YES (ignored inputs)COMMENT submitted by: Johannes Waldmann Rewrite Rules: [ c(a(?x)) -> a(a(?x)), c(c(?x)) -> a(c(?x)), c(b(?x)) -> a(c(?x)), a(a(?x)) -> c(a(?x)), b(b(?x)) -> b(b(?x)), c(a(?x)) -> b(a(?x)), a(b(?x)) -> c(c(?x)), a(c(?x)) -> b(a(?x)) ] Apply Direct Methods... Inner CPs: [ c(c(a(?x_3))) = a(a(a(?x_3))), c(c(c(?x_6))) = a(a(b(?x_6))), c(b(a(?x_7))) = a(a(c(?x_7))), c(a(a(?x))) = a(c(a(?x))), c(a(c(?x_2))) = a(c(b(?x_2))), c(b(a(?x_5))) = a(c(a(?x_5))), c(b(b(?x_4))) = a(c(b(?x_4))), a(c(c(?x_6))) = c(a(b(?x_6))), a(b(a(?x_7))) = c(a(c(?x_7))), c(c(a(?x_3))) = b(a(a(?x_3))), c(c(c(?x_6))) = b(a(b(?x_6))), c(b(a(?x_7))) = b(a(c(?x_7))), a(b(b(?x_4))) = c(c(b(?x_4))), a(a(a(?x))) = b(a(a(?x))), a(a(c(?x_1))) = b(a(c(?x_1))), a(a(c(?x_2))) = b(a(b(?x_2))), a(b(a(?x_5))) = b(a(a(?x_5))), c(a(c(?x))) = a(c(c(?x))), a(c(a(?x))) = c(a(a(?x))), b(b(b(?x))) = b(b(b(?x))) ] Outer CPs: [ a(a(?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)) = a(a(?x)), c(c(a(?x_4))) = a(a(a(?x_4))), c(c(c(?x_7))) = a(a(b(?x_7))), c(b(a(?x_8))) = a(a(c(?x_8))), a(c(c(a(?x_4)))) = c(a(a(a(?x_4)))), a(c(c(c(?x_7)))) = c(a(a(b(?x_7)))), a(c(b(a(?x_8)))) = c(a(a(c(?x_8)))), b(a(c(a(?x_4)))) = a(a(a(a(?x_4)))), b(a(c(c(?x_7)))) = a(a(a(b(?x_7)))), b(a(b(a(?x_8)))) = a(a(a(c(?x_8)))), a(c(a(?x))) = c(a(a(?x))), b(a(a(?x))) = a(a(a(?x))), c(a(c(?x_1))) = a(c(c(?x_1))), c(a(a(?x_2))) = a(c(a(?x_2))), c(a(c(?x_3))) = a(c(b(?x_3))), c(b(a(?x_6))) = a(c(a(?x_6))), a(c(a(c(?x_1)))) = c(a(c(c(?x_1)))), a(c(a(a(?x_2)))) = c(a(c(a(?x_2)))), a(c(a(c(?x_3)))) = c(a(c(b(?x_3)))), a(c(b(a(?x_6)))) = c(a(c(a(?x_6)))), b(a(a(c(?x_1)))) = a(a(c(c(?x_1)))), b(a(a(a(?x_2)))) = a(a(c(a(?x_2)))), b(a(a(c(?x_3)))) = a(a(c(b(?x_3)))), b(a(b(a(?x_6)))) = a(a(c(a(?x_6)))), a(c(c(?x))) = c(a(c(?x))), b(a(c(?x))) = a(a(c(?x))), c(b(b(?x_5))) = a(c(b(?x_5))), a(c(b(b(?x_5)))) = c(a(c(b(?x_5)))), b(a(b(b(?x_5)))) = a(a(c(b(?x_5)))), a(c(b(?x))) = c(a(c(?x))), b(a(b(?x))) = a(a(c(?x))), a(c(c(?x_7))) = c(a(b(?x_7))), a(b(a(?x_8))) = c(a(c(?x_8))), c(a(c(a(?x_1)))) = a(c(a(a(?x_1)))), c(a(c(c(?x_7)))) = a(c(a(b(?x_7)))), c(a(b(a(?x_8)))) = a(c(a(c(?x_8)))), a(a(c(a(?x_1)))) = c(c(a(a(?x_1)))), a(a(c(c(?x_7)))) = c(c(a(b(?x_7)))), a(a(b(a(?x_8)))) = c(c(a(c(?x_8)))), b(a(c(a(?x_1)))) = c(c(a(a(?x_1)))), b(a(c(c(?x_7)))) = c(c(a(b(?x_7)))), b(a(b(a(?x_8)))) = c(c(a(c(?x_8)))), a(a(a(?x))) = c(c(a(?x))), b(a(a(?x))) = c(c(a(?x))), b(b(b(?x_1))) = b(b(b(?x_1))), b(b(b(b(?x_1)))) = b(b(b(b(?x_1)))), a(c(b(b(?x_1)))) = c(b(b(b(?x_1)))), c(c(b(b(?x_1)))) = a(b(b(b(?x_1)))), a(c(b(?x))) = c(b(b(?x))), c(c(b(?x))) = a(b(b(?x))), a(a(?x)) = b(a(?x)), c(c(a(?x_5))) = b(a(a(?x_5))), c(c(c(?x_7))) = b(a(b(?x_7))), c(b(a(?x_8))) = b(a(c(?x_8))), a(c(c(a(?x_5)))) = c(b(a(a(?x_5)))), a(c(c(c(?x_7)))) = c(b(a(b(?x_7)))), a(c(b(a(?x_8)))) = c(b(a(c(?x_8)))), b(a(c(a(?x_5)))) = a(b(a(a(?x_5)))), b(a(c(c(?x_7)))) = a(b(a(b(?x_7)))), b(a(b(a(?x_8)))) = a(b(a(c(?x_8)))), a(c(a(?x))) = c(b(a(?x))), b(a(a(?x))) = a(b(a(?x))), a(b(b(?x_6))) = c(c(b(?x_6))), a(a(b(b(?x_6)))) = c(c(c(b(?x_6)))), c(a(b(b(?x_6)))) = a(c(c(b(?x_6)))), b(a(b(b(?x_6)))) = c(c(c(b(?x_6)))), a(a(b(?x))) = c(c(c(?x))), c(a(b(?x))) = a(c(c(?x))), b(a(b(?x))) = c(c(c(?x))), a(a(a(?x_2))) = b(a(a(?x_2))), a(a(c(?x_3))) = b(a(c(?x_3))), a(a(c(?x_4))) = b(a(b(?x_4))), a(b(a(?x_7))) = b(a(a(?x_7))), a(a(a(a(?x_2)))) = c(b(a(a(?x_2)))), a(a(a(c(?x_3)))) = c(b(a(c(?x_3)))), a(a(a(c(?x_4)))) = c(b(a(b(?x_4)))), a(a(b(a(?x_7)))) = c(b(a(a(?x_7)))), c(a(a(a(?x_2)))) = a(b(a(a(?x_2)))), c(a(a(c(?x_3)))) = a(b(a(c(?x_3)))), c(a(a(c(?x_4)))) = a(b(a(b(?x_4)))), c(a(b(a(?x_7)))) = a(b(a(a(?x_7)))), b(a(a(a(?x_2)))) = c(b(a(a(?x_2)))), b(a(a(c(?x_3)))) = c(b(a(c(?x_3)))), b(a(a(c(?x_4)))) = c(b(a(b(?x_4)))), b(a(b(a(?x_7)))) = c(b(a(a(?x_7)))), a(a(c(?x))) = c(b(a(?x))), c(a(c(?x))) = a(b(a(?x))), b(a(c(?x))) = c(b(a(?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 [(c,1)] joinable by a reduction of rules <[([(c,1)],0)], [([],3)]> joinable by a reduction of rules <[([],1)], [([(a,1)],3)]> Critical Pair by Rules <6, 0> preceded by [(c,1)] joinable by a reduction of rules <[([],1)], [([(a,1)],6)]> Critical Pair by Rules <7, 0> preceded by [(c,1)] joinable by a reduction of rules <[([],2),([(a,1)],5)], [([(a,1)],7)]> joinable by a reduction of rules <[], [([],3),([(c,1)],7)]> Critical Pair by Rules <0, 1> preceded by [(c,1)] joinable by a reduction of rules <[([],5)], [([],7)]> joinable by a reduction of rules <[([],0)], [([(a,1)],0)]> Critical Pair by Rules <2, 1> preceded by [(c,1)] joinable by a reduction of rules <[([],0)], [([(a,1)],2)]> Critical Pair by Rules <5, 1> preceded by [(c,1)] joinable by a reduction of rules <[([],2)], []> Critical Pair by Rules <4, 2> preceded by [(c,1)] joinable by a reduction of rules <[([],2)], []> Critical Pair by Rules <6, 3> preceded by [(a,1)] joinable by a reduction of rules <[], [([(c,1)],6),([],1)]> joinable by a reduction of rules <[], [([],0),([(a,1)],6)]> joinable by a reduction of rules <[([(a,1)],1),([],3)], [([(c,1)],6),([(c,1)],1)]> Critical Pair by Rules <7, 3> preceded by [(a,1)] joinable by a reduction of rules <[([],6),([(c,1)],5)], [([(c,1)],7)]> joinable by a reduction of rules <[], [([],0),([(a,1)],7)]> joinable by a reduction of rules <[([],6),([],1)], [([(c,1)],7),([],2)]> Critical Pair by Rules <3, 5> preceded by [(c,1)] joinable by a reduction of rules <[([(c,1)],0),([],5)], []> joinable by a reduction of rules <[([],1),([],7)], []> Critical Pair by Rules <6, 5> preceded by [(c,1)] joinable by a reduction of rules <[([(c,1)],1),([],5)], [([(b,1)],6),([(b,1)],1)]> joinable by a reduction of rules <[([],1),([],7)], [([(b,1)],6),([(b,1)],1)]> Critical Pair by Rules <7, 5> preceded by [(c,1)] joinable by a reduction of rules <[([],2),([],7),([(b,1)],3),([(b,1)],5)], [([(b,1)],7)]> Critical Pair by Rules <4, 6> preceded by [(a,1)] joinable by a reduction of rules <[([],6)], []> Critical Pair by Rules <0, 7> preceded by [(a,1)] joinable by a reduction of rules <[([(a,1)],3),([],7)], []> joinable by a reduction of rules <[([],3),([],5)], []> Critical Pair by Rules <1, 7> preceded by [(a,1)] joinable by a reduction of rules <[([],3),([],5)], []> Critical Pair by Rules <2, 7> preceded by [(a,1)] joinable by a reduction of rules <[([],3),([],5)], [([(b,1)],6),([(b,1)],1)]> Critical Pair by Rules <5, 7> preceded by [(a,1)] joinable by a reduction of rules <[([],6),([(c,1)],0),([],5)], []> joinable by a reduction of rules <[([],6),([],1),([],7)], []> Critical Pair by Rules <1, 1> preceded by [(c,1)] joinable by a reduction of rules <[([],5)], [([],7)]> joinable by a reduction of rules <[([],0)], [([(a,1)],1)]> Critical Pair by Rules <3, 3> preceded by [(a,1)] joinable by a reduction of rules <[([(a,1)],0)], [([],0)]> joinable by a reduction of rules <[([],7)], [([],5)]> Critical Pair by Rules <4, 4> preceded by [(b,1)] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 0> preceded by [] joinable by a reduction of rules <[], [([],3),([],5)]> Satisfiable by 8,7,6,5,4,3,2,1; a(1)b(1)c(1); 1,3>8,7>6>4>5,2 Diagram Decreasing Direct Methods: CR Combined result: CR 1014.trs: Success(CR) (10 msec.)