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

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

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

CPNF:
   [ b … f(c),
     a … c,
     !cl_0 … !cl_0,
     b … b ]
Time: 0.000 [s]

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

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

     b
Total Time: 0.001 [s]

problems/713.trs: Success(not UNC)
real 0.02
user 0.01
sys 0.01