YES
(ignored inputs)COMMENT doi:10.4230/LIPIcs.RTA.2012.165 [37] Example 3.1 ( R )
Input:
   [ a -> b,
     a -> f(a),
     b -> f(f(b)) ]

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

Make it Complete (R^):
   [ a = f(!cr_0),
     f(a) = !cr_0,
     f(b) = a,
     f(b) = b,
     f(b) = f(a),
     !cr_0 = a,
     !cr_0 = b,
     f(!cr_0) = !cr_0,
     f(b) = f(!cr_0),
     f(a) = f(!cr_0),
     b = f(a),
     a = b,
     a = f(a),
     !cr_0 = f(b),
     b = f(!cr_0) ]
Time: 0.002 [s]

The number of normal forms that must be checked: 8
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: 0.003 [s]

problems/212.trs: Success(UNC)
real 0.02
user 0.01
sys 0.00