NO
(ignored inputs)COMMENT Cops #647 - #721: generated ground TRSs; evenly distributed in the UNR/UNC/NFP/CR hierarchy submitted by: Bertram Felgenhauer
Input:
   [ f(a) -> c,
     b -> c,
     b -> a ]

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

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

The number of normal forms that must be checked: 13
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(c))
<->* f(f(f(c)))

proof:
     f(f(c))
->R^ f(f(b))
->R^ f(f(a))
->R^ f(c)
->R^ f(b)
->R^ f(a)
->R^ c
->R^ b
->R^ a

     f(f(f(c)))
->R^ f(f(f(b)))
->R^ f(f(f(a)))
->R^ f(f(c))
->R^ f(f(b))
->R^ f(f(a))
->R^ f(c)
->R^ f(b)
->R^ f(a)
->R^ c
->R^ b
->R^ a
Total Time: 0.003 [s]

problems/679.trs: Success(not UNC)
real 0.04
user 0.02
sys 0.00