NO
Input:
   [ g(?y) -> f(?x,?y) ]

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

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

CPNF:
   [  ]
Time: 0.000 [s]

Now checking all the pairs in CW...

Time to check pairs: 0.000 [s]

The TRS doesn't have Uniqueness of Normal Forms.
Counter Example: 
     f(?x,?y)
<->* f(?x_1,?y)

proof:
     f(?x,?y)
->R^ f(?!,?y)

     f(?x_1,?y)
->R^ f(?!,?y)
Total Time: 0.000 [s]

problems/r3.trs: Success(not UNC)
real 0.01
user 0.00
sys 0.00