YES
(ignored inputs)COMMENT TPDB SRS_Standard/Secret_06_SRS/secr6
input TRS:
   [ a(b(c(?x))) -> c(c(c(b(b(b(a(a(a(?x))))))))),
     c(b(?x)) -> a(a(a(?x))),
     a(?x) -> ?x,
     b(?x) -> ?x,
     c(?x) -> ?x ]
Try persistent and layer-preserving decomposition...
Sort Assignment:
 a : 12=>12
 b : 12=>12
 c : 12=>12
maximal types: {12}
...decomposition failed.
TRS:
   [ a(b(c(?x))) -> c(c(c(b(b(b(a(a(a(?x))))))))),
     c(b(?x)) -> a(a(a(?x))),
     a(?x) -> ?x,
     b(?x) -> ?x,
     c(?x) -> ?x ]
unknown Non-Omega-Overlapping
unknown Right-Reducible
Check distinct normal forms in critical pair closure...failed
New rules by rule reversing:
   [ c(c(c(b(b(b(a(a(a(?x))))))))) -> a(b(c(?x))),
     a(a(a(?x))) -> c(b(?x)),
     a(?x) -> ?x,
     b(?x) -> ?x,
     c(?x) -> ?x ]
unknown UNC Completion (Strongly Closed)
unknown UNC Completion (Development Closed)
Obtained TRSs:
   [ c(c(c(b(b(b(a(a(a(?x))))))))) -> a(b(c(?x))),
     a(a(a(?x))) -> c(b(?x)),
     a(?x) -> ?x,
     b(?x) -> ?x,
     c(?x) -> ?x ]
unknown UNC Completion (General)
Check distinct normal forms in critical pair closure...failed
Try to prove CR of the result of rule reversing transformation...
Rewrite Rules:
   [ c(c(c(b(b(b(a(a(a(?x))))))))) -> a(b(c(?x))),
     a(a(a(?x))) -> c(b(?x)),
     a(?x) -> ?x,
     b(?x) -> ?x,
     c(?x) -> ?x ]
Apply Direct Methods...
Inner CPs:
   [ c(c(c(b(b(b(c(b(?x_1)))))))) = a(b(c(?x_1))),
     c(c(c(b(b(b(a(c(b(?x_1))))))))) = a(b(c(a(?x_1)))),
     c(c(c(b(b(b(a(a(c(b(?x_1)))))))))) = a(b(c(a(a(?x_1))))),
     c(c(c(b(b(b(a(a(?x)))))))) = a(b(c(?x))),
     c(c(c(b(b(b(a(a(?x)))))))) = a(b(c(?x))),
     c(c(c(b(b(b(a(a(?x_2)))))))) = a(b(c(?x_2))),
     c(c(c(b(b(a(a(a(?x)))))))) = a(b(c(?x))),
     c(c(c(b(b(a(a(a(?x)))))))) = a(b(c(?x))),
     c(c(c(b(b(a(a(a(?x)))))))) = a(b(c(?x))),
     c(c(b(b(b(a(a(a(?x)))))))) = a(b(c(?x))),
     c(c(b(b(b(a(a(a(?x)))))))) = a(b(c(?x))),
     a(a(?x_1)) = c(b(?x_1)),
     a(a(?x_2)) = c(b(?x_2)),
     a(c(b(?x))) = c(b(a(?x))),
     a(a(c(b(?x)))) = c(b(a(a(?x)))) ]
Outer CPs:
   [ a(b(c(?x))) = c(c(b(b(b(a(a(a(?x)))))))),
     c(b(?x_1)) = a(a(?x_1)) ]
not Overlay, check Termination...
Terminating, WCR
Knuth & Bendix
Direct Methods: CR

Combined result: CR
...CR proof of the result of rule reversing transformation is successful.
problems/938.trs: Success(UNC)
(1716 msec.)