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

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

Make it Complete (R^):
   [ b = f(!cl_1),
     !cl_0 = f(!cl_1),
     c = f(!cl_1),
     f(!cl_1) = h(a,c),
     f(!cl_1) = h(b,c),
     f(!cl_1) = h(c,c),
     f(!cl_1) = h(b,a),
     f(!cl_1) = h(b,!cl_0),
     f(!cl_1) = h(!cl_0,a),
     f(!cl_1) = h(!cl_0,b),
     f(!cl_1) = h(!cl_0,!cl_0),
     f(!cl_1) = h(a,!cl_0),
     f(!cl_1) = h(c,!cl_0),
     f(!cl_1) = h(!cl_0,c),
     f(!cl_1) = h(c,a),
     f(!cl_1) = h(b,b),
     f(!cl_1) = h(a,b),
     f(!cl_1) = h(c,b),
     f(!cl_1) = h(a,a),
     f(!cl_1) = a,
     f(a) = !cl_1,
     f(c) = !cl_1,
     f(a) = f(b),
     f(c) = f(b),
     f(c) = f(!cl_0),
     f(c) = f(a),
     f(a) = f(!cl_0),
     f(b) = f(!cl_0),
     f(b) = !cl_1,
     f(!cl_0) = !cl_1,
     a = c,
     a = h(a,a),
     h(a,a) = !cl_0,
     h(a,a) = h(c,a),
     h(a,b) = b,
     h(b,a) = b,
     h(a,b) = c,
     h(b,a) = c,
     h(b,b) = !cl_0,
     h(c,b) = !cl_0,
     h(b,b) = h(c,a),
     h(c,a) = h(c,b),
     h(a,a) = h(c,b),
     h(b,b) = h(c,b),
     h(b,b) = h(b,a),
     h(c,a) = h(c,c),
     h(a,a) = h(c,c),
     h(b,b) = h(c,c),
     h(b,c) = h(b,a),
     h(c,c) = !cl_0,
     h(b,b) = h(b,c),
     h(c,c) = h(b,c),
     h(c,a) = h(b,c),
     h(b,b) = h(a,c),
     h(c,c) = h(a,c),
     h(c,a) = h(a,c),
     h(a,b) = h(c,b),
     h(a,c) = h(b,a),
     h(b,b) = h(a,b),
     h(c,c) = h(a,b),
     h(a,c) = h(a,b),
     h(b,b) = h(a,a),
     h(a,c) = h(a,a),
     h(a,a) = h(a,b),
     h(b,c) = b,
     h(b,b) = c,
     h(c,c) = c,
     h(a,c) = c,
     h(c,a) = c,
     h(b,b) = b,
     h(c,c) = b,
     h(c,a) = b,
     a = h(c,b),
     h(a,b) = a,
     h(b,b) = a,
     h(c,a) = a,
     h(a,!cl_0) = b,
     h(!cl_0,a) = b,
     h(a,!cl_0) = c,
     h(!cl_0,a) = c,
     h(b,!cl_0) = !cl_0,
     h(c,!cl_0) = !cl_0,
     h(b,!cl_0) = h(c,a),
     h(c,!cl_0) = h(b,a),
     !cl_0 = b,
     h(b,!cl_0) = h(c,b),
     h(b,!cl_0) = h(c,c),
     h(!cl_0,c) = h(c,b),
     h(!cl_0,c) = h(b,c),
     h(!cl_0,b) = h(b,c),
     h(a,!cl_0) = h(b,c),
     h(!cl_0,a) = h(b,c),
     h(!cl_0,c) = b,
     h(!cl_0,c) = a,
     !cl_0 = h(a,c),
     !cl_0 = h(b,c),
     b = h(b,!cl_0),
     h(c,!cl_0) = a,
     h(a,!cl_0) = a,
     h(b,!cl_0) = h(a,c),
     h(b,!cl_0) = h(b,c),
     h(a,a) = h(b,!cl_0),
     h(b,b) = h(b,!cl_0),
     h(c,a) = h(a,!cl_0),
     h(a,a) = h(a,!cl_0),
     h(b,b) = h(a,!cl_0),
     h(b,!cl_0) = h(a,!cl_0),
     h(a,a) = h(b,a),
     h(!cl_0,!cl_0) = h(b,a),
     h(a,!cl_0) = !cl_0,
     h(a,!cl_0) = h(c,b),
     h(c,b) = h(!cl_0,!cl_0),
     h(b,c) = h(!cl_0,!cl_0),
     h(!cl_0,a) = h(c,c),
     h(!cl_0,!cl_0) = a,
     h(b,!cl_0) = h(!cl_0,!cl_0),
     h(a,a) = h(!cl_0,!cl_0),
     h(b,!cl_0) = h(!cl_0,a),
     h(a,a) = h(!cl_0,a),
     h(!cl_0,!cl_0) = h(!cl_0,a),
     h(!cl_0,b) = h(a,!cl_0),
     h(c,a) = h(!cl_0,a),
     h(b,b) = h(!cl_0,a),
     h(!cl_0,b) = h(b,a),
     h(!cl_0,a) = !cl_0,
     h(!cl_0,a) = h(c,b),
     h(!cl_0,b) = a,
     h(a,b) = h(!cl_0,a),
     h(!cl_0,c) = h(!cl_0,a),
     h(!cl_0,b) = h(a,c),
     h(!cl_0,!cl_0) = h(a,c),
     h(a,b) = h(a,!cl_0),
     h(b,!cl_0) = h(!cl_0,c),
     h(a,a) = h(!cl_0,c),
     h(!cl_0,!cl_0) = h(!cl_0,c),
     h(!cl_0,c) = h(b,a),
     h(!cl_0,c) = h(c,c),
     h(!cl_0,b) = h(a,b),
     h(c,c) = h(!cl_0,b),
     h(!cl_0,c) = h(c,a),
     h(a,b) = h(c,a),
     h(c,!cl_0) = h(!cl_0,b),
     h(c,a) = h(!cl_0,!cl_0),
     h(!cl_0,c) = !cl_0,
     h(a,b) = !cl_0,
     !cl_0 = h(!cl_0,!cl_0),
     h(c,!cl_0) = h(c,b),
     h(b,a) = h(a,b),
     h(b,!cl_0) = h(a,b),
     h(b,!cl_0) = h(!cl_0,b),
     h(b,!cl_0) = c,
     h(c,!cl_0) = h(a,!cl_0),
     h(c,!cl_0) = h(!cl_0,!cl_0),
     h(c,!cl_0) = h(c,c),
     h(c,!cl_0) = b,
     h(c,!cl_0) = c,
     h(c,!cl_0) = h(b,b),
     h(a,c) = h(c,!cl_0),
     h(c,a) = h(c,!cl_0),
     h(!cl_0,a) = h(c,!cl_0),
     h(a,a) = h(c,!cl_0),
     h(b,!cl_0) = h(c,!cl_0),
     h(c,!cl_0) = h(b,c),
     h(c,!cl_0) = h(!cl_0,c),
     h(c,!cl_0) = h(a,b),
     !cl_0 = c,
     h(!cl_0,b) = !cl_0,
     h(c,a) = h(!cl_0,b),
     h(!cl_0,c) = c,
     h(!cl_0,b) = c,
     h(a,b) = h(!cl_0,!cl_0),
     h(!cl_0,!cl_0) = h(b,b),
     c = h(!cl_0,!cl_0),
     h(!cl_0,!cl_0) = b,
     h(!cl_0,!cl_0) = h(!cl_0,b),
     h(!cl_0,a) = h(!cl_0,b),
     h(!cl_0,b) = h(a,a),
     h(!cl_0,b) = b,
     h(c,b) = h(!cl_0,b),
     h(!cl_0,b) = h(b,b),
     h(b,b) = h(!cl_0,c),
     h(!cl_0,b) = h(!cl_0,c),
     h(a,b) = h(!cl_0,c),
     h(!cl_0,c) = h(a,c),
     h(!cl_0,c) = h(a,!cl_0),
     h(a,c) = h(a,!cl_0),
     h(!cl_0,a) = h(a,c),
     h(!cl_0,a) = a,
     h(!cl_0,a) = h(b,a),
     h(!cl_0,a) = h(a,!cl_0),
     h(!cl_0,!cl_0) = h(a,!cl_0),
     h(!cl_0,!cl_0) = h(c,c),
     h(a,!cl_0) = h(c,c),
     h(a,!cl_0) = h(b,a),
     h(b,!cl_0) = h(b,a),
     h(b,!cl_0) = a,
     a = !cl_0,
     a = h(b,a),
     h(c,c) = a,
     h(b,c) = a,
     a = h(a,c),
     b = h(a,c),
     b = h(c,b),
     c = h(c,b),
     h(b,c) = c,
     h(a,a) = h(b,c),
     h(a,b) = h(b,c),
     h(a,c) = h(b,c),
     h(a,c) = h(c,b),
     h(b,c) = h(c,b),
     h(c,c) = h(c,b),
     h(c,c) = h(b,a),
     h(c,b) = h(b,a),
     a = b,
     h(c,a) = h(b,a),
     h(c,a) = !cl_0,
     h(b,a) = !cl_0,
     c = h(a,a),
     h(a,a) = b,
     b = c ]
Time: 1.704 [s]

CPNF:
   [ !cl_0 … h(c,c),
     !cl_0 … c ]
Time: 0.000 [s]

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

proof:
     h(c,c)
->R^ h(b,c)
->R^ h(a,c)
->R^ h(!cl_0,c)
->R^ h(!cl_0,b)
->R^ h(!cl_0,a)
->R^ h(!cl_0,!cl_0)
->R^ b
->R^ a
->R^ !cl_0

     c
->R^ b
->R^ a
->R^ !cl_0
Total Time: 1.713 [s]

problems/682.trs: Success(not UNC)
real 1.73
user 1.72
sys 0.00