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

Make it flat:
   [ h(!cl_3,!cl_12) -> h(!cr_0,!cr_1),
     h(c,!cl_11) -> !cl_12,
     h(!cl_9,b) -> !cl_10,
     f(!cl_7) -> !cl_8,
     f(!cl_5) -> !cl_6,
     !cl_4 -> !cl_4,
     h(c,!cl_2) -> !cl_4,
     !cl_2 -> !cl_2,
     h(b,!cl_0) -> !cl_2,
     !cr_1 -> f(c),
     !cr_0 -> h(a,a),
     !cl_0 -> !cl_0,
     h(a,b) -> !cl_0,
     a -> f(!cr_3),
     !cr_3 -> f(b),
     !cl_1 -> f(!cr_2),
     !cr_2 -> f(a),
     f(c) -> !cl_1,
     !cl_1 -> !cl_1,
     f(!cl_1) -> !cl_3,
     !cl_3 -> !cl_3,
     f(b) -> !cl_5,
     h(b,!cl_4) -> a,
     f(!cl_6) -> !cl_7,
     h(!cl_5,!cl_8) -> !cl_9,
     h(c,!cl_10) -> !cl_11 ]
Time: 0.004 [s]

Make it Complete (R^):
   [ h(!cr_0,!cl_1) = h(!cl_3,!cl_12),
     h(!cr_0,!cl_1) = h(!cr_0,!cl_8),
     h(!cr_0,!cl_1) = h(!cr_0,!cr_1),
     h(!cr_0,!cl_8) = h(!cr_0,!cr_1),
     h(!cr_0,!cl_8) = h(!cl_3,!cl_12),
     h(!cl_3,!cl_12) = h(!cr_0,!cr_1),
     h(c,!cl_11) = !cl_12,
     h(!cl_9,b) = !cl_10,
     f(!cr_2) = !cl_8,
     !cl_8 = !cr_1,
     !cl_8 = f(c),
     f(!cl_8) = !cl_3,
     f(!cl_1) = f(!cl_8),
     f(!cl_8) = f(!cr_1),
     h(!cl_5,!cl_1) = !cl_9,
     h(!cr_3,!cl_1) = !cl_9,
     h(!cl_5,!cl_1) = h(!cr_3,!cl_8),
     h(!cr_3,!cl_8) = h(!cr_3,!cl_1),
     h(!cl_5,!cl_1) = h(!cr_3,!cl_1),
     h(!cl_5,!cl_1) = h(!cl_5,!cl_8),
     h(!cr_3,!cl_8) = h(!cr_3,!cr_1),
     h(!cl_5,!cl_1) = h(!cr_3,!cr_1),
     h(!cl_5,!cr_1) = h(!cl_5,!cl_8),
     h(!cr_3,!cr_1) = !cl_9,
     h(!cl_5,!cl_1) = h(!cl_5,!cr_1),
     h(!cr_3,!cr_1) = h(!cl_5,!cr_1),
     h(!cl_5,!cr_1) = !cl_9,
     h(!cr_3,!cl_8) = h(!cl_5,!cr_1),
     h(!cl_5,!cr_1) = h(!cr_3,!cl_1),
     h(!cr_3,!cr_1) = h(!cr_3,!cl_1),
     h(!cr_3,!cr_1) = h(!cl_5,!cl_8),
     h(!cr_3,!cl_1) = h(!cl_5,!cl_8),
     !cl_8 = !cl_1,
     f(!cl_7) = !cl_8,
     f(!cr_3) = !cl_6,
     !cl_6 = h(b,!cl_4),
     f(!cl_6) = !cr_2,
     h(!cl_6,b) = h(a,b),
     h(!cl_6,b) = !cl_0,
     h(a,!cl_6) = !cr_0,
     h(!cl_6,!cl_6) = !cr_0,
     h(a,!cl_6) = h(!cl_6,a),
     h(a,!cl_6) = h(!cl_6,!cl_6),
     h(!cl_6,a) = h(!cl_6,!cl_6),
     h(a,!cl_6) = h(a,a),
     h(!cl_6,!cl_6) = h(a,a),
     h(!cl_6,a) = h(a,a),
     h(!cl_6,a) = !cr_0,
     f(a) = f(!cl_6),
     f(!cl_7) = !cl_1,
     f(!cl_7) = f(c),
     f(!cl_7) = f(!cr_2),
     f(!cl_7) = !cr_1,
     !cl_7 = !cr_2,
     f(a) = !cl_7,
     !cl_6 = a,
     f(!cl_5) = !cl_6,
     h(c,!cl_2) = !cl_4,
     h(b,!cl_0) = !cl_2,
     f(!cr_1) = f(!cl_1),
     f(!cr_1) = !cl_3,
     !cr_1 = !cl_1,
     !cr_1 = f(!cr_2),
     !cr_1 = f(c),
     !cr_0 = h(a,a),
     h(a,b) = !cl_0,
     f(!cl_5) = a,
     f(!cl_5) = f(!cr_3),
     f(!cl_5) = h(b,!cl_4),
     f(!cr_3) = h(b,!cl_4),
     a = f(!cr_3),
     h(!cr_3,!cl_8) = h(!cl_5,!cl_8),
     h(!cr_3,!cl_8) = !cl_9,
     !cr_3 = !cl_5,
     !cr_3 = f(b),
     f(!cr_2) = f(c),
     !cl_1 = f(!cr_2),
     !cr_2 = f(a),
     f(c) = !cl_1,
     f(!cl_1) = !cl_3,
     f(b) = !cl_5,
     h(b,!cl_4) = a,
     f(!cl_6) = !cl_7,
     h(!cl_5,!cl_8) = !cl_9,
     h(c,!cl_10) = !cl_11 ]
Time: 0.039 [s]

CPNF:
   [ !cl_6 … h(b,h(c,h(b,h(!cl_6,b)))),
     !cl_4 … h(c,h(b,h(!cl_6,b))),
     !cl_2 … h(b,h(!cl_6,b)),
     !cr_0 … h(!cl_6,!cl_6),
     !cl_0 … h(!cl_6,b),
     !cl_3 … f(!cl_8),
     !cl_12 … !cl_12,
     b … b,
     !cl_6 … !cl_6,
     !cl_7 … !cl_7,
     !cl_1 … !cl_8,
     !cl_5 … !cl_5,
     !cl_9 … !cl_9,
     !cl_10 … !cl_10,
     c … c,
     !cl_11 … !cl_11 ]
Time: 0.000 [s]

The TRS doesn't have Uniqueness of Normal Forms.
Counter Example: 
     h(b,h(c,h(b,h(!cl_6,b))))
<->* !cl_6

proof:
     h(b,h(c,h(b,h(!cl_6,b))))
->R^ h(b,h(c,h(b,!cl_0)))
->R^ h(b,h(c,!cl_2))
->R^ h(b,!cl_4)
->R^ a
->R^ !cl_6

     !cl_6
Total Time: 0.046 [s]

problems/708.trs: Success(not UNC)
real 0.06
user 0.05
sys 0.00