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

Combined result: CR
1006.trs: Success(CR)
YES
(108 msec.)