NO
Input:
   [ a -> b,
     b -> a,
     f(?x,?y) -> a,
     f(?x,?y) -> ?z ]

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

The TRS doesn't have Uniqueness of Normal Forms because it is inconsistent.
Total Time: 0.000 [s]

problems/r5.trs: Success(not UNC)
real 0.01
user 0.01
sys 0.00