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]

The number of normal forms that must be checked: 1686
Time: 0.561 [s]

Now checking all the pairs...

Time to check pairs: 0.338 [s]

The TRS has Uniqueness of Normal Forms.
Total Time: 0.900 [s]

problems/r12.trs: Success(UNC)
real 0.95
user 0.90
sys 0.01