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]

The number of normal forms that must be checked: 6
Time: 0.000 [s]

Now checking all the pairs...

Time to check pairs: 0.000 [s]

The TRS doesn't have Uniqueness of Normal Forms.
Counter Example: 
     f(?!cx_1,?!cx)
<->* f(?!cx,?!cx)

proof:
     f(?!cx_1,?!cx)
->R^ f(?!,?!cx)

     f(?!cx,?!cx)
->R^ f(?!,?!cx)
Total Time: 0.001 [s]

problems/r3.trs: Success(not UNC)
real 0.02
user 0.00
sys 0.01