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]

The number of normal forms that must be checked: 905
Time: 0.176 [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(f(?!cx_2,?!cx_3),b)
<->* f(f(?!cx_3,?!cx_3),b)

proof:
     f(f(?!cx_2,?!cx_3),b)
->R^ f(f(?!cx_2,?!cx_3),a)
->R^ a

     f(f(?!cx_3,?!cx_3),b)
->R^ f(f(?!cx_3,?!cx_3),a)
->R^ a
Total Time: 0.177 [s]

problems/r2.trs: Success(not UNC)
real 0.23
user 0.18
sys 0.01