YES
(ignored inputs)COMMENT doi:10.1007/s10817-011-9238-x [33] Example 13 ( R_5 )
Input:
   [ a1 -> b1,
     a1 -> c1,
     b1 -> b2,
     c1 -> c2,
     a2 -> b2,
     a2 -> c2,
     b2 -> b3,
     c2 -> c3,
     a3 -> b3,
     a3 -> c3,
     b3 -> b4,
     c3 -> c4,
     a4 -> b4,
     a4 -> c4,
     b4 -> b5,
     c4 -> c5,
     a5 -> b6,
     b5 -> b6,
     c5 -> b6 ]

Make it flat:
   [ a1 -> b1,
     a1 -> c1,
     b1 -> b2,
     c1 -> c2,
     a2 -> b2,
     a2 -> c2,
     b2 -> b3,
     c2 -> c3,
     a3 -> b3,
     a3 -> c3,
     b3 -> b4,
     c3 -> c4,
     a4 -> b4,
     a4 -> c4,
     b4 -> b5,
     c4 -> c5,
     a5 -> b6,
     b5 -> b6,
     c5 -> b6 ]
Time: 0.000 [s]

Make it Complete (R^):
   [ a1 = b1,
     a1 = c2,
     a1 = a2,
     a1 = b2,
     a1 = c4,
     a1 = a4,
     a1 = b4,
     a1 = b6,
     a1 = b5,
     a1 = a5,
     a1 = c5,
     a1 = b3,
     a1 = a3,
     a1 = c3,
     a1 = c1,
     b1 = b3,
     b1 = c2,
     b1 = a3,
     b1 = b5,
     b1 = c4,
     b1 = a5,
     b1 = c5,
     b1 = b6,
     b1 = a4,
     b1 = c3,
     b1 = b4,
     b1 = a2,
     b1 = c1,
     b1 = b2,
     c1 = c3,
     c1 = a3,
     c1 = b3,
     c1 = c5,
     c1 = a5,
     c1 = b5,
     c1 = b6,
     c1 = b4,
     c1 = a4,
     c1 = c4,
     c1 = b2,
     c1 = a2,
     c1 = c2,
     a2 = b2,
     a2 = c3,
     a2 = a3,
     a2 = b3,
     a2 = c5,
     a2 = a5,
     a2 = b5,
     a2 = b6,
     a2 = b4,
     a2 = a4,
     a2 = c4,
     a2 = c2,
     b2 = b4,
     b2 = c3,
     b2 = a4,
     b2 = b6,
     b2 = c5,
     b2 = a5,
     b2 = c4,
     b2 = b5,
     b2 = a3,
     b2 = c2,
     b2 = b3,
     c2 = c4,
     c2 = a4,
     c2 = b4,
     c2 = b6,
     c2 = b5,
     c2 = a5,
     c2 = c5,
     c2 = b3,
     c2 = a3,
     c2 = c3,
     a3 = b3,
     a3 = c4,
     a3 = a4,
     a3 = b4,
     a3 = b6,
     a3 = b5,
     a3 = a5,
     a3 = c5,
     a3 = c3,
     b3 = b5,
     b3 = c4,
     b3 = a5,
     b3 = c5,
     b3 = b6,
     b3 = a4,
     b3 = c3,
     b3 = b4,
     c3 = c5,
     c3 = a5,
     c3 = b5,
     c3 = b6,
     c3 = b4,
     c3 = a4,
     c3 = c4,
     a4 = b4,
     a4 = c5,
     a4 = a5,
     a4 = b5,
     a4 = b6,
     a4 = c4,
     b4 = b6,
     b4 = c5,
     b4 = a5,
     b4 = c4,
     b4 = b5,
     c4 = b6,
     c4 = b5,
     c4 = a5,
     c4 = c5,
     a5 = c5,
     a5 = b5,
     a5 = b6,
     b5 = c5,
     b5 = b6,
     c5 = b6 ]
Time: 0.177 [s]

The number of normal forms that must be checked: 1
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: 0.177 [s]

problems/114.trs: Success(UNC)
real 0.21
user 0.18
sys 0.00