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

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

Make it Complete (R^):
   [ b = f(?x,a),
     b = f(?x,b),
     f(?x,b) = a,
     f(?x,b) = f(?x_1,b),
     f(?x_1,b) = f(?x,a),
     f(?x,a) = f(?x_1,a),
     f(?x,a) = a,
     a = b ]
Time: 0.001 [s]

CPNF:
   [ a … f(?x,b),
     a … b ]
Time: 0.000 [s]

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

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

     b
->R^ a
Total Time: 0.002 [s]

problems/r2.trs: Success(not UNC)
real 0.02
user 0.01
sys 0.01