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

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

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

CPNF:
   [ a … f(b),
     a … b ]
Time: 0.000 [s]

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

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

     b
->R^ a
Total Time: 0.002 [s]

problems/670.trs: Success(not UNC)
real 0.01
user 0.01
sys 0.00