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

Make it flat:
   [ f(!cl_0,?y) -> ?y,
     g(a) -> !cl_0 ]
Time: 0.000 [s]

Make it Complete (R^):
   [ f(!cl_0,!cl_0) = !cl_0,
     g(a) = f(!cl_0,!cl_0),
     f(!cl_0,?y) = ?y,
     g(a) = !cl_0 ]
Time: 0.000 [s]

CPNF:
   [ a … a,
     !cl_0 … !cl_0 ]
Time: 0.000 [s]

Now checking all the pairs in CW...

Time to check pairs: 0.000 [s]

The TRS has Uniqueness of Normal Forms.
Total Time: 0.000 [s]

problems/r6.trs: Success(UNC)
real 0.01
user 0.01
sys 0.00