YES
(ignored inputs)COMMENT submitted by: Johannes Waldmann
input TRS:
   [ a(c(?x)) -> c(a(?x)),
     a(a(?x)) -> a(a(?x)),
     a(b(?x)) -> c(a(?x)),
     a(a(?x)) -> a(c(?x)),
     c(a(?x)) -> c(b(?x)),
     b(b(?x)) -> a(c(?x)),
     b(a(?x)) -> a(c(?x)),
     c(b(?x)) -> a(b(?x)),
     a(a(?x)) -> c(a(?x)) ]
Try persistent and layer-preserving decomposition...
Sort Assignment:
 a : 16=>16
 b : 16=>16
 c : 16=>16
maximal types: {16}
...decomposition failed.
TRS:
   [ a(c(?x)) -> c(a(?x)),
     a(a(?x)) -> a(a(?x)),
     a(b(?x)) -> c(a(?x)),
     a(a(?x)) -> a(c(?x)),
     c(a(?x)) -> c(b(?x)),
     b(b(?x)) -> a(c(?x)),
     b(a(?x)) -> a(c(?x)),
     c(b(?x)) -> a(b(?x)),
     a(a(?x)) -> c(a(?x)) ]
unknown Non-Omega-Overlapping
Right-Reducible
problems/1019.trs: Success(UNC)
(0 msec.)