YES
(ignored inputs)COMMENT cops number: 706 submitted by: Bertram Felgenhauer Cops #647 - #721: generated ground TRSs; evenly distributed in the UNR/UNC/NFP/CR hierarchy
input TRS:
   [ f(h(c,c)) -> a,
     a -> b,
     f(b) -> f(c),
     c -> f(c) ]
Try persistent and layer-preserving decomposition...
Sort Assignment:
 a : =>9
 b : =>9
 c : =>9
 f : 9=>9
 h : 9*9=>9
maximal types: {9}
...decomposition failed.
TRS:
   [ f(h(c,c)) -> a,
     a -> b,
     f(b) -> f(c),
     c -> f(c) ]
Input:
   [ f(h(c,c)) -> a,
     a -> b,
     f(b) -> f(c),
     c -> f(c) ]

Make it flat:
   [ f(!cl_0) -> a,
     !cl_0 -> !cl_0,
     h(c,c) -> !cl_0,
     c -> f(c),
     f(b) -> f(c),
     a -> b ]
Time: 0.000 [s]

Make it Complete (R^):
   [ b = f(!cl_0),
     f(!cl_0) = a,
     h(c,c) = !cl_0,
     c = f(b),
     c = f(a),
     c = f(c),
     f(a) = f(b),
     f(a) = f(c),
     f(b) = f(c),
     a = b ]
Time: 0.001 [s]

CPNF:
   [ a … b ]
Time: 0.000 [s]

Now checking all the pairs in CW...

Time to check pairs: 0.000 [s]

The TRS has Uniqueness of Normal Forms.
Total Time: 0.001 [s]

cops-0ebQkme3.trs: Success(UNC)
(1 msec.)