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 -> a,
     b -> f(h(a,a)),
     f(a) -> b,
     h(a,b) -> a ]

Make it flat:
   [ c -> a,
     !cr_0 -> h(a,a),
     b -> f(!cr_0),
     f(a) -> b,
     h(a,b) -> a ]
Time: 0.000 [s]

Make it Complete (R^):
   [ c = h(a,b),
     c = h(c,b),
     h(c,b) = h(a,b),
     h(c,b) = a,
     f(c) = b,
     f(c) = f(a),
     f(c) = f(!cr_0),
     h(a,c) = !cr_0,
     h(c,c) = !cr_0,
     h(a,c) = h(c,a),
     h(a,c) = h(c,c),
     h(c,a) = h(c,c),
     h(a,c) = h(a,a),
     h(c,c) = h(a,a),
     h(c,a) = h(a,a),
     h(c,a) = !cr_0,
     c = a,
     !cr_0 = h(a,a),
     f(!cr_0) = f(a),
     b = f(!cr_0),
     f(a) = b,
     h(a,b) = a ]
Time: 0.004 [s]

CPNF:
   [ a … h(a,f(h(a,a))),
     b … f(h(a,a)),
     !cr_0 … h(a,a),
     a … a ]
Time: 0.000 [s]

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

proof:
     h(a,f(h(a,a)))
->R^ h(a,f(!cr_0))
->R^ h(a,b)
->R^ a

     a
Total Time: 0.005 [s]

problems/653.trs: Success(not UNC)
real 0.02
user 0.01
sys 0.01