 0> by Rules <5, 3> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 27*27=>27 0 : =>27 < : 27*27=>30 s : 16=>27 if : 30*27*27=>27 mod : 27*27=>27 true : =>30 false : =>30 maximal types: {16,27,30} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{5}{6}{7}{10} {0,5,6,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] joinable by a reduction of rules <[([(if,1)],2),([],0)], []> Critical Pair <0, 0> by Rules <6, 4> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 29*29=>29 0 : =>29 < : 29*29=>32 s : 29=>29 if : 32*29*29=>29 mod : 29*29=>29 true : =>32 false : =>32 maximal types: {29,32} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{4}{5}{6}{7}{10} {0,4,5,6,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] joinable by a reduction of rules <[([(if,1)],3),([],0)], []> Critical Pair <0, 0> by Rules <7, 5> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 30*30=>30 0 : =>30 < : 30*30=>33 s : 30=>30 if : 33*30*30=>30 mod : 30*30=>30 true : =>33 false : =>33 maximal types: {30,33} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{3}{4}{5}{6}{7}{10} {0,3,4,5,6,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] joinable by a reduction of rules <[([(if,1)],4),([],0)], []> Critical Pair <0, 0> by Rules <8, 6> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 31*31=>31 0 : =>31 < : 31*31=>34 s : 31=>31 if : 34*31*31=>31 mod : 31*31=>31 true : =>34 false : =>34 maximal types: {31,34} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {0}{2}{3}{4}{5}{6}{7}{10} {0,2,3,4,5,6,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <8, 7> preceded by [] joinable by a reduction of rules <[([(if,1)],5),([],0)], []> Critical Pair <0, 0> by Rules <9, 7> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 33*33=>33 0 : =>33 < : 33*33=>36 s : 33=>33 if : 36*33*33=>33 mod : 33*33=>33 true : =>36 false : =>36 maximal types: {33,36} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1} {1,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <2, 1> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 6*7=>6 0 : =>6 < : 6*7=>15 s : 13=>7 if : 15*6*6=>6 mod : 6*7=>6 false : =>15 maximal types: {6,7,13,15} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{2} {1,2,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 13*13=>13 0 : =>13 < : 13*13=>17 s : 13=>13 if : 17*13*13=>13 mod : 13*13=>13 false : =>17 maximal types: {13,17} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{2}{3} {1,2,3,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 19*19=>19 0 : =>19 < : 19*19=>18 s : 19=>19 if : 18*19*19=>19 mod : 19*19=>19 false : =>18 maximal types: {18,19} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{2}{3}{4} {1,2,3,4,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {1}{2}{3}{4}{5} {1,2,3,4,5,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {1}{2}{3}{4}{5}{6} {1,2,3,4,5,6,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_7)),0,0)> from mod(0,s(?y_7)) Not Confluent Direct Methods: not CR Add {1}{2}{3}{4}{5}{6}{7} {1,2,3,4,5,6,7,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <8, 7> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_8)),0,0)> from mod(0,s(?y_8)) Not Confluent Direct Methods: not CR Add {1}{2}{3}{4}{5}{6}{10} {1,2,3,4,5,6,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_7)),0,0)> from mod(0,s(?y_7)) Not Confluent Direct Methods: not CR Add {1}{2}{3}{4}{5}{7} {1,2,3,4,5,7,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_7)),0,0)> from mod(0,s(?y_7)) Not Confluent Direct Methods: not CR Add {1}{2}{3}{4}{5}{10} {1,2,3,4,5,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {1}{2}{3}{4}{5}{7}{10} {1,2,3,4,5,7,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_7)),0,0)> from mod(0,s(?y_7)) Not Confluent Direct Methods: not CR Add {1}{2}{3}{4}{6} {1,2,3,4,6,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {1}{2}{3}{4}{6}{7} {1,2,3,4,6,7,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_7)),0,0)> from mod(0,s(?y_7)) Not Confluent Direct Methods: not CR Add {1}{2}{3}{4}{6}{10} {1,2,3,4,6,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {1}{2}{3}{4}{7} {1,2,3,4,7,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {1}{2}{3}{4}{10} {1,2,3,4,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {1}{2}{3}{4}{7}{10} {1,2,3,4,7,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {1}{2}{3}{4}{6}{7}{10} {1,2,3,4,6,7,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_7)),0,0)> from mod(0,s(?y_7)) Not Confluent Direct Methods: not CR Add {1}{2}{3}{5} {1,2,3,5,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 21*21=>21 0 : =>21 < : 21*21=>20 s : 21=>21 if : 20*21*21=>21 mod : 21*21=>21 false : =>20 maximal types: {20,21} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{2}{3}{5}{6} {1,2,3,5,6,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 22*22=>22 0 : =>22 < : 22*22=>21 s : 22=>22 if : 21*22*22=>22 mod : 22*22=>22 true : =>21 false : =>21 maximal types: {21,22} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{2}{3}{5}{6}{7} {1,2,3,5,6,7,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 23*23=>23 0 : =>23 < : 23*23=>33 s : 23=>23 if : 33*23*23=>23 mod : 23*23=>23 true : =>33 false : =>33 maximal types: {23,33} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{2}{3}{5}{6}{10} {1,2,3,5,6,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 31*31=>31 0 : =>31 < : 31*31=>22 s : 31=>31 if : 22*31*31=>31 mod : 31*31=>31 true : =>22 false : =>22 maximal types: {22,31} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{2}{3}{5}{7} {1,2,3,5,7,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 22*22=>22 0 : =>22 < : 22*22=>31 s : 22=>22 if : 31*22*22=>22 mod : 22*22=>22 false : =>31 maximal types: {22,31} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{2}{3}{5}{10} {1,2,3,5,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 29*29=>29 0 : =>29 < : 29*29=>21 s : 29=>29 if : 21*29*29=>29 mod : 29*29=>29 false : =>21 maximal types: {21,29} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{2}{3}{5}{7}{10} {1,2,3,5,7,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 30*30=>30 0 : =>30 < : 30*30=>33 s : 30=>30 if : 33*30*30=>30 mod : 30*30=>30 false : =>33 maximal types: {30,33} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{2}{3}{6} {1,2,3,6,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 20*20=>20 0 : =>20 < : 20*20=>19 s : 20=>20 if : 19*20*20=>20 mod : 20*20=>20 true : =>19 false : =>19 maximal types: {19,20} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{2}{3}{6}{7} {1,2,3,6,7,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 21*21=>21 0 : =>21 < : 21*21=>31 s : 21=>21 if : 31*21*21=>21 mod : 21*21=>21 true : =>31 false : =>31 maximal types: {21,31} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{2}{3}{6}{10} {1,2,3,6,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 29*29=>29 0 : =>29 < : 29*29=>20 s : 29=>29 if : 20*29*29=>29 mod : 29*29=>29 true : =>20 false : =>20 maximal types: {20,29} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{2}{3}{7} {1,2,3,7,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 20*20=>20 0 : =>20 < : 20*20=>29 s : 20=>20 if : 29*20*20=>20 mod : 20*20=>20 false : =>29 maximal types: {20,29} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{2}{3}{10} {1,2,3,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 27*27=>27 0 : =>27 < : 27*27=>19 s : 27=>27 if : 19*27*27=>27 mod : 27*27=>27 false : =>19 maximal types: {19,27} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{2}{3}{7}{10} {1,2,3,7,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 28*28=>28 0 : =>28 < : 28*28=>31 s : 28=>28 if : 31*28*28=>28 mod : 28*28=>28 false : =>31 maximal types: {28,31} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{2}{3}{6}{7}{10} {1,2,3,6,7,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 30*30=>30 0 : =>30 < : 30*30=>33 s : 30=>30 if : 33*30*30=>30 mod : 30*30=>30 true : =>33 false : =>33 maximal types: {30,33} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{2}{3}{5}{6}{7}{10} {1,2,3,5,6,7,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 32*32=>32 0 : =>32 < : 32*32=>35 s : 32=>32 if : 35*32*32=>32 mod : 32*32=>32 true : =>35 false : =>35 maximal types: {32,35} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{2}{4} {1,2,4,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {1}{2}{4}{5} {1,2,4,5,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {1}{2}{4}{5}{6} {1,2,4,5,6,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {1}{2}{4}{5}{6}{7} {1,2,4,5,6,7,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_7)),0,0)> from mod(0,s(?y_7)) Not Confluent Direct Methods: not CR Add {1}{2}{4}{5}{6}{10} {1,2,4,5,6,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {1}{2}{4}{5}{7} {1,2,4,5,7,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {1}{2}{4}{5}{10} {1,2,4,5,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {1}{2}{4}{5}{7}{10} {1,2,4,5,7,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {1}{2}{4}{6} {1,2,4,6,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {1}{2}{4}{6}{7} {1,2,4,6,7,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {1}{2}{4}{6}{10} {1,2,4,6,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {1}{2}{4}{7} {1,2,4,7,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {1}{2}{4}{10} {1,2,4,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {1}{2}{4}{7}{10} {1,2,4,7,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {1}{2}{4}{6}{7}{10} {1,2,4,6,7,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {1}{2}{5} {1,2,5,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 20*20=>20 0 : =>20 < : 20*20=>19 s : 20=>20 if : 19*20*20=>20 mod : 20*20=>20 false : =>19 maximal types: {19,20} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{2}{5}{6} {1,2,5,6,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 21*21=>21 0 : =>21 < : 21*21=>20 s : 21=>21 if : 20*21*21=>21 mod : 21*21=>21 true : =>20 false : =>20 maximal types: {20,21} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{2}{5}{6}{7} {1,2,5,6,7,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 22*22=>22 0 : =>22 < : 22*22=>32 s : 22=>22 if : 32*22*22=>22 mod : 22*22=>22 true : =>32 false : =>32 maximal types: {22,32} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{2}{5}{6}{10} {1,2,5,6,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 30*30=>30 0 : =>30 < : 30*30=>21 s : 30=>30 if : 21*30*30=>30 mod : 30*30=>30 true : =>21 false : =>21 maximal types: {21,30} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{2}{5}{7} {1,2,5,7,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 21*21=>21 0 : =>21 < : 21*21=>30 s : 21=>21 if : 30*21*21=>21 mod : 21*21=>21 false : =>30 maximal types: {21,30} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{2}{5}{10} {1,2,5,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 28*28=>28 0 : =>28 < : 28*28=>20 s : 28=>28 if : 20*28*28=>28 mod : 28*28=>28 false : =>20 maximal types: {20,28} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{2}{5}{7}{10} {1,2,5,7,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 29*29=>29 0 : =>29 < : 29*29=>32 s : 29=>29 if : 32*29*29=>29 mod : 29*29=>29 false : =>32 maximal types: {29,32} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{2}{6} {1,2,6,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 23*23=>23 0 : =>23 < : 23*23=>18 s : 23=>23 if : 18*23*23=>23 mod : 23*23=>23 true : =>18 false : =>18 maximal types: {18,23} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{2}{6}{7} {1,2,6,7,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 20*20=>20 0 : =>20 < : 20*20=>30 s : 20=>20 if : 30*20*20=>20 mod : 20*20=>20 true : =>30 false : =>30 maximal types: {20,30} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{2}{6}{10} {1,2,6,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 28*28=>28 0 : =>28 < : 28*28=>19 s : 28=>28 if : 19*28*28=>28 mod : 28*28=>28 true : =>19 false : =>19 maximal types: {19,28} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{2}{7} {1,2,7,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 19*19=>19 0 : =>19 < : 19*19=>28 s : 19=>19 if : 28*19*19=>19 mod : 19*19=>19 false : =>28 maximal types: {19,28} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{2}{10} {1,2,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 26*26=>26 0 : =>26 < : 26*26=>18 s : 26=>26 if : 18*26*26=>26 mod : 26*26=>26 false : =>18 maximal types: {18,26} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{2}{7}{10} {1,2,7,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 27*27=>27 0 : =>27 < : 27*27=>30 s : 27=>27 if : 30*27*27=>27 mod : 27*27=>27 false : =>30 maximal types: {27,30} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{2}{6}{7}{10} {1,2,6,7,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 29*29=>29 0 : =>29 < : 29*29=>32 s : 29=>29 if : 32*29*29=>29 mod : 29*29=>29 true : =>32 false : =>32 maximal types: {29,32} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{2}{5}{6}{7}{10} {1,2,5,6,7,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 31*31=>31 0 : =>31 < : 31*31=>34 s : 31=>31 if : 34*31*31=>31 mod : 31*31=>31 true : =>34 false : =>34 maximal types: {31,34} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{2}{4}{5}{6}{7}{10} {1,2,4,5,6,7,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_7)),0,0)> from mod(0,s(?y_7)) Not Confluent Direct Methods: not CR Add {1}{3} {1,3,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 17*17=>17 0 : =>17 < : 17*17=>16 s : 14=>17 if : 16*17*17=>17 mod : 17*17=>17 false : =>16 maximal types: {14,16,17} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{3}{4} {1,3,4,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {1}{3}{4}{5} {1,3,4,5,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {1}{3}{4}{5}{6} {1,3,4,5,6,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {1}{3}{4}{5}{6}{7} {1,3,4,5,6,7,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_7)),0,0)> from mod(0,s(?y_7)) Not Confluent Direct Methods: not CR Add {1}{3}{4}{5}{6}{10} {1,3,4,5,6,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {1}{3}{4}{5}{7} {1,3,4,5,7,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {1}{3}{4}{5}{10} {1,3,4,5,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {1}{3}{4}{5}{7}{10} {1,3,4,5,7,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {1}{3}{4}{6} {1,3,4,6,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {1}{3}{4}{6}{7} {1,3,4,6,7,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {1}{3}{4}{6}{10} {1,3,4,6,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {1}{3}{4}{7} {1,3,4,7,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {1}{3}{4}{10} {1,3,4,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {1}{3}{4}{7}{10} {1,3,4,7,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {1}{3}{4}{6}{7}{10} {1,3,4,6,7,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {1}{3}{5} {1,3,5,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 19*19=>19 0 : =>19 < : 19*19=>18 s : 19=>19 if : 18*19*19=>19 mod : 19*19=>19 false : =>18 maximal types: {18,19} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{3}{5}{6} {1,3,5,6,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 20*20=>20 0 : =>20 < : 20*20=>19 s : 20=>20 if : 19*20*20=>20 mod : 20*20=>20 true : =>19 false : =>19 maximal types: {19,20} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{3}{5}{6}{7} {1,3,5,6,7,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 21*21=>21 0 : =>21 < : 21*21=>31 s : 21=>21 if : 31*21*21=>21 mod : 21*21=>21 true : =>31 false : =>31 maximal types: {21,31} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{3}{5}{6}{10} {1,3,5,6,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 29*29=>29 0 : =>29 < : 29*29=>20 s : 29=>29 if : 20*29*29=>29 mod : 29*29=>29 true : =>20 false : =>20 maximal types: {20,29} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{3}{5}{7} {1,3,5,7,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 20*20=>20 0 : =>20 < : 20*20=>29 s : 20=>20 if : 29*20*20=>20 mod : 20*20=>20 false : =>29 maximal types: {20,29} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{3}{5}{10} {1,3,5,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 27*27=>27 0 : =>27 < : 27*27=>19 s : 27=>27 if : 19*27*27=>27 mod : 27*27=>27 false : =>19 maximal types: {19,27} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{3}{5}{7}{10} {1,3,5,7,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 28*28=>28 0 : =>28 < : 28*28=>31 s : 28=>28 if : 31*28*28=>28 mod : 28*28=>28 false : =>31 maximal types: {28,31} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{3}{6} {1,3,6,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 18*18=>18 0 : =>18 < : 18*18=>17 s : 15=>18 if : 17*18*18=>18 mod : 18*18=>18 true : =>17 false : =>17 maximal types: {15,17,18} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{3}{6}{7} {1,3,6,7,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 19*19=>19 0 : =>19 < : 19*19=>29 s : 16=>19 if : 29*19*19=>19 mod : 19*19=>19 true : =>29 false : =>29 maximal types: {16,19,29} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{3}{6}{10} {1,3,6,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 27*27=>27 0 : =>27 < : 27*27=>18 s : 16=>27 if : 18*27*27=>27 mod : 27*27=>27 true : =>18 false : =>18 maximal types: {16,18,27} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{3}{7} {1,3,7,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 18*18=>18 0 : =>18 < : 18*18=>27 s : 15=>18 if : 27*18*18=>18 mod : 18*18=>18 false : =>27 maximal types: {15,18,27} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{3}{10} {1,3,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 25*25=>25 0 : =>25 < : 25*25=>17 s : 15=>25 if : 17*25*25=>25 mod : 25*25=>25 false : =>17 maximal types: {15,17,25} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{3}{7}{10} {1,3,7,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 26*26=>26 0 : =>26 < : 26*26=>29 s : 16=>26 if : 29*26*26=>26 mod : 26*26=>26 false : =>29 maximal types: {16,26,29} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{3}{6}{7}{10} {1,3,6,7,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 28*28=>28 0 : =>28 < : 28*28=>31 s : 17=>28 if : 31*28*28=>28 mod : 28*28=>28 true : =>31 false : =>31 maximal types: {17,28,31} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{3}{5}{6}{7}{10} {1,3,5,6,7,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 30*30=>30 0 : =>30 < : 30*30=>33 s : 30=>30 if : 33*30*30=>30 mod : 30*30=>30 true : =>33 false : =>33 maximal types: {30,33} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{4} {1,4,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_3)),0,0)> from mod(0,s(?y_3)) Not Confluent Direct Methods: not CR Add {1}{4}{5} {1,4,5,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {1}{4}{5}{6} {1,4,5,6,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {1}{4}{5}{6}{7} {1,4,5,6,7,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {1}{4}{5}{6}{10} {1,4,5,6,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {1}{4}{5}{7} {1,4,5,7,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {1}{4}{5}{10} {1,4,5,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {1}{4}{5}{7}{10} {1,4,5,7,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {1}{4}{6} {1,4,6,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {1}{4}{6}{7} {1,4,6,7,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {1}{4}{6}{10} {1,4,6,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {1}{4}{7} {1,4,7,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {1}{4}{10} {1,4,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_3)),0,0)> from mod(0,s(?y_3)) Not Confluent Direct Methods: not CR Add {1}{4}{7}{10} {1,4,7,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {1}{4}{6}{7}{10} {1,4,6,7,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {1}{5} {1,5,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 9*9=>9 0 : =>9 < : 9*9=>17 s : 9=>9 if : 17*9*9=>9 mod : 9*9=>9 false : =>17 maximal types: {9,17} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{5}{6} {1,5,6,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 10*10=>10 0 : =>10 < : 10*10=>18 s : 10=>10 if : 18*10*10=>10 mod : 10*10=>10 true : =>18 false : =>18 maximal types: {10,18} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{5}{6}{7} {1,5,6,7,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 11*11=>11 0 : =>11 < : 11*11=>30 s : 11=>11 if : 30*11*11=>11 mod : 11*11=>11 true : =>30 false : =>30 maximal types: {11,30} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{5}{6}{10} {1,5,6,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 28*28=>28 0 : =>28 < : 28*28=>19 s : 28=>28 if : 19*28*28=>28 mod : 28*28=>28 true : =>19 false : =>19 maximal types: {19,28} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{5}{7} {1,5,7,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 10*10=>10 0 : =>10 < : 10*10=>28 s : 10=>10 if : 28*10*10=>10 mod : 10*10=>10 false : =>28 maximal types: {10,28} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{5}{10} {1,5,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 26*26=>26 0 : =>26 < : 26*26=>18 s : 26=>26 if : 18*26*26=>26 mod : 26*26=>26 false : =>18 maximal types: {18,26} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{5}{7}{10} {1,5,7,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 27*27=>27 0 : =>27 < : 27*27=>30 s : 27=>27 if : 30*27*27=>27 mod : 27*27=>27 false : =>30 maximal types: {27,30} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{6} {1,6,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 7*8=>7 0 : =>7 < : 7*8=>16 s : 14=>8 if : 16*7*7=>7 mod : 7*8=>7 true : =>16 false : =>16 maximal types: {7,8,14,16} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{6}{7} {1,6,7,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 9*9=>9 0 : =>9 < : 9*9=>28 s : 15=>9 if : 28*9*9=>9 mod : 9*9=>9 true : =>28 false : =>28 maximal types: {9,15,28} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{6}{10} {1,6,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 9*9=>9 0 : =>9 < : 9*9=>17 s : 15=>9 if : 17*9*9=>9 mod : 9*9=>9 true : =>17 false : =>17 maximal types: {9,15,17} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{7} {1,7,8,9} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Sort Assignment: - : 8*8=>8 0 : =>8 < : 8*8=>26 s : 14=>8 if : 26*8*8=>8 mod : 8*8=>8 false : =>26 maximal types: {8,14,26} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{10} {1,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <2, 1> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 8*8=>8 0 : =>8 < : 8*8=>16 s : 14=>8 if : 16*8*8=>8 mod : 8*8=>8 false : =>16 maximal types: {8,14,16} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{7}{10} {1,7,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 25*25=>25 0 : =>25 < : 25*25=>28 s : 15=>25 if : 28*25*25=>25 mod : 25*25=>25 false : =>28 maximal types: {15,25,28} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{6}{7}{10} {1,6,7,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 27*27=>27 0 : =>27 < : 27*27=>30 s : 16=>27 if : 30*27*27=>27 mod : 27*27=>27 true : =>30 false : =>30 maximal types: {16,27,30} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{5}{6}{7}{10} {1,5,6,7,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 29*29=>29 0 : =>29 < : 29*29=>32 s : 29=>29 if : 32*29*29=>29 mod : 29*29=>29 true : =>32 false : =>32 maximal types: {29,32} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(false,?x,?y) -> ?y, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Add {1}{4}{5}{6}{7}{10} {1,4,5,6,7,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {1}{3}{4}{5}{6}{7}{10} {1,3,4,5,6,7,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_7)),0,0)> from mod(0,s(?y_7)) Not Confluent Direct Methods: not CR Add {2} {2,8,9} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <2, 1> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_2)),0,if(<(-(0,s(?y_2)),s(?y_2)),-(0,s(?y_2)),if(<(-(-(0,s(?y_2)),s(?y_2)),s(?y_2)),-(-(0,s(?y_2)),s(?y_2)),mod(-(-(-(0,s(?y_2)),s(?y_2)),s(?y_2)),s(?y_2)))))> from mod(0,s(?y_2)) Not Confluent Direct Methods: not CR Add {2}{3} {2,3,8,9} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_3)),0,if(<(-(0,s(?y_3)),s(?y_3)),-(0,s(?y_3)),if(<(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),-(-(0,s(?y_3)),s(?y_3)),mod(-(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),s(?y_3)))))> from mod(0,s(?y_3)) Not Confluent Direct Methods: not CR Add {2}{3}{4} {2,3,4,8,9} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {2}{3}{4}{5} {2,3,4,5,8,9} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {2}{3}{4}{5}{6} {2,3,4,5,6,8,9} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {2}{3}{4}{5}{6}{7} {2,3,4,5,6,7,8,9} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_7)),0,0)> from mod(0,s(?y_7)) Not Confluent Direct Methods: not CR Add {2}{3}{4}{5}{6}{10} {2,3,4,5,6,8,9,10} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {2}{3}{4}{5}{7} {2,3,4,5,7,8,9} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {2}{3}{4}{5}{10} {2,3,4,5,8,9,10} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {2}{3}{4}{5}{7}{10} {2,3,4,5,7,8,9,10} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {2}{3}{4}{6} {2,3,4,6,8,9} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {2}{3}{4}{6}{7} {2,3,4,6,7,8,9} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {2}{3}{4}{6}{10} {2,3,4,6,8,9,10} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {2}{3}{4}{7} {2,3,4,7,8,9} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {2}{3}{4}{10} {2,3,4,8,9,10} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {2}{3}{4}{7}{10} {2,3,4,7,8,9,10} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {2}{3}{4}{6}{7}{10} {2,3,4,6,7,8,9,10} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {2}{3}{5} {2,3,5,8,9} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,if(<(-(0,s(?y_4)),s(?y_4)),-(0,s(?y_4)),if(<(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),-(-(0,s(?y_4)),s(?y_4)),mod(-(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),s(?y_4)))))> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {2}{3}{5}{6} {2,3,5,6,8,9} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,if(<(-(0,s(?y_5)),s(?y_5)),-(0,s(?y_5)),if(<(-(-(0,s(?y_5)),s(?y_5)),s(?y_5)),-(-(0,s(?y_5)),s(?y_5)),mod(-(-(-(0,s(?y_5)),s(?y_5)),s(?y_5)),s(?y_5)))))> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {2}{3}{5}{6}{7} {2,3,5,6,7,8,9} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,if(<(-(0,s(?y_6)),s(?y_6)),-(0,s(?y_6)),if(<(-(-(0,s(?y_6)),s(?y_6)),s(?y_6)),-(-(0,s(?y_6)),s(?y_6)),mod(-(-(-(0,s(?y_6)),s(?y_6)),s(?y_6)),s(?y_6)))))> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {2}{3}{5}{6}{10} {2,3,5,6,8,9,10} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,if(<(-(0,s(?y_5)),s(?y_5)),-(0,s(?y_5)),if(<(-(-(0,s(?y_5)),s(?y_5)),s(?y_5)),-(-(0,s(?y_5)),s(?y_5)),mod(-(-(-(0,s(?y_5)),s(?y_5)),s(?y_5)),s(?y_5)))))> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {2}{3}{5}{7} {2,3,5,7,8,9} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,if(<(-(0,s(?y_5)),s(?y_5)),-(0,s(?y_5)),if(<(-(-(0,s(?y_5)),s(?y_5)),s(?y_5)),-(-(0,s(?y_5)),s(?y_5)),mod(-(-(-(0,s(?y_5)),s(?y_5)),s(?y_5)),s(?y_5)))))> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {2}{3}{5}{10} {2,3,5,8,9,10} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,if(<(-(0,s(?y_4)),s(?y_4)),-(0,s(?y_4)),if(<(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),-(-(0,s(?y_4)),s(?y_4)),mod(-(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),s(?y_4)))))> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {2}{3}{5}{7}{10} {2,3,5,7,8,9,10} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,if(<(-(0,s(?y_5)),s(?y_5)),-(0,s(?y_5)),if(<(-(-(0,s(?y_5)),s(?y_5)),s(?y_5)),-(-(0,s(?y_5)),s(?y_5)),mod(-(-(-(0,s(?y_5)),s(?y_5)),s(?y_5)),s(?y_5)))))> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {2}{3}{6} {2,3,6,8,9} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,if(<(-(0,s(?y_4)),s(?y_4)),-(0,s(?y_4)),if(<(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),-(-(0,s(?y_4)),s(?y_4)),mod(-(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),s(?y_4)))))> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {2}{3}{6}{7} {2,3,6,7,8,9} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,if(<(-(0,s(?y_5)),s(?y_5)),-(0,s(?y_5)),if(<(-(-(0,s(?y_5)),s(?y_5)),s(?y_5)),-(-(0,s(?y_5)),s(?y_5)),mod(-(-(-(0,s(?y_5)),s(?y_5)),s(?y_5)),s(?y_5)))))> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {2}{3}{6}{10} {2,3,6,8,9,10} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,if(<(-(0,s(?y_4)),s(?y_4)),-(0,s(?y_4)),if(<(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),-(-(0,s(?y_4)),s(?y_4)),mod(-(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),s(?y_4)))))> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {2}{3}{7} {2,3,7,8,9} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,if(<(-(0,s(?y_4)),s(?y_4)),-(0,s(?y_4)),if(<(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),-(-(0,s(?y_4)),s(?y_4)),mod(-(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),s(?y_4)))))> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {2}{3}{10} {2,3,8,9,10} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_3)),0,if(<(-(0,s(?y_3)),s(?y_3)),-(0,s(?y_3)),if(<(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),-(-(0,s(?y_3)),s(?y_3)),mod(-(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),s(?y_3)))))> from mod(0,s(?y_3)) Not Confluent Direct Methods: not CR Add {2}{3}{7}{10} {2,3,7,8,9,10} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,if(<(-(0,s(?y_4)),s(?y_4)),-(0,s(?y_4)),if(<(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),-(-(0,s(?y_4)),s(?y_4)),mod(-(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),s(?y_4)))))> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {2}{3}{6}{7}{10} {2,3,6,7,8,9,10} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,if(<(-(0,s(?y_5)),s(?y_5)),-(0,s(?y_5)),if(<(-(-(0,s(?y_5)),s(?y_5)),s(?y_5)),-(-(0,s(?y_5)),s(?y_5)),mod(-(-(-(0,s(?y_5)),s(?y_5)),s(?y_5)),s(?y_5)))))> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {2}{3}{5}{6}{7}{10} {2,3,5,6,7,8,9,10} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,if(<(-(0,s(?y_6)),s(?y_6)),-(0,s(?y_6)),if(<(-(-(0,s(?y_6)),s(?y_6)),s(?y_6)),-(-(0,s(?y_6)),s(?y_6)),mod(-(-(-(0,s(?y_6)),s(?y_6)),s(?y_6)),s(?y_6)))))> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {2}{4} {2,4,8,9} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_3)),0,0)> from mod(0,s(?y_3)) Not Confluent Direct Methods: not CR Add {2}{4}{5} {2,4,5,8,9} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {2}{4}{5}{6} {2,4,5,6,8,9} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {2}{4}{5}{6}{7} {2,4,5,6,7,8,9} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {2}{4}{5}{6}{10} {2,4,5,6,8,9,10} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {2}{4}{5}{7} {2,4,5,7,8,9} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {2}{4}{5}{10} {2,4,5,8,9,10} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {2}{4}{5}{7}{10} {2,4,5,7,8,9,10} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {2}{4}{6} {2,4,6,8,9} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {2}{4}{6}{7} {2,4,6,7,8,9} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {2}{4}{6}{10} {2,4,6,8,9,10} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {2}{4}{7} {2,4,7,8,9} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {2}{4}{10} {2,4,8,9,10} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_3)),0,0)> from mod(0,s(?y_3)) Not Confluent Direct Methods: not CR Add {2}{4}{7}{10} {2,4,7,8,9,10} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {2}{4}{6}{7}{10} {2,4,6,7,8,9,10} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {2}{5} {2,5,8,9} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_3)),0,if(<(-(0,s(?y_3)),s(?y_3)),-(0,s(?y_3)),if(<(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),-(-(0,s(?y_3)),s(?y_3)),mod(-(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),s(?y_3)))))> from mod(0,s(?y_3)) Not Confluent Direct Methods: not CR Add {2}{5}{6} {2,5,6,8,9} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,if(<(-(0,s(?y_4)),s(?y_4)),-(0,s(?y_4)),if(<(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),-(-(0,s(?y_4)),s(?y_4)),mod(-(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),s(?y_4)))))> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {2}{5}{6}{7} {2,5,6,7,8,9} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,if(<(-(0,s(?y_5)),s(?y_5)),-(0,s(?y_5)),if(<(-(-(0,s(?y_5)),s(?y_5)),s(?y_5)),-(-(0,s(?y_5)),s(?y_5)),mod(-(-(-(0,s(?y_5)),s(?y_5)),s(?y_5)),s(?y_5)))))> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {2}{5}{6}{10} {2,5,6,8,9,10} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,if(<(-(0,s(?y_4)),s(?y_4)),-(0,s(?y_4)),if(<(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),-(-(0,s(?y_4)),s(?y_4)),mod(-(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),s(?y_4)))))> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {2}{5}{7} {2,5,7,8,9} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,if(<(-(0,s(?y_4)),s(?y_4)),-(0,s(?y_4)),if(<(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),-(-(0,s(?y_4)),s(?y_4)),mod(-(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),s(?y_4)))))> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {2}{5}{10} {2,5,8,9,10} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_3)),0,if(<(-(0,s(?y_3)),s(?y_3)),-(0,s(?y_3)),if(<(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),-(-(0,s(?y_3)),s(?y_3)),mod(-(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),s(?y_3)))))> from mod(0,s(?y_3)) Not Confluent Direct Methods: not CR Add {2}{5}{7}{10} {2,5,7,8,9,10} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,if(<(-(0,s(?y_4)),s(?y_4)),-(0,s(?y_4)),if(<(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),-(-(0,s(?y_4)),s(?y_4)),mod(-(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),s(?y_4)))))> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {2}{6} {2,6,8,9} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_3)),0,if(<(-(0,s(?y_3)),s(?y_3)),-(0,s(?y_3)),if(<(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),-(-(0,s(?y_3)),s(?y_3)),mod(-(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),s(?y_3)))))> from mod(0,s(?y_3)) Not Confluent Direct Methods: not CR Add {2}{6}{7} {2,6,7,8,9} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,if(<(-(0,s(?y_4)),s(?y_4)),-(0,s(?y_4)),if(<(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),-(-(0,s(?y_4)),s(?y_4)),mod(-(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),s(?y_4)))))> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {2}{6}{10} {2,6,8,9,10} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_3)),0,if(<(-(0,s(?y_3)),s(?y_3)),-(0,s(?y_3)),if(<(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),-(-(0,s(?y_3)),s(?y_3)),mod(-(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),s(?y_3)))))> from mod(0,s(?y_3)) Not Confluent Direct Methods: not CR Add {2}{7} {2,7,8,9} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_3)),0,if(<(-(0,s(?y_3)),s(?y_3)),-(0,s(?y_3)),if(<(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),-(-(0,s(?y_3)),s(?y_3)),mod(-(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),s(?y_3)))))> from mod(0,s(?y_3)) Not Confluent Direct Methods: not CR Add {2}{10} {2,8,9,10} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <2, 1> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_2)),0,if(<(-(0,s(?y_2)),s(?y_2)),-(0,s(?y_2)),if(<(-(-(0,s(?y_2)),s(?y_2)),s(?y_2)),-(-(0,s(?y_2)),s(?y_2)),mod(-(-(-(0,s(?y_2)),s(?y_2)),s(?y_2)),s(?y_2)))))> from mod(0,s(?y_2)) Not Confluent Direct Methods: not CR Add {2}{7}{10} {2,7,8,9,10} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_3)),0,if(<(-(0,s(?y_3)),s(?y_3)),-(0,s(?y_3)),if(<(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),-(-(0,s(?y_3)),s(?y_3)),mod(-(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),s(?y_3)))))> from mod(0,s(?y_3)) Not Confluent Direct Methods: not CR Add {2}{6}{7}{10} {2,6,7,8,9,10} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,if(<(-(0,s(?y_4)),s(?y_4)),-(0,s(?y_4)),if(<(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),-(-(0,s(?y_4)),s(?y_4)),mod(-(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),s(?y_4)))))> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {2}{5}{6}{7}{10} {2,5,6,7,8,9,10} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,if(<(-(0,s(?y_5)),s(?y_5)),-(0,s(?y_5)),if(<(-(-(0,s(?y_5)),s(?y_5)),s(?y_5)),-(-(0,s(?y_5)),s(?y_5)),mod(-(-(-(0,s(?y_5)),s(?y_5)),s(?y_5)),s(?y_5)))))> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {2}{4}{5}{6}{7}{10} {2,4,5,6,7,8,9,10} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {3} {3,8,9} (cm)Rewrite Rules: [ -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <2, 1> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_2)),0,if(<(-(0,s(?y_2)),s(?y_2)),-(0,s(?y_2)),if(<(-(-(0,s(?y_2)),s(?y_2)),s(?y_2)),-(-(0,s(?y_2)),s(?y_2)),mod(-(-(-(0,s(?y_2)),s(?y_2)),s(?y_2)),s(?y_2)))))> from mod(0,s(?y_2)) Not Confluent Direct Methods: not CR Add {3}{4} {3,4,8,9} (cm)Rewrite Rules: [ -(?x,0) -> ?x, -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <1, 0> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_3)),0,0)> from mod(0,s(?y_3)) Not Confluent Direct Methods: not CR Add {3}{4}{5} {3,4,5,8,9} (cm)Rewrite Rules: [ -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <1, 0> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {3}{4}{5}{6} {3,4,5,6,8,9} (cm)Rewrite Rules: [ -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <1, 0> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {3}{4}{5}{6}{7} {3,4,5,6,7,8,9} (cm)Rewrite Rules: [ -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <1, 0> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {3}{4}{5}{6}{10} {3,4,5,6,8,9,10} (cm)Rewrite Rules: [ -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <1, 0> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {3}{4}{5}{7} {3,4,5,7,8,9} (cm)Rewrite Rules: [ -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <1, 0> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {3}{4}{5}{10} {3,4,5,8,9,10} (cm)Rewrite Rules: [ -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <1, 0> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {3}{4}{5}{7}{10} {3,4,5,7,8,9,10} (cm)Rewrite Rules: [ -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <1, 0> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {3}{4}{6} {3,4,6,8,9} (cm)Rewrite Rules: [ -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <1, 0> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {3}{4}{6}{7} {3,4,6,7,8,9} (cm)Rewrite Rules: [ -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <1, 0> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {3}{4}{6}{10} {3,4,6,8,9,10} (cm)Rewrite Rules: [ -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <1, 0> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {3}{4}{7} {3,4,7,8,9} (cm)Rewrite Rules: [ -(?x,0) -> ?x, -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <1, 0> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {3}{4}{10} {3,4,8,9,10} (cm)Rewrite Rules: [ -(?x,0) -> ?x, -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <1, 0> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_3)),0,0)> from mod(0,s(?y_3)) Not Confluent Direct Methods: not CR Add {3}{4}{7}{10} {3,4,7,8,9,10} (cm)Rewrite Rules: [ -(?x,0) -> ?x, -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <1, 0> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {3}{4}{6}{7}{10} {3,4,6,7,8,9,10} (cm)Rewrite Rules: [ -(?x,0) -> ?x, -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <1, 0> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {3}{5} {3,5,8,9} (cm)Rewrite Rules: [ -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_3)),0,if(<(-(0,s(?y_3)),s(?y_3)),-(0,s(?y_3)),if(<(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),-(-(0,s(?y_3)),s(?y_3)),mod(-(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),s(?y_3)))))> from mod(0,s(?y_3)) Not Confluent Direct Methods: not CR Add {3}{5}{6} {3,5,6,8,9} (cm)Rewrite Rules: [ -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,if(<(-(0,s(?y_4)),s(?y_4)),-(0,s(?y_4)),if(<(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),-(-(0,s(?y_4)),s(?y_4)),mod(-(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),s(?y_4)))))> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {3}{5}{6}{7} {3,5,6,7,8,9} (cm)Rewrite Rules: [ -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,if(<(-(0,s(?y_5)),s(?y_5)),-(0,s(?y_5)),if(<(-(-(0,s(?y_5)),s(?y_5)),s(?y_5)),-(-(0,s(?y_5)),s(?y_5)),mod(-(-(-(0,s(?y_5)),s(?y_5)),s(?y_5)),s(?y_5)))))> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {3}{5}{6}{10} {3,5,6,8,9,10} (cm)Rewrite Rules: [ -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,if(<(-(0,s(?y_4)),s(?y_4)),-(0,s(?y_4)),if(<(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),-(-(0,s(?y_4)),s(?y_4)),mod(-(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),s(?y_4)))))> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {3}{5}{7} {3,5,7,8,9} (cm)Rewrite Rules: [ -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,if(<(-(0,s(?y_4)),s(?y_4)),-(0,s(?y_4)),if(<(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),-(-(0,s(?y_4)),s(?y_4)),mod(-(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),s(?y_4)))))> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {3}{5}{10} {3,5,8,9,10} (cm)Rewrite Rules: [ -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_3)),0,if(<(-(0,s(?y_3)),s(?y_3)),-(0,s(?y_3)),if(<(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),-(-(0,s(?y_3)),s(?y_3)),mod(-(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),s(?y_3)))))> from mod(0,s(?y_3)) Not Confluent Direct Methods: not CR Add {3}{5}{7}{10} {3,5,7,8,9,10} (cm)Rewrite Rules: [ -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,if(<(-(0,s(?y_4)),s(?y_4)),-(0,s(?y_4)),if(<(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),-(-(0,s(?y_4)),s(?y_4)),mod(-(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),s(?y_4)))))> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {3}{6} {3,6,8,9} (cm)Rewrite Rules: [ -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_3)),0,if(<(-(0,s(?y_3)),s(?y_3)),-(0,s(?y_3)),if(<(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),-(-(0,s(?y_3)),s(?y_3)),mod(-(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),s(?y_3)))))> from mod(0,s(?y_3)) Not Confluent Direct Methods: not CR Add {3}{6}{7} {3,6,7,8,9} (cm)Rewrite Rules: [ -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,if(<(-(0,s(?y_4)),s(?y_4)),-(0,s(?y_4)),if(<(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),-(-(0,s(?y_4)),s(?y_4)),mod(-(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),s(?y_4)))))> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {3}{6}{10} {3,6,8,9,10} (cm)Rewrite Rules: [ -(?x,0) -> ?x, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_3)),0,if(<(-(0,s(?y_3)),s(?y_3)),-(0,s(?y_3)),if(<(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),-(-(0,s(?y_3)),s(?y_3)),mod(-(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),s(?y_3)))))> from mod(0,s(?y_3)) Not Confluent Direct Methods: not CR Add {3}{7} {3,7,8,9} (cm)Rewrite Rules: [ -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_3)),0,if(<(-(0,s(?y_3)),s(?y_3)),-(0,s(?y_3)),if(<(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),-(-(0,s(?y_3)),s(?y_3)),mod(-(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),s(?y_3)))))> from mod(0,s(?y_3)) Not Confluent Direct Methods: not CR Add {3}{10} {3,8,9,10} (cm)Rewrite Rules: [ -(?x,0) -> ?x, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <2, 1> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_2)),0,if(<(-(0,s(?y_2)),s(?y_2)),-(0,s(?y_2)),if(<(-(-(0,s(?y_2)),s(?y_2)),s(?y_2)),-(-(0,s(?y_2)),s(?y_2)),mod(-(-(-(0,s(?y_2)),s(?y_2)),s(?y_2)),s(?y_2)))))> from mod(0,s(?y_2)) Not Confluent Direct Methods: not CR Add {3}{7}{10} {3,7,8,9,10} (cm)Rewrite Rules: [ -(?x,0) -> ?x, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_3)),0,if(<(-(0,s(?y_3)),s(?y_3)),-(0,s(?y_3)),if(<(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),-(-(0,s(?y_3)),s(?y_3)),mod(-(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),s(?y_3)))))> from mod(0,s(?y_3)) Not Confluent Direct Methods: not CR Add {3}{6}{7}{10} {3,6,7,8,9,10} (cm)Rewrite Rules: [ -(?x,0) -> ?x, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,if(<(-(0,s(?y_4)),s(?y_4)),-(0,s(?y_4)),if(<(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),-(-(0,s(?y_4)),s(?y_4)),mod(-(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),s(?y_4)))))> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {3}{5}{6}{7}{10} {3,5,6,7,8,9,10} (cm)Rewrite Rules: [ -(?x,0) -> ?x, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,if(<(-(0,s(?y_5)),s(?y_5)),-(0,s(?y_5)),if(<(-(-(0,s(?y_5)),s(?y_5)),s(?y_5)),-(-(0,s(?y_5)),s(?y_5)),mod(-(-(-(0,s(?y_5)),s(?y_5)),s(?y_5)),s(?y_5)))))> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {4} {4,8,9} (cm)Rewrite Rules: [ -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <2, 1> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_2)),0,0)> from mod(0,s(?y_2)) Not Confluent Direct Methods: not CR Add {4}{5} {4,5,8,9} (cm)Rewrite Rules: [ -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_3)),0,0)> from mod(0,s(?y_3)) Not Confluent Direct Methods: not CR Add {4}{5}{6} {4,5,6,8,9} (cm)Rewrite Rules: [ -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {4}{5}{6}{7} {4,5,6,7,8,9} (cm)Rewrite Rules: [ -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {4}{5}{6}{10} {4,5,6,8,9,10} (cm)Rewrite Rules: [ -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {4}{5}{7} {4,5,7,8,9} (cm)Rewrite Rules: [ -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {4}{5}{10} {4,5,8,9,10} (cm)Rewrite Rules: [ -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_3)),0,0)> from mod(0,s(?y_3)) Not Confluent Direct Methods: not CR Add {4}{5}{7}{10} {4,5,7,8,9,10} (cm)Rewrite Rules: [ -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {4}{6} {4,6,8,9} (cm)Rewrite Rules: [ -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_3)),0,0)> from mod(0,s(?y_3)) Not Confluent Direct Methods: not CR Add {4}{6}{7} {4,6,7,8,9} (cm)Rewrite Rules: [ -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {4}{6}{10} {4,6,8,9,10} (cm)Rewrite Rules: [ -(0,?x) -> 0, <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_3)),0,0)> from mod(0,s(?y_3)) Not Confluent Direct Methods: not CR Add {4}{7} {4,7,8,9} (cm)Rewrite Rules: [ -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_3)),0,0)> from mod(0,s(?y_3)) Not Confluent Direct Methods: not CR Add {4}{10} {4,8,9,10} (cm)Rewrite Rules: [ -(0,?x) -> 0, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <2, 1> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_2)),0,0)> from mod(0,s(?y_2)) Not Confluent Direct Methods: not CR Add {4}{7}{10} {4,7,8,9,10} (cm)Rewrite Rules: [ -(0,?x) -> 0, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_3)),0,0)> from mod(0,s(?y_3)) Not Confluent Direct Methods: not CR Add {4}{6}{7}{10} {4,6,7,8,9,10} (cm)Rewrite Rules: [ -(0,?x) -> 0, <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,0)> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {5} {5,8,9} (cm)Rewrite Rules: [ <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <2, 1> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_2)),0,if(<(-(0,s(?y_2)),s(?y_2)),-(0,s(?y_2)),if(<(-(-(0,s(?y_2)),s(?y_2)),s(?y_2)),-(-(0,s(?y_2)),s(?y_2)),mod(-(-(-(0,s(?y_2)),s(?y_2)),s(?y_2)),s(?y_2)))))> from mod(0,s(?y_2)) Not Confluent Direct Methods: not CR Add {5}{6} {5,6,8,9} (cm)Rewrite Rules: [ <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_3)),0,if(<(-(0,s(?y_3)),s(?y_3)),-(0,s(?y_3)),if(<(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),-(-(0,s(?y_3)),s(?y_3)),mod(-(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),s(?y_3)))))> from mod(0,s(?y_3)) Not Confluent Direct Methods: not CR Add {5}{6}{7} {5,6,7,8,9} (cm)Rewrite Rules: [ <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,if(<(-(0,s(?y_4)),s(?y_4)),-(0,s(?y_4)),if(<(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),-(-(0,s(?y_4)),s(?y_4)),mod(-(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),s(?y_4)))))> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {5}{6}{10} {5,6,8,9,10} (cm)Rewrite Rules: [ <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_3)),0,if(<(-(0,s(?y_3)),s(?y_3)),-(0,s(?y_3)),if(<(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),-(-(0,s(?y_3)),s(?y_3)),mod(-(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),s(?y_3)))))> from mod(0,s(?y_3)) Not Confluent Direct Methods: not CR Add {5}{7} {5,7,8,9} (cm)Rewrite Rules: [ <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_3)),0,if(<(-(0,s(?y_3)),s(?y_3)),-(0,s(?y_3)),if(<(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),-(-(0,s(?y_3)),s(?y_3)),mod(-(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),s(?y_3)))))> from mod(0,s(?y_3)) Not Confluent Direct Methods: not CR Add {5}{10} {5,8,9,10} (cm)Rewrite Rules: [ <(s(?x),s(?y)) -> <(?x,?y), mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <2, 1> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_2)),0,if(<(-(0,s(?y_2)),s(?y_2)),-(0,s(?y_2)),if(<(-(-(0,s(?y_2)),s(?y_2)),s(?y_2)),-(-(0,s(?y_2)),s(?y_2)),mod(-(-(-(0,s(?y_2)),s(?y_2)),s(?y_2)),s(?y_2)))))> from mod(0,s(?y_2)) Not Confluent Direct Methods: not CR Add {5}{7}{10} {5,7,8,9,10} (cm)Rewrite Rules: [ <(s(?x),s(?y)) -> <(?x,?y), <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_3)),0,if(<(-(0,s(?y_3)),s(?y_3)),-(0,s(?y_3)),if(<(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),-(-(0,s(?y_3)),s(?y_3)),mod(-(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),s(?y_3)))))> from mod(0,s(?y_3)) Not Confluent Direct Methods: not CR Add {6} {6,8,9} (cm)Rewrite Rules: [ <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <2, 1> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_2)),0,if(<(-(0,s(?y_2)),s(?y_2)),-(0,s(?y_2)),if(<(-(-(0,s(?y_2)),s(?y_2)),s(?y_2)),-(-(0,s(?y_2)),s(?y_2)),mod(-(-(-(0,s(?y_2)),s(?y_2)),s(?y_2)),s(?y_2)))))> from mod(0,s(?y_2)) Not Confluent Direct Methods: not CR Add {6}{7} {6,7,8,9} (cm)Rewrite Rules: [ <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_3)),0,if(<(-(0,s(?y_3)),s(?y_3)),-(0,s(?y_3)),if(<(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),-(-(0,s(?y_3)),s(?y_3)),mod(-(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),s(?y_3)))))> from mod(0,s(?y_3)) Not Confluent Direct Methods: not CR Add {6}{10} {6,8,9,10} (cm)Rewrite Rules: [ <(0,s(?x)) -> true, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <2, 1> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_2)),0,if(<(-(0,s(?y_2)),s(?y_2)),-(0,s(?y_2)),if(<(-(-(0,s(?y_2)),s(?y_2)),s(?y_2)),-(-(0,s(?y_2)),s(?y_2)),mod(-(-(-(0,s(?y_2)),s(?y_2)),s(?y_2)),s(?y_2)))))> from mod(0,s(?y_2)) Not Confluent Direct Methods: not CR Add {7} {7,8,9} (cm)Rewrite Rules: [ <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))) ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))) ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <2, 1> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_2)),0,if(<(-(0,s(?y_2)),s(?y_2)),-(0,s(?y_2)),if(<(-(-(0,s(?y_2)),s(?y_2)),s(?y_2)),-(-(0,s(?y_2)),s(?y_2)),mod(-(-(-(0,s(?y_2)),s(?y_2)),s(?y_2)),s(?y_2)))))> from mod(0,s(?y_2)) Not Confluent Direct Methods: not CR Add {10} {8,9,10} (cm)Rewrite Rules: [ mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_1)),0,mod(-(0,s(?y_1)),s(?y_1))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_1)),0,mod(-(0,s(?y_1)),s(?y_1))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <1, 0> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_1)),0,if(<(-(0,s(?y_1)),s(?y_1)),-(0,s(?y_1)),if(<(-(-(0,s(?y_1)),s(?y_1)),s(?y_1)),-(-(0,s(?y_1)),s(?y_1)),mod(-(-(-(0,s(?y_1)),s(?y_1)),s(?y_1)),s(?y_1)))))> from mod(0,s(?y_1)) Not Confluent Direct Methods: not CR Add {7}{10} {7,8,9,10} (cm)Rewrite Rules: [ <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_2)),0,mod(-(0,s(?y_2)),s(?y_2))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <2, 1> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_2)),0,if(<(-(0,s(?y_2)),s(?y_2)),-(0,s(?y_2)),if(<(-(-(0,s(?y_2)),s(?y_2)),s(?y_2)),-(-(0,s(?y_2)),s(?y_2)),mod(-(-(-(0,s(?y_2)),s(?y_2)),s(?y_2)),s(?y_2)))))> from mod(0,s(?y_2)) Not Confluent Direct Methods: not CR Add {6}{7}{10} {6,7,8,9,10} (cm)Rewrite Rules: [ <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_3)),0,mod(-(0,s(?y_3)),s(?y_3))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <3, 2> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_3)),0,if(<(-(0,s(?y_3)),s(?y_3)),-(0,s(?y_3)),if(<(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),-(-(0,s(?y_3)),s(?y_3)),mod(-(-(-(0,s(?y_3)),s(?y_3)),s(?y_3)),s(?y_3)))))> from mod(0,s(?y_3)) Not Confluent Direct Methods: not CR Add {5}{6}{7}{10} {5,6,7,8,9,10} (cm)Rewrite Rules: [ <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_4)),0,mod(-(0,s(?y_4)),s(?y_4))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <4, 3> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_4)),0,if(<(-(0,s(?y_4)),s(?y_4)),-(0,s(?y_4)),if(<(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),-(-(0,s(?y_4)),s(?y_4)),mod(-(-(-(0,s(?y_4)),s(?y_4)),s(?y_4)),s(?y_4)))))> from mod(0,s(?y_4)) Not Confluent Direct Methods: not CR Add {4}{5}{6}{7}{10} {4,5,6,7,8,9,10} (cm)Rewrite Rules: [ -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), 0 = 0, if(<(0,s(?y_5)),0,mod(-(0,s(?y_5)),s(?y_5))) = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <5, 4> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_5)),0,0)> from mod(0,s(?y_5)) Not Confluent Direct Methods: not CR Add {3}{4}{5}{6}{7}{10} {3,4,5,6,7,8,9,10} (cm)Rewrite Rules: [ -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_6)),0,mod(-(0,s(?y_6)),s(?y_6))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <1, 0> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <6, 5> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_6)),0,0)> from mod(0,s(?y_6)) Not Confluent Direct Methods: not CR Add {2}{3}{4}{5}{6}{7}{10} {2,3,4,5,6,7,8,9,10} (cm)Rewrite Rules: [ -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_7)),0,mod(-(0,s(?y_7)),s(?y_7))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <2, 1> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <7, 6> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_7)),0,0)> from mod(0,s(?y_7)) Not Confluent Direct Methods: not CR Add {1}{2}{3}{4}{5}{6}{7}{10} {1,2,3,4,5,6,7,8,9,10} (cm)Rewrite Rules: [ if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_8)),0,mod(-(0,s(?y_8)),s(?y_8))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <3, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <8, 7> preceded by [] unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Find Non-Joinable CP reducts: <0, if(<(0,s(?y_8)),0,0)> from mod(0,s(?y_8)) Not Confluent Direct Methods: not CR Add {0}{1}{2}{3}{4}{5}{6}{7}{10} {0,1,2,3,4,5,6,7,8,9,10} (cm)Rewrite Rules: [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Apply Direct Methods... Inner CPs: [ ] Outer CPs: [ 0 = 0, 0 = if(<(0,s(?y_9)),0,mod(-(0,s(?y_9)),s(?y_9))), 0 = 0 ] Overlay, check Innermost Termination... unknown Innermost Terminating unknown Knuth&Bendix Left-Linear, not Right-Linear unknown Development Closed unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ 0 = if(<(0,s(?y)),0,mod(-(0,s(?y)),s(?y))), if(<(0,s(?y_9)),0,mod(-(0,s(?y_9)),s(?y_9))) = 0, 0 = 0 ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair <0, 0> by Rules <4, 3> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <9, 8> preceded by [] joinable by a reduction of rules <[([(if,1)],6),([],0)], []> Critical Pair <0, 0> by Rules <10, 8> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check Non-Confluence...Unknown Direct Methods: Can't judge Try Persistent Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Sort Assignment: - : 35*35=>35 0 : =>35 < : 35*35=>38 s : 35=>35 if : 38*35*35=>35 mod : 35*35=>35 true : =>38 false : =>38 maximal types: {35,38} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ if(true,?x,?y) -> ?x, if(false,?x,?y) -> ?y, -(s(?x),s(?y)) -> -(?x,?y), -(?x,0) -> ?x, -(0,?x) -> 0, <(s(?x),s(?y)) -> <(?x,?y), <(0,s(?x)) -> true, <(?x,0) -> false, mod(0,?y) -> 0, mod(?x,s(?y)) -> if(<(?x,s(?y)),?x,mod(-(?x,s(?y)),s(?y))), mod(?x,0) -> ?x ] Layer Preserving Decomposition failed: Can't judge No further decomposition possible Commutative Decomposition failed: Can't judge No further decomposition possible Final result: Can't judge /local-scratch/hzankl/2012/cops2012/62.trs: Failure(unknown) (12701 msec.)