YES
(ignored inputs)COMMENT cops number: 992 submitted by: Johannes Waldmann
Rewrite Rules:
[ a(c(?x)) -> b(b(?x)),
a(c(?x)) -> b(a(?x)),
b(a(?x)) -> c(c(?x)),
c(b(?x)) -> c(b(?x)),
b(b(?x)) -> b(c(?x)),
b(c(?x)) -> c(b(?x)),
c(c(?x)) -> b(c(?x)) ]
Apply Direct Methods...
Inner CPs:
[ a(c(b(?x_3))) = b(b(b(?x_3))),
a(b(c(?x_6))) = b(b(c(?x_6))),
a(c(b(?x_3))) = b(a(b(?x_3))),
a(b(c(?x_6))) = b(a(c(?x_6))),
b(b(b(?x))) = c(c(c(?x))),
b(b(a(?x_1))) = c(c(c(?x_1))),
c(c(c(?x_2))) = c(b(a(?x_2))),
c(b(c(?x_4))) = c(b(b(?x_4))),
c(c(b(?x_5))) = c(b(c(?x_5))),
b(c(c(?x_2))) = b(c(a(?x_2))),
b(c(b(?x_5))) = b(c(c(?x_5))),
b(c(b(?x_3))) = c(b(b(?x_3))),
b(b(c(?x_6))) = c(b(c(?x_6))),
c(c(b(?x_3))) = b(c(b(?x_3))),
b(b(c(?x))) = b(c(b(?x))),
c(b(c(?x))) = b(c(c(?x))) ]
Outer CPs:
[ b(b(?x)) = b(a(?x)) ]
not Overlay, check Termination...
unknown/not Terminating
unknown Knuth & Bendix
Linear
unknown Development Closed
unknown Strongly Closed
unknown Weakly-Non-Overlapping & Non-Collapsing & Shallow
unknown Upside-Parallel-Closed/Outside-Closed
(inner) Parallel CPs: (not computed)
unknown Toyama (Parallel CPs)
Simultaneous CPs:
[ b(a(?x)) = b(b(?x)),
a(c(b(?x_4))) = b(b(b(?x_4))),
a(b(c(?x_7))) = b(b(c(?x_7))),
c(c(c(b(?x_4)))) = b(b(b(b(?x_4)))),
c(c(b(c(?x_7)))) = b(b(b(c(?x_7)))),
c(c(c(?x))) = b(b(b(?x))),
b(b(?x)) = b(a(?x)),
a(c(b(?x_4))) = b(a(b(?x_4))),
a(b(c(?x_7))) = b(a(c(?x_7))),
c(c(c(b(?x_4)))) = b(b(a(b(?x_4)))),
c(c(b(c(?x_7)))) = b(b(a(c(?x_7)))),
c(c(c(?x))) = b(b(a(?x))),
b(b(b(?x_2))) = c(c(c(?x_2))),
b(b(a(?x_3))) = c(c(c(?x_3))),
c(b(b(b(?x_2)))) = c(c(c(c(?x_2)))),
c(b(b(a(?x_3)))) = c(c(c(c(?x_3)))),
b(c(b(b(?x_2)))) = b(c(c(c(?x_2)))),
b(c(b(a(?x_3)))) = b(c(c(c(?x_3)))),
c(b(a(?x))) = c(c(c(?x))),
b(c(a(?x))) = b(c(c(?x))),
c(c(c(?x_4))) = c(b(a(?x_4))),
c(b(c(?x_5))) = c(b(b(?x_5))),
c(c(b(?x_6))) = c(b(c(?x_6))),
b(b(c(c(?x_4)))) = a(c(b(a(?x_4)))),
b(b(b(c(?x_5)))) = a(c(b(b(?x_5)))),
b(b(c(b(?x_6)))) = a(c(b(c(?x_6)))),
b(a(c(c(?x_4)))) = a(c(b(a(?x_4)))),
b(a(b(c(?x_5)))) = a(c(b(b(?x_5)))),
b(a(c(b(?x_6)))) = a(c(b(c(?x_6)))),
c(b(c(c(?x_4)))) = b(c(b(a(?x_4)))),
c(b(b(c(?x_5)))) = b(c(b(b(?x_5)))),
c(b(c(b(?x_6)))) = b(c(b(c(?x_6)))),
b(c(c(c(?x_4)))) = c(c(b(a(?x_4)))),
b(c(b(c(?x_5)))) = c(c(b(b(?x_5)))),
b(c(c(b(?x_6)))) = c(c(b(c(?x_6)))),
b(b(b(?x))) = a(c(b(?x))),
b(a(b(?x))) = a(c(b(?x))),
c(b(b(?x))) = b(c(b(?x))),
b(c(b(?x))) = c(c(b(?x))),
b(b(c(?x_1))) = b(c(b(?x_1))),
b(c(c(?x_4))) = b(c(a(?x_4))),
b(c(b(?x_6))) = b(c(c(?x_6))),
b(c(b(c(?x_1)))) = b(b(c(b(?x_1)))),
b(c(c(c(?x_4)))) = b(b(c(a(?x_4)))),
b(c(c(b(?x_6)))) = b(b(c(c(?x_6)))),
c(b(b(c(?x_1)))) = c(b(c(b(?x_1)))),
c(b(c(c(?x_4)))) = c(b(c(a(?x_4)))),
c(b(c(b(?x_6)))) = c(b(c(c(?x_6)))),
b(c(b(?x))) = b(b(c(?x))),
c(b(b(?x))) = c(b(c(?x))),
b(c(b(?x_5))) = c(b(b(?x_5))),
b(b(c(?x_7))) = c(b(c(?x_7))),
c(b(c(b(?x_5)))) = c(c(b(b(?x_5)))),
c(b(b(c(?x_7)))) = c(c(b(c(?x_7)))),
b(c(c(b(?x_5)))) = b(c(b(b(?x_5)))),
b(c(b(c(?x_7)))) = b(c(b(c(?x_7)))),
c(b(c(?x))) = c(c(b(?x))),
b(c(c(?x))) = b(c(b(?x))),
c(b(c(?x_1))) = b(c(c(?x_1))),
c(c(b(?x_5))) = b(c(b(?x_5))),
b(c(b(c(?x_1)))) = c(b(c(c(?x_1)))),
b(c(c(b(?x_5)))) = c(b(c(b(?x_5)))),
b(b(b(c(?x_1)))) = a(b(c(c(?x_1)))),
b(b(c(b(?x_5)))) = a(b(c(b(?x_5)))),
b(a(b(c(?x_1)))) = a(b(c(c(?x_1)))),
b(a(c(b(?x_5)))) = a(b(c(b(?x_5)))),
c(b(b(c(?x_1)))) = b(b(c(c(?x_1)))),
c(b(c(b(?x_5)))) = b(b(c(b(?x_5)))),
b(c(c(?x))) = c(b(c(?x))),
b(b(c(?x))) = a(b(c(?x))),
b(a(c(?x))) = a(b(c(?x))),
c(b(c(?x))) = b(b(c(?x))) ]
unknown Okui (Simultaneous CPs)
unknown Strongly Depth-Preserving & Root-E-Closed/Non-E-Overlapping
unknown Strongly Weight-Preserving & Root-E-Closed/Non-E-Overlapping
check Locally Decreasing Diagrams by Rule Labelling...
Critical Pair by Rules <3, 0> preceded by [(a,1)]
joinable by a reduction of rules <[([],0)], []>
Critical Pair by Rules <6, 0> preceded by [(a,1)]
joinable by a reduction of rules <[([(a,1)],5),([],0),([(b,1)],4)], []>
joinable by a reduction of rules <[([(a,1)],5),([],0),([],4)], [([(b,1)],5)]>
joinable by a reduction of rules <[([(a,1)],5),([],1),([],2)], [([],4),([],5),([(c,1)],5)]>
Critical Pair by Rules <3, 1> preceded by [(a,1)]
joinable by a reduction of rules <[([],1)], []>
Critical Pair by Rules <6, 1> preceded by [(a,1)]
joinable by a reduction of rules <[([(a,1)],5),([],0)], [([(b,1)],0)]>
Critical Pair by Rules <0, 2> preceded by [(b,1)]
joinable by a reduction of rules <[([(b,1)],4),([],4)], [([],6)]>
joinable by a reduction of rules <[([(b,1)],4)], [([],6),([(b,1)],6)]>
Critical Pair by Rules <1, 2> preceded by [(b,1)]
joinable by a reduction of rules <[([(b,1)],2)], [([],6)]>
Critical Pair by Rules <2, 3> preceded by [(c,1)]
joinable by a reduction of rules <[], [([(c,1)],2)]>
Critical Pair by Rules <4, 3> preceded by [(c,1)]
joinable by a reduction of rules <[], [([(c,1)],4)]>
Critical Pair by Rules <5, 3> preceded by [(c,1)]
joinable by a reduction of rules <[], [([(c,1)],5)]>
Critical Pair by Rules <2, 4> preceded by [(b,1)]
joinable by a reduction of rules <[], [([],5),([(c,1)],2),([],6)]>
joinable by a reduction of rules <[([],5)], [([],5),([(c,1)],2),([(c,1)],6)]>
Critical Pair by Rules <5, 4> preceded by [(b,1)]
joinable by a reduction of rules <[([],5),([(c,1)],4)], [([],5)]>
joinable by a reduction of rules <[], [([(b,1)],6),([(b,1)],5)]>
Critical Pair by Rules <3, 5> preceded by [(b,1)]
joinable by a reduction of rules <[([],5)], []>
Critical Pair by Rules <6, 5> preceded by [(b,1)]
joinable by a reduction of rules <[([],4),([],5)], []>
joinable by a reduction of rules <[([(b,1)],5)], [([(c,1)],5),([],6)]>
Critical Pair by Rules <3, 6> preceded by [(c,1)]
joinable by a reduction of rules <[([],6)], []>
Critical Pair by Rules <4, 4> preceded by [(b,1)]
joinable by a reduction of rules <[([(b,1)],5)], []>
Critical Pair by Rules <6, 6> preceded by [(c,1)]
joinable by a reduction of rules <[], [([],5)]>
Critical Pair by Rules <1, 0> preceded by []
joinable by a reduction of rules <[([],2),([],6)], [([],4)]>
Satisfiable by 2>1>5>3>7>6,4; a(2)b(1)c(1); 2>3>1>5>7>6,4
Diagram Decreasing
Direct Methods: CR
Combined result: CR
cops-aa6dOFao.trs: Success(CR)
(10 msec.)