YES
(ignored inputs)COMMENT doi:10.1007/s10817-011-9238-x [33] Example 8
Input:
   [ f(a,a) -> c,
     f(b,?x) -> f(?x,?x),
     f(?x,b) -> f(?x,?x),
     a -> b ]

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

Make it Complete (R^):
   [ f(a,b) = c,
     f(b,a) = c,
     c = f(b,b),
     f(a,a) = c,
     f(a,?x) = f(?x,?x),
     f(b,?x) = f(?x,b),
     f(?x,b) = f(a,?x),
     f(a,?x) = f(b,?x),
     f(a,?x) = f(?x,a),
     f(b,?x) = f(?x,a),
     f(b,?x) = f(?x,?x),
     f(?x,a) = f(?x,b),
     f(b,a) = f(b,b),
     f(b,b) = f(a,a),
     f(a,a) = f(b,a),
     f(b,b) = f(a,b),
     f(b,a) = f(a,b),
     f(a,a) = f(a,b),
     f(?x,a) = f(?x,?x),
     f(?x,b) = f(?x,?x),
     a = b ]
Time: 0.007 [s]

CPNF:
   [ c … c,
     a … b ]
Time: 0.000 [s]

Now checking all the pairs in CW...

Time to check pairs: 0.000 [s]

The TRS has Uniqueness of Normal Forms.
Total Time: 0.007 [s]

problems/113.trs: Success(UNC)
real 0.02
user 0.01
sys 0.01