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

Make it flat:
   [ f(!cl_3) -> f(c),
     c -> h(c,c),
     h(!cl_2,a) -> c,
     !cl_3 -> !cl_3,
     h(b,!cl_1) -> !cl_3,
     f(a) -> !cl_1,
     h(a,a) -> a,
     f(b) -> !cl_0,
     !cl_0 -> !cl_0,
     b -> a,
     f(!cl_0) -> !cl_2,
     !cl_2 -> !cl_2 ]
Time: 0.000 [s]

Make it Complete (R^):
   [ f(!cl_3) = f(c),
     h(c,c) = h(!cl_2,a),
     h(c,c) = h(!cl_2,b),
     c = h(c,c),
     h(!cl_2,b) = h(!cl_2,a),
     h(!cl_2,b) = c,
     h(!cl_2,a) = c,
     h(a,!cl_1) = !cl_3,
     h(a,!cl_0) = !cl_3,
     h(a,!cl_1) = h(b,!cl_0),
     h(a,!cl_1) = h(a,!cl_0),
     h(b,!cl_0) = h(a,!cl_0),
     h(a,!cl_1) = h(b,!cl_1),
     h(a,!cl_0) = h(b,!cl_1),
     h(b,!cl_0) = h(b,!cl_1),
     h(b,!cl_0) = !cl_3,
     h(b,!cl_1) = !cl_3,
     f(b) = !cl_1,
     f(!cl_1) = f(!cl_0),
     f(!cl_1) = !cl_2,
     !cl_1 = !cl_0,
     f(a) = !cl_1,
     b = h(a,a),
     h(a,b) = a,
     b = h(b,a),
     h(a,b) = b,
     b = h(b,b),
     h(b,b) = a,
     h(a,b) = h(b,a),
     h(a,b) = h(b,b),
     h(b,a) = h(b,b),
     h(a,b) = h(a,a),
     h(b,b) = h(a,a),
     h(b,a) = h(a,a),
     h(b,a) = a,
     h(a,a) = a,
     f(a) = f(b),
     f(a) = !cl_0,
     f(b) = !cl_0,
     b = a,
     f(!cl_0) = !cl_2 ]
Time: 0.010 [s]

CPNF:
   [ c … h(h(f(!cl_1),a),h(f(!cl_1),a)),
     c … h(f(!cl_1),a),
     !cl_3 … h(a,!cl_1),
     !cl_2 … f(!cl_1),
     !cl_0 … !cl_1,
     a … a ]
Time: 0.000 [s]

The TRS doesn't have Uniqueness of Normal Forms.
Counter Example: 
     h(h(f(!cl_1),a),h(f(!cl_1),a))
<->* h(f(!cl_1),a)

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

     h(f(!cl_1),a)
->R^ h(f(!cl_0),a)
->R^ h(!cl_2,a)
->R^ c
Total Time: 0.011 [s]

problems/655.trs: Success(not UNC)
real 0.03
user 0.02
sys 0.01