NO
(ignored inputs)COMMENT generated by FORT -f "a:0 b:0 f:2" -r 5 "UN & ~UNC & GUNC" submitted by: Franziska Rapp
Input:
   [ a -> a,
     a -> b,
     a -> f(a,a),
     f(b,b) -> f(a,b),
     f(?x0,a) -> f(b,b) ]

Make it flat:
   [ a -> a,
     a -> b,
     a -> f(a,a),
     f(b,b) -> f(a,b),
     f(?x0,a) -> f(b,b) ]
Time: 0.000 [s]

Make it Complete (R^):
   [ f(b,a) = f(?x0,a),
     f(b,a) = f(a,b),
     f(b,a) = f(a,a),
     f(b,a) = a,
     f(?x0,b) = f(b,b),
     f(?x0_1,b) = f(?x0,a),
     f(?x0_1,b) = f(a,b),
     b = f(a,a),
     b = f(a,b),
     f(?x0_2,b) = f(a,a),
     f(b,a) = f(b,b),
     f(?x0_1,b) = a,
     f(?x0_1,b) = f(b,a),
     f(?x0_1,b) = f(?x0_3,b),
     f(?x0_1,b) = b,
     b = f(?x0_1,a),
     f(b,a) = b,
     b = f(b,b),
     a = b,
     a = f(b,b),
     a = f(?x0_1,a),
     f(a,a) = f(b,b),
     f(a,a) = f(?x0_2,a),
     f(a,b) = f(a,a),
     a = f(a,b),
     a = f(a,a),
     f(a,b) = f(?x0_1,a),
     f(b,b) = f(a,b),
     f(?x0,a) = f(?x0_1,a),
     f(?x0,a) = f(b,b) ]
Time: 0.034 [s]

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

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

proof:
     f(?x,b)
->R^ f(?x,a)
->R^ f(?!,a)
->R^ a

     b
->R^ a
Total Time: 0.034 [s]

problems/733.trs: Success(not UNC)
real 0.05
user 0.05
sys 0.00