YES (ignored inputs)COMMENT 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 992.trs: Success(CR) (9 msec.)