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

Make it flat:
   [ f(!cl_2) -> f(a),
     h(a,!cl_1) -> f(!cr_1),
     !cl_2 -> !cl_2,
     h(b,!cl_0) -> !cl_2,
     !cr_1 -> h(b,!cr_0),
     !cr_0 -> f(c),
     a -> f(a),
     h(b,a) -> b,
     c -> b,
     !cl_0 -> !cl_0,
     f(c) -> !cl_0,
     h(c,c) -> !cl_1,
     !cl_1 -> !cl_1 ]
Time: 0.000 [s]

Make it Complete (R^):
   [ f(!cr_1) = f(a),
     f(!cl_2) = a,
     a = f(!cr_1),
     h(a,!cl_1) = a,
     f(a) = h(a,!cl_1),
     f(!cl_2) = f(a),
     f(!cl_2) = f(!cr_1),
     f(!cl_2) = h(a,!cl_1),
     h(a,!cl_1) = f(!cr_1),
     h(c,!cl_0) = !cl_2,
     h(b,!cr_0) = !cl_2,
     !cl_2 = !cr_1,
     !cl_2 = h(c,!cr_0),
     h(b,!cl_0) = !cl_2,
     h(c,!cr_0) = !cr_1,
     h(c,!cl_0) = !cr_1,
     h(c,!cr_0) = h(b,!cl_0),
     h(c,!cr_0) = h(c,!cl_0),
     h(b,!cl_0) = h(c,!cl_0),
     h(c,!cr_0) = h(b,!cr_0),
     h(c,!cl_0) = h(b,!cr_0),
     h(b,!cl_0) = h(b,!cr_0),
     h(b,!cl_0) = !cr_1,
     !cr_1 = h(b,!cr_0),
     f(b) = !cr_0,
     !cr_0 = !cl_0,
     !cr_0 = f(c),
     a = f(a),
     c = h(b,a),
     c = h(c,a),
     h(c,a) = h(b,a),
     h(c,a) = b,
     h(b,a) = b,
     h(c,b) = !cl_1,
     h(b,b) = !cl_1,
     h(c,b) = h(b,c),
     h(c,b) = h(b,b),
     h(b,c) = h(b,b),
     h(c,b) = h(c,c),
     h(b,b) = h(c,c),
     h(b,c) = h(c,c),
     h(b,c) = !cl_1,
     f(b) = f(c),
     f(b) = !cl_0,
     c = b,
     f(c) = !cl_0,
     h(c,c) = !cl_1 ]
Time: 0.016 [s]

CPNF:
   [ a … h(f(h(b,f(b))),h(b,b)),
     a … f(h(b,f(b))),
     !cl_2 … h(b,f(b)),
     !cl_0 … f(b),
     !cl_1 … h(b,b),
     b … b ]
Time: 0.000 [s]

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

proof:
     h(f(h(b,f(b))),h(b,b))
->R^ h(f(h(b,!cl_0)),h(b,b))
->R^ h(f(!cr_1),h(b,b))
->R^ h(f(!cl_2),h(b,b))
->R^ h(a,h(b,b))
->R^ h(a,!cl_1)
->R^ f(!cr_1)
->R^ f(!cl_2)
->R^ a

     f(h(b,f(b)))
->R^ f(h(b,!cl_0))
->R^ f(!cr_1)
->R^ f(!cl_2)
->R^ a
Total Time: 0.018 [s]

problems/694.trs: Success(not UNC)
real 0.04
user 0.03
sys 0.00