YES
Input:
   [ f(?x,?x) -> g(?x),
     f(a,b) -> g(a) ]

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

Make it Complete (R^):
   [ f(a,a) = g(a),
     f(a,a) = f(a,b),
     f(?x,?x) = g(?x),
     f(a,b) = g(a) ]
Time: 0.000 [s]

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

problems/r12.trs: Success(UNC)
real 0.01
user 0.00
sys 0.01