YES
(ignored inputs)COMMENT the following rules are removed from the original TRS b ( b ( x ) ) -> b ( b ( x ) )
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)),
     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_5))) = a(a(b(?x_5))),
     c(b(a(?x_6))) = a(a(c(?x_6))),
     c(a(a(?x))) = a(c(a(?x))),
     c(a(c(?x_2))) = a(c(b(?x_2))),
     c(b(a(?x_4))) = a(c(a(?x_4))),
     a(c(c(?x_5))) = c(a(b(?x_5))),
     a(b(a(?x_6))) = c(a(c(?x_6))),
     c(c(a(?x_3))) = b(a(a(?x_3))),
     c(c(c(?x_5))) = b(a(b(?x_5))),
     c(b(a(?x_6))) = b(a(c(?x_6))),
     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_4))) = b(a(a(?x_4))),
     c(a(c(?x))) = a(c(c(?x))),
     a(c(a(?x))) = c(a(a(?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_6))) = a(a(b(?x_6))),
     c(b(a(?x_7))) = a(a(c(?x_7))),
     a(c(c(a(?x_4)))) = c(a(a(a(?x_4)))),
     a(c(c(c(?x_6)))) = c(a(a(b(?x_6)))),
     a(c(b(a(?x_7)))) = c(a(a(c(?x_7)))),
     b(a(c(a(?x_4)))) = a(a(a(a(?x_4)))),
     b(a(c(c(?x_6)))) = a(a(a(b(?x_6)))),
     b(a(b(a(?x_7)))) = a(a(a(c(?x_7)))),
     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_5))) = a(c(a(?x_5))),
     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_5)))) = c(a(c(a(?x_5)))),
     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_5)))) = a(a(c(a(?x_5)))),
     a(c(c(?x))) = c(a(c(?x))),
     b(a(c(?x))) = a(a(c(?x))),
     a(c(b(?x))) = c(a(c(?x))),
     b(a(b(?x))) = a(a(c(?x))),
     a(c(c(?x_6))) = c(a(b(?x_6))),
     a(b(a(?x_7))) = c(a(c(?x_7))),
     c(a(c(a(?x_1)))) = a(c(a(a(?x_1)))),
     c(a(c(c(?x_6)))) = a(c(a(b(?x_6)))),
     c(a(b(a(?x_7)))) = a(c(a(c(?x_7)))),
     a(a(c(a(?x_1)))) = c(c(a(a(?x_1)))),
     a(a(c(c(?x_6)))) = c(c(a(b(?x_6)))),
     a(a(b(a(?x_7)))) = c(c(a(c(?x_7)))),
     b(a(c(a(?x_1)))) = c(c(a(a(?x_1)))),
     b(a(c(c(?x_6)))) = c(c(a(b(?x_6)))),
     b(a(b(a(?x_7)))) = c(c(a(c(?x_7)))),
     a(a(a(?x))) = c(c(a(?x))),
     b(a(a(?x))) = c(c(a(?x))),
     a(a(?x)) = b(a(?x)),
     c(c(a(?x_5))) = b(a(a(?x_5))),
     c(c(c(?x_6))) = b(a(b(?x_6))),
     c(b(a(?x_7))) = b(a(c(?x_7))),
     a(c(c(a(?x_5)))) = c(b(a(a(?x_5)))),
     a(c(c(c(?x_6)))) = c(b(a(b(?x_6)))),
     a(c(b(a(?x_7)))) = c(b(a(c(?x_7)))),
     b(a(c(a(?x_5)))) = a(b(a(a(?x_5)))),
     b(a(c(c(?x_6)))) = a(b(a(b(?x_6)))),
     b(a(b(a(?x_7)))) = a(b(a(c(?x_7)))),
     a(c(a(?x))) = c(b(a(?x))),
     b(a(a(?x))) = a(b(a(?x))),
     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_6))) = b(a(a(?x_6))),
     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_6)))) = c(b(a(a(?x_6)))),
     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_6)))) = a(b(a(a(?x_6)))),
     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_6)))) = c(b(a(a(?x_6)))),
     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 <c(c(a(?x_3))), a(a(a(?x_3)))> 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 <c(c(c(?x_5))), a(a(b(?x_5)))> by Rules <5, 0> preceded by [(c,1)]
 joinable by a reduction of rules <[([],1)], [([(a,1)],5)]>
Critical Pair <c(b(a(?x_6))), a(a(c(?x_6)))> by Rules <6, 0> preceded by [(c,1)]
 joinable by a reduction of rules <[([],2),([(a,1)],4)], [([(a,1)],6)]>
 joinable by a reduction of rules <[], [([],3),([(c,1)],6)]>
Critical Pair <c(a(a(?x))), a(c(a(?x)))> by Rules <0, 1> preceded by [(c,1)]
 joinable by a reduction of rules <[([],4)], [([],6)]>
 joinable by a reduction of rules <[([],0)], [([(a,1)],0)]>
Critical Pair <c(a(c(?x_2))), a(c(b(?x_2)))> by Rules <2, 1> preceded by [(c,1)]
 joinable by a reduction of rules <[([],0)], [([(a,1)],2)]>
Critical Pair <c(b(a(?x_4))), a(c(a(?x_4)))> by Rules <4, 1> preceded by [(c,1)]
 joinable by a reduction of rules <[([],2)], []>
Critical Pair <a(c(c(?x_5))), c(a(b(?x_5)))> by Rules <5, 3> preceded by [(a,1)]
 joinable by a reduction of rules <[], [([(c,1)],5),([],1)]>
 joinable by a reduction of rules <[], [([],0),([(a,1)],5)]>
 joinable by a reduction of rules <[([(a,1)],1),([],3)], [([(c,1)],5),([(c,1)],1)]>
Critical Pair <a(b(a(?x_6))), c(a(c(?x_6)))> by Rules <6, 3> preceded by [(a,1)]
 joinable by a reduction of rules <[([],5),([(c,1)],4)], [([(c,1)],6)]>
 joinable by a reduction of rules <[], [([],0),([(a,1)],6)]>
 joinable by a reduction of rules <[([],5),([],1)], [([(c,1)],6),([],2)]>
Critical Pair <c(c(a(?x_3))), b(a(a(?x_3)))> by Rules <3, 4> preceded by [(c,1)]
 joinable by a reduction of rules <[([(c,1)],0),([],4)], []>
 joinable by a reduction of rules <[([],1),([],6)], []>
Critical Pair <c(c(c(?x_5))), b(a(b(?x_5)))> by Rules <5, 4> preceded by [(c,1)]
 joinable by a reduction of rules <[([(c,1)],1),([],4)], [([(b,1)],5),([(b,1)],1)]>
 joinable by a reduction of rules <[([],1),([],6)], [([(b,1)],5),([(b,1)],1)]>
Critical Pair <c(b(a(?x_6))), b(a(c(?x_6)))> by Rules <6, 4> preceded by [(c,1)]
 joinable by a reduction of rules <[([],2),([],6),([(b,1)],3),([(b,1)],4)], [([(b,1)],6)]>
Critical Pair <a(a(a(?x))), b(a(a(?x)))> by Rules <0, 6> preceded by [(a,1)]
 joinable by a reduction of rules <[([(a,1)],3),([],6)], []>
 joinable by a reduction of rules <[([],3),([],4)], []>
Critical Pair <a(a(c(?x_1))), b(a(c(?x_1)))> by Rules <1, 6> preceded by [(a,1)]
 joinable by a reduction of rules <[([],3),([],4)], []>
Critical Pair <a(a(c(?x_2))), b(a(b(?x_2)))> by Rules <2, 6> preceded by [(a,1)]
 joinable by a reduction of rules <[([],3),([],4)], [([(b,1)],5),([(b,1)],1)]>
Critical Pair <a(b(a(?x_4))), b(a(a(?x_4)))> by Rules <4, 6> preceded by [(a,1)]
 joinable by a reduction of rules <[([],5),([(c,1)],0),([],4)], []>
 joinable by a reduction of rules <[([],5),([],1),([],6)], []>
Critical Pair <c(a(c(?x))), a(c(c(?x)))> by Rules <1, 1> preceded by [(c,1)]
 joinable by a reduction of rules <[([],4)], [([],6)]>
 joinable by a reduction of rules <[([],0)], [([(a,1)],1)]>
Critical Pair <a(c(a(?x))), c(a(a(?x)))> by Rules <3, 3> preceded by [(a,1)]
 joinable by a reduction of rules <[([(a,1)],0)], [([],0)]>
 joinable by a reduction of rules <[([],6)], [([],4)]>
Critical Pair <b(a(?x_4)), a(a(?x_4))> by Rules <4, 0> preceded by []
 joinable by a reduction of rules <[], [([],3),([],4)]>
Satisfiable by 7,6,5,4,3,2,1; a(1)b(1)c(1); 7>5>6,3>1,2>4
Diagram Decreasing
Direct Methods: CR

Combined result: CR
/tmp/file12uSb4.trs: Success(CR)
(29 msec.)