YES
(ignored inputs)COMMENT [111] p. 29 ( GCR & ~CR & ~GSCR )
Input:
   [ a -> b,
     b -> f(a,a),
     f(?x,a) -> b ]

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

Make it Complete (R^):
   [ a = f(?x,a),
     a = f(a,a),
     f(?x,b) = b,
     f(?x_1,b) = f(?x,a),
     f(a,b) = b,
     f(b,a) = b,
     f(?x_1,b) = f(a,a),
     f(a,b) = f(?x_1,a),
     f(?x_1,b) = f(b,a),
     f(a,b) = f(?x_1,b),
     f(?x_1,b) = a,
     f(?x_1,b) = f(?x_3,b),
     f(?x_1,b) = f(b,b),
     f(b,b) = f(?x_1,a),
     f(a,b) = f(b,a),
     f(a,b) = f(b,b),
     f(b,a) = f(b,b),
     f(a,b) = f(a,a),
     f(b,a) = a,
     f(a,b) = a,
     a = f(b,b),
     f(b,b) = b,
     f(b,b) = f(a,a),
     f(b,a) = f(a,a),
     f(b,a) = f(?x_1,a),
     a = b,
     f(a,a) = f(?x_1,a),
     b = f(a,a),
     f(?x,a) = f(?x_1,a),
     f(?x,a) = b ]
Time: 0.033 [s]

The number of normal forms that must be checked: 404
Time: 0.058 [s]

Now checking all the pairs...

Time to check pairs: 0.067 [s]

The TRS has Uniqueness of Normal Forms.
Total Time: 0.158 [s]

problems/508.trs: Success(UNC)
real 0.18
user 0.16
sys 0.02