0.00/0.15 NO 0.00/0.15 (ignored inputs)COMMENT [5] p. 287 , attributed to Sivakumar submitted by: Takahito Aoto , Junichi Yoshida , and Yoshihito Toyama 0.00/0.15 Rewrite Rules: 0.00/0.15 [ f(?x,?x) -> g(?x), 0.00/0.15 f(?x,g(?x)) -> b, 0.00/0.15 h(c,?y) -> f(h(?y,c),h(?y,?y)) ] 0.00/0.15 Apply Direct Methods... 0.00/0.15 Inner CPs: 0.00/0.15 [ ] 0.00/0.15 Outer CPs: 0.00/0.15 [ ] 0.00/0.15 Overlay, check Innermost Termination... 0.00/0.15 unknown Innermost Terminating 0.00/0.15 unknown Knuth & Bendix 0.00/0.15 not Left-Linear, not Right-Linear 0.00/0.15 unknown Weakly-Non-Overlapping & Non-Collapsing & Shallow 0.00/0.15 unknown Strongly Depth-Preserving & Root-E-Closed/Non-E-Overlapping 0.00/0.15 unknown Strongly Weight-Preserving & Root-E-Closed/Non-E-Overlapping 0.00/0.15 [ f(?x,?x) -> g(?x), 0.00/0.15 f(?x_1,g(?x_1)) -> b, 0.00/0.15 h(c,?y_2) -> f(h(?y_2,c),h(?y_2,?y_2)) ] 0.00/0.15 Sort Assignment: 0.00/0.15 b : =>14 0.00/0.15 c : =>11 0.00/0.15 f : 14*14=>14 0.00/0.15 g : 14=>14 0.00/0.15 h : 11*11=>14 0.00/0.15 non-linear variables: {?x,?x_1} 0.00/0.15 non-linear types: {14} 0.00/0.15 types leq non-linear types: {14} 0.00/0.15 rules applicable to terms of non-linear types: 0.00/0.15 [ f(?x,?x) -> g(?x), 0.00/0.15 f(?x_1,g(?x_1)) -> b, 0.00/0.15 h(c,?y_2) -> f(h(?y_2,c),h(?y_2,?y_2)) ] 0.00/0.15 unknown innermost-termination for terms of non-linear types 0.00/0.15 unknown Quasi-Left-Linear & Parallel-Closed 0.00/0.15 [ f(?x,?x) -> g(?x), 0.00/0.15 f(?x_1,g(?x_1)) -> b, 0.00/0.15 h(c,?y_2) -> f(h(?y_2,c),h(?y_2,?y_2)) ] 0.00/0.15 Sort Assignment: 0.00/0.15 b : =>14 0.00/0.15 c : =>11 0.00/0.15 f : 14*14=>14 0.00/0.15 g : 14=>14 0.00/0.15 h : 11*11=>14 0.00/0.15 non-linear variables: {?x,?x_1,?y_2} 0.00/0.15 non-linear types: {14,11} 0.00/0.15 types leq non-linear types: {14,11} 0.00/0.15 rules applicable to terms of non-linear types: 0.00/0.15 [ f(?x,?x) -> g(?x), 0.00/0.15 f(?x_1,g(?x_1)) -> b, 0.00/0.15 h(c,?y_2) -> f(h(?y_2,c),h(?y_2,?y_2)) ] 0.00/0.15 Rnl: 0.00/0.15 0: {0,1,2} 0.00/0.15 1: {0,1,2} 0.00/0.15 2: {} 0.00/0.15 unknown innermost-termination for terms of non-linear types 0.00/0.15 unknown Quasi-Linear & Linearized-Decreasing 0.00/0.15 [ f(?x,?x) -> g(?x), 0.00/0.15 f(?x_1,g(?x_1)) -> b, 0.00/0.15 h(c,?y_2) -> f(h(?y_2,c),h(?y_2,?y_2)) ] 0.00/0.15 Sort Assignment: 0.00/0.15 b : =>14 0.00/0.15 c : =>11 0.00/0.15 f : 14*14=>14 0.00/0.15 g : 14=>14 0.00/0.15 h : 11*11=>14 0.00/0.15 non-linear variables: {?x,?x_1,?y_2} 0.00/0.15 non-linear types: {14,11} 0.00/0.15 types leq non-linear types: {14,11} 0.00/0.15 rules applicable to terms of non-linear types: 0.00/0.15 [ f(?x,?x) -> g(?x), 0.00/0.15 f(?x_1,g(?x_1)) -> b, 0.00/0.15 h(c,?y_2) -> f(h(?y_2,c),h(?y_2,?y_2)) ] 0.00/0.15 unknown innermost-termination for terms of non-linear types 0.00/0.15 unknown Strongly Quasi-Linear & Hierarchically Decreasing 0.00/0.15 check Non-Confluence... 0.00/0.15 obtain 11 rules by 3 steps unfolding 0.00/0.15 obtain 100 candidates for checking non-joinability 0.00/0.15 check by TCAP-Approximation (success) 0.00/0.15 Witness for Non-Confluence: b> 0.00/0.15 Direct Methods: not CR 0.00/0.15 0.00/0.15 Combined result: not CR 0.00/0.15 /export/starexec/sandbox2/benchmark/theBenchmark.trs: Success(not CR) 0.00/0.15 (100 msec.) 0.00/0.16 EOF