NO
(ignored inputs)COMMENT generated by FORT "NFP & ~CR" submitted by: Franziska Rapp
Input:
   [ a -> a,
     a -> b,
     f(a,a) -> f(b,f(f(a,b),a)) ]

Make it flat:
   [ a -> a,
     a -> b,
     !cr_0 -> f(a,b),
     !cr_1 -> f(!cr_0,a),
     f(a,a) -> f(b,!cr_1) ]
Time: 0.000 [s]

Make it Complete (R^):
   [ f(a,!cr_1) = f(a,a),
     f(a,a) = !cr_0,
     f(a,b) = f(b,!cr_1),
     f(b,a) = f(b,!cr_1),
     f(!cr_0,b) = f(!cr_0,a),
     f(!cr_0,b) = !cr_1,
     f(b,a) = !cr_0,
     f(a,!cr_1) = f(b,b),
     f(a,!cr_1) = f(b,a),
     f(a,!cr_1) = f(a,b),
     f(a,!cr_1) = f(b,!cr_1),
     f(a,!cr_1) = !cr_0,
     f(b,!cr_1) = !cr_0,
     f(b,b) = f(b,!cr_1),
     f(a,a) = f(b,b),
     f(a,a) = f(b,a),
     f(b,b) = f(b,a),
     f(a,a) = f(a,b),
     f(b,a) = f(a,b),
     f(b,b) = f(a,b),
     f(b,b) = !cr_0,
     a = b,
     !cr_0 = f(a,b),
     !cr_1 = f(!cr_0,a),
     f(a,a) = f(b,!cr_1) ]
Time: 0.010 [s]

CPNF:
   [ !cr_0 … f(b,f(f(b,b),b)),
     !cr_1 … f(f(b,b),b),
     !cr_0 … f(b,b),
     a … b ]
Time: 0.000 [s]

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

proof:
     f(b,f(f(b,b),b))
->R^ f(b,f(f(a,b),b))
->R^ f(b,f(f(a,a),b))
->R^ f(b,f(!cr_0,b))
->R^ f(b,f(!cr_0,a))
->R^ f(a,f(!cr_0,a))
->R^ f(a,!cr_1)
->R^ !cr_0

     f(b,b)
->R^ f(a,b)
->R^ f(a,a)
->R^ !cr_0
Total Time: 0.011 [s]

problems/735.trs: Success(not UNC)
real 0.03
user 0.02
sys 0.02