NO
(ignored inputs)COMMENT doi:10.1007/3-540-45744-5_49 [153] Example 13 submitted by: Raul Gutierrez and Salvador Lucas
Input:
   [ a -> b,
     f(g(a)) -> f(a) ]

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

Make it Complete (R^):
   [ f(b) = f(a),
     f(b) = f(!cl_0),
     f(!cl_0) = f(a),
     g(b) = g(a),
     g(b) = !cl_0,
     a = b,
     g(a) = !cl_0 ]
Time: 0.000 [s]

CPNF:
   [ !cl_0 … g(b),
     a … b ]
Time: 0.000 [s]

Now checking all the pairs in CW...

Time to check pairs: 0.000 [s]

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

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

     f(g(b))
->R^ f(g(a))
->R^ f(!cl_0)
Total Time: 0.001 [s]

problems/800.trs: Success(not UNC)
real 0.02
user 0.00
sys 0.01