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

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

Make it Complete (R^):
   [ b = h(c,c),
     h(c,b) = c,
     h(b,c) = c,
     h(b,c) = a,
     h(c,c) = a,
     h(b,c) = h(c,b),
     h(b,c) = h(c,c),
     h(c,b) = h(c,c),
     h(b,c) = h(b,b),
     b = h(b,b),
     h(c,a) = c,
     h(a,c) = c,
     a = b,
     h(a,b) = a,
     h(a,b) = h(b,b),
     h(c,a) = h(b,b),
     h(b,c) = h(a,c),
     h(c,b) = h(a,c),
     h(a,a) = h(b,b),
     h(a,c) = a,
     h(c,a) = h(a,c),
     h(a,b) = h(c,c),
     h(c,b) = h(a,a),
     h(b,c) = h(a,a),
     h(c,a) = h(a,a),
     h(a,c) = h(a,a),
     h(c,a) = h(c,c),
     b = h(a,a),
     h(b,a) = a,
     h(a,b) = h(c,a),
     h(b,b) = h(b,a),
     h(c,c) = h(b,a),
     h(a,b) = h(b,a),
     h(a,c) = h(b,a),
     h(c,a) = b,
     h(b,c) = h(a,b),
     h(b,c) = b,
     c = h(a,b),
     h(a,a) = h(a,b),
     h(a,c) = h(a,b),
     h(a,c) = b,
     h(a,b) = h(c,b),
     h(a,b) = b,
     b = h(c,b),
     b = h(b,a),
     h(b,a) = c,
     h(a,a) = h(b,a),
     h(b,a) = h(b,c),
     h(b,c) = h(c,a),
     h(b,a) = h(c,a),
     h(b,a) = h(c,b),
     h(c,a) = h(c,b),
     h(c,a) = a,
     a = h(a,a),
     h(a,a) = c,
     h(a,a) = h(c,c),
     h(a,c) = h(c,c),
     h(a,c) = h(b,b),
     c = a,
     h(b,b) = c,
     h(c,c) = h(b,b),
     h(c,b) = h(b,b),
     h(c,b) = a,
     b = c,
     h(b,b) = a,
     h(c,c) = c ]
Time: 0.084 [s]

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

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

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

     a
Total Time: 0.085 [s]

problems/673.trs: Success(not UNC)
real 0.10
user 0.09
sys 0.01