YES
(ignored inputs)COMMENT doi:10.1007/3-540-61064-2_39 [10] Example 9 submitted by: Takahito Aoto , Junichi Yoshida , and Yoshihito Toyama
Input:
   [ f(a) -> f(f(a)),
     a -> b,
     f(?x) -> f(b) ]

Make it flat:
   [ !cr_0 -> f(a),
     f(a) -> f(!cr_0),
     a -> b,
     f(?x) -> f(b) ]
Time: 0.000 [s]

Make it Complete (R^):
   [ f(b) = !cr_0,
     !cr_0 = f(?x_1),
     !cr_0 = f(!cr_0),
     !cr_0 = f(a),
     f(b) = f(!cr_0),
     f(!cr_0) = f(?x_1),
     f(a) = f(!cr_0),
     f(a) = f(b),
     f(a) = f(?x),
     a = b,
     f(?x) = f(?x_1),
     f(?x) = f(b) ]
Time: 0.004 [s]

The number of normal forms that must be checked: 3
Time: 0.000 [s]

Now checking all the pairs...

Time to check pairs: 0.000 [s]

The TRS has Uniqueness of Normal Forms.
Total Time: 0.004 [s]

problems/36.trs: Success(UNC)
real 0.04
user 0.02
sys 0.00