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

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

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

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

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

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

     f(c)
->R^ f(a)
->R^ b
Total Time: 0.005 [s]

problems/669.trs: Success(not UNC)
real 0.02
user 0.02
sys 0.00