YES
(ignored inputs)COMMENT submitted by: Johannes Waldmann
input TRS:
   [ c(a(?x)) -> c(b(?x)),
     b(a(?x)) -> b(a(?x)),
     a(b(?x)) -> c(c(?x)),
     c(c(?x)) -> b(a(?x)),
     c(b(?x)) -> a(b(?x)),
     a(c(?x)) -> c(c(?x)),
     a(a(?x)) -> b(a(?x)) ]
Try persistent and layer-preserving decomposition...
Sort Assignment:
 a : 14=>14
 b : 14=>14
 c : 14=>14
maximal types: {14}
...decomposition failed.
TRS:
   [ c(a(?x)) -> c(b(?x)),
     b(a(?x)) -> b(a(?x)),
     a(b(?x)) -> c(c(?x)),
     c(c(?x)) -> b(a(?x)),
     c(b(?x)) -> a(b(?x)),
     a(c(?x)) -> c(c(?x)),
     a(a(?x)) -> b(a(?x)) ]
unknown Non-Omega-Overlapping
Right-Reducible
problems/1000.trs: Success(UNC)
(0 msec.)