NO
(ignored inputs)COMMENT cops number: 38 submitted by: Takahito Aoto , Junichi Yoshida , Yoshihito Toyama [11] Example 3.3.1
input TRS:
   [ b -> a,
     b -> c,
     c -> b,
     c -> d ]
Try persistent and layer-preserving decomposition...
Sort Assignment:
 a : =>5
 b : =>5
 c : =>5
 d : =>5
maximal types: {5}
...decomposition failed.
TRS:
   [ b -> a,
     b -> c,
     c -> b,
     c -> d ]
Input:
   [ b -> a,
     b -> c,
     c -> b,
     c -> d ]

Make it flat:
   [ b -> a,
     b -> c,
     c -> b,
     c -> d ]
Time: 0.000 [s]

Make it Complete (R^):
   [ a = c,
     a = d,
     b = a,
     b = d,
     b = c,
     c = d ]
Time: 0.001 [s]

CPNF:
   [ a … a,
     a … d ]
Time: 0.000 [s]

The TRS doesn't have Uniqueness of Normal Forms.
Counter Example: 
     a
<->* d

proof:
     a

     d
->R^ c
->R^ b
->R^ a
Total Time: 0.001 [s]

cops-LMxTnH3N.trs: Success(not UNC)
(1 msec.)