NO
(ignored inputs)COMMENT [111] p. 29 ( GUNC & ~UNC & ~GNFP )
Input:
   [ a -> a,
     f(b,?x) -> b,
     f(?x,a) -> a ]

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

Make it Complete (R^):
   [ f(b,?x) = f(b,?x_1),
     f(?x,b) = a,
     f(?x_1,b) = f(?x,a),
     f(?x_1,b) = b,
     f(?x_1,b) = f(b,?x_2),
     f(a,?x) = b,
     f(?x_1,b) = f(?x_4,b),
     f(?x_1,b) = f(a,?x_2),
     f(a,?x_2) = f(?x_1,a),
     f(a,?x_2) = f(b,?x_5),
     f(a,?x_2) = f(a,?x_5),
     f(a,?x_2) = a,
     b = a,
     f(b,?x_2) = a,
     f(?x_1,a) = f(b,?x_2),
     b = f(?x_1,a),
     f(b,?x) = b,
     f(?x,a) = f(?x_1,a),
     f(?x,a) = a ]
Time: 0.011 [s]

The number of normal forms that must be checked: 605
Time: 0.083 [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(?!cx_2,?!cx_3),b)
<->* f(f(?!cx_3,?!cx_3),b)

proof:
     f(f(?!cx_2,?!cx_3),b)
->R^ f(f(?!cx_2,?!cx_3),a)
->R^ a

     f(f(?!cx_3,?!cx_3),b)
->R^ f(f(?!cx_3,?!cx_3),a)
->R^ a
Total Time: 0.094 [s]

problems/510.trs: Success(not UNC)
real 0.11
user 0.10
sys 0.00