YES
(ignored inputs)COMMENT doi:10.1016/0890-5401 ( 90 ) 90015-A [24] Example 1 submitted by: Takahito Aoto , Junichi Yoshida , and Yoshihito Toyama
Input:
   [ a -> f(a,b),
     f(a,b) -> f(b,a) ]

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

Make it Complete (R^):
   [ a = f(b,a),
     a = f(a,b),
     f(a,b) = f(b,a) ]
Time: 0.000 [s]

The number of normal forms that must be checked: 905
Time: 0.178 [s]

Now checking all the pairs...

Time to check pairs: 0.153 [s]

The TRS has Uniqueness of Normal Forms.
Total Time: 0.331 [s]

problems/80.trs: Success(UNC)
real 0.37
user 0.34
sys 0.00