YES
(ignored inputs)COMMENT the following rules are removed from the original TRS b ( c ( x ) ) -> b ( c ( x ) ) a ( a ( x ) ) -> a ( a ( x ) )
Rewrite Rules:
   [ b(b(?x)) -> b(a(?x)),
     a(c(?x)) -> b(a(?x)),
     a(c(?x)) -> c(b(?x)),
     c(c(?x)) -> b(c(?x)),
     c(b(?x)) -> b(a(?x)),
     a(b(?x)) -> a(c(?x)) ]
Apply Direct Methods...
Inner CPs:
   [ a(b(c(?x_3))) = b(a(c(?x_3))),
     a(b(a(?x_4))) = b(a(b(?x_4))),
     a(b(c(?x_3))) = c(b(c(?x_3))),
     a(b(a(?x_4))) = c(b(b(?x_4))),
     c(b(a(?x_4))) = b(c(b(?x_4))),
     c(b(a(?x))) = b(a(b(?x))),
     a(b(a(?x))) = a(c(b(?x))),
     b(b(a(?x))) = b(a(b(?x))),
     c(b(c(?x))) = b(c(c(?x))) ]
Outer CPs:
   [ b(a(?x_1)) = c(b(?x_1)) ]
not Overlay, check Termination...
unknown/not Terminating
unknown Knuth & Bendix
Linear
unknown Development Closed
unknown Strongly Closed
unknown Weakly-Non-Overlapping & Non-Collapsing & Shallow
inner CP cond (upside-parallel)
innter CP Cond (outside)
unknown Upside-Parallel-Closed/Outside-Closed
(inner) Parallel CPs: (not computed)
unknown Toyama (Parallel CPs)
Simultaneous CPs:
   [ b(b(a(?x_1))) = b(a(b(?x_1))),
     b(a(b(a(?x_1)))) = b(b(a(b(?x_1)))),
     b(a(b(a(?x_1)))) = c(b(a(b(?x_1)))),
     a(c(b(a(?x_1)))) = a(b(a(b(?x_1)))),
     b(a(b(?x))) = b(b(a(?x))),
     b(a(b(?x))) = c(b(a(?x))),
     a(c(b(?x))) = a(b(a(?x))),
     c(b(?x)) = b(a(?x)),
     a(b(c(?x_4))) = b(a(c(?x_4))),
     a(b(a(?x_5))) = b(a(b(?x_5))),
     b(a(?x)) = c(b(?x)),
     a(b(c(?x_4))) = c(b(c(?x_4))),
     a(b(a(?x_5))) = c(b(b(?x_5))),
     c(b(c(?x_1))) = b(c(c(?x_1))),
     c(b(a(?x_5))) = b(c(b(?x_5))),
     b(c(b(c(?x_1)))) = c(b(c(c(?x_1)))),
     b(c(b(a(?x_5)))) = c(b(c(b(?x_5)))),
     b(a(b(c(?x_1)))) = a(b(c(c(?x_1)))),
     b(a(b(a(?x_5)))) = a(b(c(b(?x_5)))),
     c(b(b(c(?x_1)))) = a(b(c(c(?x_1)))),
     c(b(b(a(?x_5)))) = a(b(c(b(?x_5)))),
     b(c(c(?x))) = c(b(c(?x))),
     b(a(c(?x))) = a(b(c(?x))),
     c(b(c(?x))) = a(b(c(?x))),
     c(b(a(?x_2))) = b(a(b(?x_2))),
     b(a(b(a(?x_2)))) = a(b(a(b(?x_2)))),
     c(b(b(a(?x_2)))) = a(b(a(b(?x_2)))),
     b(c(b(a(?x_2)))) = c(b(a(b(?x_2)))),
     b(a(b(?x))) = a(b(a(?x))),
     c(b(b(?x))) = a(b(a(?x))),
     b(c(b(?x))) = c(b(a(?x))),
     a(b(a(?x_2))) = a(c(b(?x_2))) ]
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_3))), b(a(c(?x_3)))> by Rules <3, 1> preceded by [(a,1)]
 joinable by a reduction of rules <[([],5),([],1)], []>
Critical Pair <a(b(a(?x_4))), b(a(b(?x_4)))> by Rules <4, 1> preceded by [(a,1)]
 joinable by a reduction of rules <[([],5),([],1)], [([(b,1)],5),([(b,1)],1),([],0)]>
 joinable by a reduction of rules <[([],5),([],2),([],4)], [([(b,1)],5),([(b,1)],1),([],0)]>
Critical Pair <a(b(c(?x_3))), c(b(c(?x_3)))> by Rules <3, 2> preceded by [(a,1)]
 joinable by a reduction of rules <[([],5),([],2)], []>
 joinable by a reduction of rules <[([],5),([],1)], [([],4)]>
Critical Pair <a(b(a(?x_4))), c(b(b(?x_4)))> by Rules <4, 2> preceded by [(a,1)]
 joinable by a reduction of rules <[([],5),([],2)], [([(c,1)],0)]>
 joinable by a reduction of rules <[([],5),([],1)], [([(c,1)],0),([],4)]>
Critical Pair <c(b(a(?x_4))), b(c(b(?x_4)))> by Rules <4, 3> preceded by [(c,1)]
 joinable by a reduction of rules <[([],4)], [([(b,1)],4),([],0)]>
Critical Pair <c(b(a(?x))), b(a(b(?x)))> by Rules <0, 4> preceded by [(c,1)]
 joinable by a reduction of rules <[([],4)], [([(b,1)],5),([(b,1)],1),([],0)]>
Critical Pair <a(b(a(?x))), a(c(b(?x)))> by Rules <0, 5> preceded by [(a,1)]
 joinable by a reduction of rules <[], [([(a,1)],4)]>
Critical Pair <b(b(a(?x))), b(a(b(?x)))> by Rules <0, 0> preceded by [(b,1)]
 joinable by a reduction of rules <[], [([(b,1)],5),([(b,1)],1)]>
Critical Pair <c(b(c(?x))), b(c(c(?x)))> by Rules <3, 3> preceded by [(c,1)]
 joinable by a reduction of rules <[([],4)], [([(b,1)],3),([],0)]>
Critical Pair <c(b(?x_2)), b(a(?x_2))> by Rules <2, 1> preceded by []
 joinable by a reduction of rules <[([],4)], []>
Satisfiable by 4>5,2,1>3>6; a(1)b(1)c(1); 4>3>2,1,5>6
Diagram Decreasing
Direct Methods: CR

Combined result: CR
/tmp/fileSplHNS.trs: Success(CR)
(27 msec.)