YES
(ignored inputs)COMMENT [26] Example 5.1 submitted by: Takahito Aoto , Junichi Yoshida , and Yoshihito Toyama
Input:
   [ a -> b,
     f(a) -> g(a),
     f(b) -> g(b) ]

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

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

CPNF:
   [ a … b ]
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: 0.001 [s]

problems/84.trs: Success(UNC)
real 0.01
user 0.01
sys 0.00