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

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

Make it Complete (R^):
   [ f(!cl_0) = c,
     c = !cl_0,
     c = f(c),
     f(a) = !cl_0,
     c = f(a),
     f(!cl_0) = a,
     f(a) = f(!cl_0),
     f(!cl_0) = !cl_0,
     f(!cl_0) = f(c),
     f(a) = f(c),
     f(a) = a,
     c = a,
     a = f(c),
     f(c) = !cl_0,
     !cl_0 = a ]
Time: 0.002 [s]

The number of normal forms that must be checked: 12
Time: 0.000 [s]

Now checking all the pairs...

Time to check pairs: 0.000 [s]

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

proof:
     f(f(a))
->R^ f(f(!cl_0))
->R^ f(!cl_0)
->R^ !cl_0

     f(f(f(a)))
->R^ f(f(f(!cl_0)))
->R^ f(f(!cl_0))
->R^ f(!cl_0)
->R^ !cl_0
Total Time: 0.003 [s]

problems/707.trs: Success(not UNC)
real 0.04
user 0.01
sys 0.01