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

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

Make it Complete (R^):
   [ h(c,c) = b,
     h(a,a) = b,
     h(c,c) = f(b),
     h(c,a) = f(b),
     h(c,c) = h(a,a),
     h(c,c) = h(c,a),
     h(a,a) = h(c,a),
     h(c,c) = h(a,c),
     h(c,a) = b,
     h(c,a) = h(a,c),
     h(a,a) = h(a,c),
     h(a,a) = f(b),
     h(a,c) = f(b),
     h(a,c) = b,
     c = a,
     b = f(b) ]
Time: 0.003 [s]

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

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

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

     h(a,a)
->R^ f(b)
->R^ b
Total Time: 0.003 [s]

problems/696.trs: Success(not UNC)
real 0.02
user 0.01
sys 0.00