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

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

Make it Complete (R^):
   [ f(!cr_0) = a,
     a = b,
     f(a) = !cl_0,
     f(a) = f(b),
     f(a) = f(c),
     f(a) = !cr_0,
     a = c,
     f(!cl_0) = a,
     f(c) = !cr_0,
     c = f(!cr_0),
     f(b) = f(c),
     c = f(!cl_0),
     f(!cl_0) = f(!cr_0),
     f(!cl_0) = b,
     !cl_0 = !cr_0,
     f(b) = !cl_0,
     c = b,
     b = f(!cr_0),
     !cr_0 = f(b),
     f(c) = !cl_0 ]
Time: 0.002 [s]

The number of normal forms that must be checked: 18
Time: 0.001 [s]

Now checking all the pairs...

Time to check pairs: 0.001 [s]

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

proof:
     f(f(f(a)))
->R^ f(f(!cr_0))
->R^ f(f(!cl_0))
->R^ f(b)
->R^ f(a)
->R^ !cr_0
->R^ !cl_0

     f(f(f(f(f(a)))))
->R^ f(f(f(f(!cr_0))))
->R^ f(f(f(f(!cl_0))))
->R^ f(f(f(b)))
->R^ f(f(f(a)))
->R^ f(f(!cr_0))
->R^ f(f(!cl_0))
->R^ f(b)
->R^ f(a)
->R^ !cr_0
->R^ !cl_0
Total Time: 0.005 [s]

problems/674.trs: Success(not UNC)
real 0.04
user 0.01
sys 0.00