YES
(ignored inputs)COMMENT doi:10.1007/3-540-61064-2_39 [10] Example 6 submitted by: Takahito Aoto , Junichi Yoshida , and Yoshihito Toyama
Input:
   [ f(a) -> f(g(b,b)),
     a -> g(c,c),
     c -> d,
     d -> b,
     b -> d ]

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

Make it Complete (R^):
   [ g(b,d) = !cr_0,
     g(d,b) = !cr_0,
     g(b,c) = !cr_0,
     g(c,b) = !cr_0,
     !cr_0 = g(c,c),
     !cr_0 = g(d,d),
     !cr_0 = g(d,c),
     !cr_0 = g(c,d),
     !cr_0 = a,
     !cr_0 = g(b,b),
     f(a) = f(!cr_0),
     g(c,d) = a,
     g(d,c) = a,
     g(c,b) = a,
     g(b,d) = a,
     g(b,b) = a,
     g(c,d) = g(b,c),
     g(d,c) = g(b,c),
     g(c,b) = g(b,c),
     g(d,c) = g(c,c),
     g(b,d) = g(c,c),
     g(c,d) = g(b,b),
     g(d,c) = g(b,b),
     g(c,b) = g(b,b),
     g(b,c) = g(b,b),
     g(d,b) = g(c,c),
     g(c,d) = g(c,b),
     g(d,c) = g(c,b),
     g(d,c) = g(c,d),
     g(c,d) = g(d,d),
     g(d,c) = g(d,d),
     g(c,b) = g(d,d),
     g(b,c) = g(d,d),
     g(d,d) = a,
     g(b,d) = g(d,d),
     g(d,b) = g(d,d),
     g(d,b) = g(b,b),
     g(d,b) = a,
     g(b,c) = g(d,b),
     g(c,d) = g(d,b),
     g(d,b) = g(c,b),
     g(d,b) = g(d,c),
     g(d,b) = g(b,d),
     g(d,c) = g(b,d),
     g(b,c) = g(b,d),
     g(c,d) = g(b,d),
     g(c,b) = g(b,d),
     g(b,d) = g(b,b),
     g(d,d) = g(b,b),
     g(d,d) = g(c,c),
     g(c,d) = g(c,c),
     g(c,b) = g(c,c),
     g(b,b) = g(c,c),
     g(b,c) = g(c,c),
     g(b,c) = a,
     a = g(c,c),
     c = b,
     c = d,
     d = b ]
Time: 0.057 [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: 0.059 [s]

problems/33.trs: Success(UNC)
real 0.07
user 0.06
sys 0.01