YES
(ignored inputs)COMMENT TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-95
input TRS:
   [ a(?x) -> ?x,
     a(a(?x)) -> b(c(?x)),
     b(?x) -> ?x,
     c(?x) -> ?x,
     c(b(?x)) -> b(a(c(?x))) ]
TRS:
   [ a(?x) -> ?x,
     a(a(?x)) -> b(c(?x)),
     b(?x) -> ?x,
     c(?x) -> ?x,
     c(b(?x)) -> b(a(c(?x))) ]
unknown Non-Omega-Overlapping
unknown Right-Reducible
Check distinct normal forms in critical pair closure...failed
New rules by rule reversing:
   [ a(?x) -> ?x,
     a(a(?x)) -> b(c(?x)),
     b(?x) -> ?x,
     c(?x) -> ?x,
     b(a(c(?x))) -> c(b(?x)) ]
unknown UNC Completion (Strongly Closed)
unknown UNC Completion (Development Closed)
Obtained TRSs:
   [ a(?x) -> ?x,
     a(a(?x)) -> b(c(?x)),
     b(?x) -> ?x,
     c(?x) -> ?x,
     b(a(c(?x))) -> c(b(?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:
   [ a(?x) -> ?x,
     a(a(?x)) -> b(c(?x)),
     b(?x) -> ?x,
     c(?x) -> ?x,
     b(a(c(?x))) -> c(b(?x)) ]
Apply Direct Methods...
Inner CPs:
   [ a(?x) = b(c(?x)),
     b(c(?x_4)) = c(b(?x_4)),
     b(a(?x_3)) = c(b(?x_3)),
     a(b(c(?x))) = b(c(a(?x))) ]
Outer CPs:
   [ a(?x_1) = b(c(?x_1)),
     a(c(?x_4)) = c(b(?x_4)) ]
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/982.trs: Success(UNC)
(20 msec.)