NO
(ignored inputs)COMMENT Cops #647 - #721: generated ground TRSs; evenly distributed in the UNR/UNC/NFP/CR hierarchy submitted by: Bertram Felgenhauer
Input:
   [ c -> f(b),
     c -> b ]

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

Make it Complete (R^):
   [ f(c) = c,
     f(c) = f(b),
     f(c) = b,
     b = f(b),
     c = f(b),
     c = b ]
Time: 0.000 [s]

CPNF:
   [ b … f(b),
     b … b ]
Time: 0.000 [s]

The TRS doesn't have Uniqueness of Normal Forms.
Counter Example: 
     f(b)
<->* b

proof:
     f(b)
->R^ c
->R^ b

     b
Total Time: 0.000 [s]

problems/710.trs: Success(not UNC)
real 0.02
user 0.00
sys 0.01