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

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

Make it Complete (R^):
   [ g(a,?x) = g(?x,?x),
     g(a,?x) = g(?x,a),
     f(?x) = g(a,?x),
     g(a,a) = f(a),
     g(?x,a) = g(?x,?x),
     f(?x) = g(?x,a),
     g(?x,?x) = f(?x) ]
Time: 0.001 [s]

CPNF:
   [ a … a ]
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: 
     g(a,?x)
<->* g(?x,a)

proof:
     g(a,?x)
->R^ f(?x)

     g(?x,a)
->R^ f(?x)
Total Time: 0.001 [s]

problems/r11.trs: Success(not UNC)
real 0.02
user 0.00
sys 0.01