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)),
     f(f(f(b))) -> b ]

Make it flat:
   [ f(!cl_1) -> b,
     !cl_1 -> !cl_1,
     f(!cl_0) -> !cl_1,
     f(b) -> !cl_0,
     !cl_0 -> !cl_0,
     a -> b,
     a -> f(a),
     !cr_0 -> f(b),
     b -> f(!cr_0) ]
Time: 0.000 [s]

Make it Complete (R^):
   [ f(!cl_1) = b,
     f(a) = !cl_1,
     f(b) = !cl_1,
     f(!cr_0) = !cl_1,
     !cl_1 = !cr_0,
     !cl_1 = !cl_0,
     !cl_1 = b,
     f(!cl_1) = a,
     f(!cl_1) = f(!cr_0),
     f(!cl_1) = f(b),
     f(!cl_1) = !cr_0,
     f(!cl_1) = !cl_1,
     f(!cl_1) = f(!cl_0),
     f(!cl_1) = f(a),
     f(!cl_1) = !cl_0,
     !cl_1 = a,
     f(!cl_0) = !cl_1,
     f(a) = !cl_0,
     f(!cr_0) = !cl_0,
     !cl_0 = !cr_0,
     !cl_0 = b,
     f(!cl_0) = a,
     f(!cl_0) = b,
     f(!cl_0) = f(!cr_0),
     f(!cl_0) = !cl_0,
     f(!cl_0) = f(b),
     f(!cl_0) = f(a),
     f(!cl_0) = !cr_0,
     !cl_0 = a,
     f(b) = !cl_0,
     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: 0.022 [s]

CPNF:
   [  ]
Time: 0.000 [s]

Now checking all the pairs in CW...

Time to check pairs: 0.000 [s]

The TRS has Uniqueness of Normal Forms.
Total Time: 0.022 [s]

problems/213.trs: Success(UNC)
real 0.04
user 0.02
sys 0.01