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

Make it flat:
   [ c -> a,
     !cr_0 -> h(b,c),
     f(c) -> f(!cr_0),
     a -> c,
     !cr_1 -> f(c),
     !cr_2 -> h(b,c),
     !cr_3 -> h(!cr_2,a),
     !cr_4 -> h(b,!cr_3),
     c -> h(!cr_1,!cr_4),
     c -> b ]
Time: 0.000 [s]

Make it Complete (R^):
   [ h(!cr_2,c) = !cr_3,
     h(!cr_0,c) = !cr_3,
     h(!cr_2,c) = h(!cr_0,a),
     h(!cr_0,c) = h(!cr_2,a),
     h(!cr_2,b) = !cr_3,
     h(!cr_0,b) = !cr_3,
     h(!cr_2,b) = h(!cr_0,a),
     h(!cr_0,a) = h(!cr_0,b),
     h(!cr_2,c) = h(!cr_0,b),
     h(!cr_2,b) = h(!cr_0,b),
     h(!cr_2,c) = h(!cr_0,c),
     h(!cr_0,a) = h(!cr_0,c),
     h(!cr_0,b) = h(!cr_0,c),
     h(!cr_0,c) = h(!cr_2,b),
     h(!cr_2,c) = h(!cr_2,b),
     h(!cr_2,c) = h(!cr_2,a),
     h(!cr_2,b) = h(!cr_2,a),
     h(!cr_0,b) = h(!cr_2,a),
     a = b,
     a = h(!cr_1,!cr_4),
     h(a,!cr_3) = !cr_4,
     h(c,!cr_3) = h(a,!cr_3),
     h(a,!cr_3) = h(b,!cr_3),
     h(b,a) = !cr_2,
     h(b,a) = h(b,b),
     h(b,a) = h(c,b),
     h(a,b) = h(b,c),
     h(b,a) = h(c,c),
     h(c,a) = h(b,c),
     h(a,c) = h(b,c),
     h(a,b) = h(b,b),
     h(a,b) = h(c,c),
     h(c,a) = h(c,b),
     h(a,c) = h(c,b),
     h(c,a) = h(b,b),
     h(a,c) = h(b,b),
     h(a,b) = !cr_2,
     h(c,a) = !cr_2,
     h(a,c) = !cr_2,
     f(a) = !cr_1,
     f(a) = f(b),
     f(a) = f(!cr_0),
     h(b,a) = !cr_0,
     h(a,b) = !cr_0,
     f(a) = f(c),
     f(a) = f(!cr_2),
     h(c,a) = !cr_0,
     h(a,a) = !cr_0,
     h(c,a) = h(a,c),
     h(c,b) = h(a,b),
     h(c,b) = h(a,a),
     h(b,c) = h(b,a),
     h(b,c) = h(a,a),
     h(c,a) = h(a,a),
     h(a,c) = h(a,b),
     h(a,c) = h(b,a),
     h(b,a) = h(a,a),
     h(b,a) = h(c,a),
     h(b,a) = h(a,b),
     h(c,a) = h(a,b),
     h(a,b) = h(a,a),
     h(a,c) = h(a,a),
     h(c,a) = h(c,c),
     h(a,a) = h(b,b),
     h(a,a) = !cr_2,
     h(a,a) = h(c,c),
     h(a,c) = h(c,c),
     h(a,c) = !cr_0,
     c = a,
     h(c,c) = !cr_0,
     h(b,b) = !cr_0,
     h(!cr_0,a) = h(!cr_2,a),
     h(!cr_0,a) = !cr_3,
     f(!cr_2) = f(c),
     f(!cr_2) = !cr_1,
     f(!cr_2) = f(!cr_0),
     f(!cr_2) = f(b),
     !cr_0 = !cr_2,
     !cr_0 = h(c,b),
     !cr_0 = h(b,c),
     f(b) = f(!cr_0),
     f(!cr_0) = !cr_1,
     f(c) = f(!cr_0),
     f(b) = f(c),
     f(b) = !cr_1,
     !cr_1 = f(c),
     h(c,c) = !cr_2,
     h(c,b) = !cr_2,
     h(c,c) = h(b,b),
     h(c,c) = h(c,b),
     h(b,b) = h(c,b),
     h(c,c) = h(b,c),
     h(c,b) = h(b,c),
     h(b,b) = h(b,c),
     h(b,b) = !cr_2,
     !cr_2 = h(b,c),
     !cr_3 = h(!cr_2,a),
     h(c,!cr_3) = h(b,!cr_3),
     h(c,!cr_3) = !cr_4,
     !cr_4 = h(b,!cr_3),
     b = h(!cr_1,!cr_4),
     c = h(!cr_1,!cr_4),
     c = b ]
Time: 0.125 [s]

CPNF:
   [ !cr_1 … f(h(b,b)),
     !cr_3 … h(h(b,b),b),
     !cr_0 … h(b,b),
     !cr_1 … f(b),
     a … b ]
Time: 0.000 [s]

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

proof:
     f(h(b,b))
->R^ f(h(a,b))
->R^ f(h(a,a))
->R^ f(!cr_2)
->R^ f(!cr_0)
->R^ !cr_1

     f(b)
->R^ f(a)
->R^ f(!cr_2)
->R^ f(!cr_0)
->R^ !cr_1
Total Time: 0.128 [s]

problems/712.trs: Success(not UNC)
real 0.15
user 0.14
sys 0.00