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

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

Make it Complete (R^):
   [ b = f(?x,?y),
     a = b,
     f(?x,?y) = f(?x_1,?y_1),
     f(?x,?y) = a ]
Time: 0.000 [s]

The number of normal forms that must be checked: 4
Time: 0.000 [s]

Now checking all the pairs...

Time to check pairs: 0.000 [s]

The TRS has Uniqueness of Normal Forms.
Total Time: 0.001 [s]

problems/r4.trs: Success(UNC)
real 0.03
user 0.00
sys 0.01