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

Combined result: CR
/tmp/fileT8UGER.trs: Success(CR)
(30 msec.)