YES
(ignored inputs)COMMENT doi:10.1007/BF01190830 [30] Example 5.12 submitted by: Aart Middeldorp
Input:
   [ f(?x,?x) -> g(i(b),?x),
     g(?x,?x) -> f(?x,i(a)),
     i(?x) -> j(?x),
     a -> b ]

Make it flat:
   [ !cr_0 -> i(b),
     f(?x,?x) -> g(!cr_0,?x),
     !cr_1 -> i(a),
     g(?x,?x) -> f(?x,!cr_1),
     i(?x) -> j(?x),
     a -> b ]
Time: 0.000 [s]

Make it Complete (R^):
   [ i(a) = !cr_0,
     !cr_0 = j(b),
     !cr_0 = j(a),
     f(?x,!cr_0) = f(?x,!cr_1),
     f(?x,!cr_0) = g(?x,?x),
     g(!cr_1,!cr_0) = g(!cr_0,!cr_1),
     g(!cr_0,!cr_0) = g(!cr_1,!cr_1),
     f(!cr_1,!cr_0) = g(!cr_1,!cr_1),
     f(!cr_0,!cr_1) = g(!cr_1,!cr_1),
     g(!cr_1,!cr_0) = f(!cr_1,!cr_1),
     f(!cr_1,!cr_0) = g(!cr_0,!cr_1),
     f(!cr_0,!cr_1) = g(!cr_0,!cr_1),
     g(!cr_0,!cr_0) = f(!cr_1,!cr_1),
     g(!cr_1,?x) = g(!cr_0,?x),
     g(!cr_1,?x) = f(?x,?x),
     f(!cr_1,!cr_1) = f(!cr_0,!cr_0),
     f(!cr_1,!cr_1) = f(!cr_1,!cr_0),
     f(!cr_1,!cr_1) = f(!cr_0,!cr_1),
     f(!cr_1,!cr_0) = f(!cr_0,!cr_1),
     g(!cr_1,!cr_0) = f(!cr_0,!cr_1),
     g(!cr_0,!cr_1) = g(!cr_0,!cr_0),
     g(!cr_0,!cr_1) = f(!cr_0,!cr_0),
     g(!cr_1,!cr_1) = g(!cr_1,!cr_0),
     g(!cr_1,!cr_1) = f(!cr_0,!cr_0),
     g(!cr_1,!cr_0) = f(!cr_0,!cr_0),
     g(!cr_1,!cr_0) = g(!cr_0,!cr_0),
     g(!cr_1,!cr_0) = f(!cr_1,!cr_0),
     f(!cr_1,!cr_0) = f(!cr_0,!cr_0),
     f(!cr_1,!cr_0) = g(!cr_0,!cr_0),
     !cr_0 = !cr_1,
     !cr_0 = i(b),
     f(!cr_0,!cr_0) = g(!cr_0,!cr_0),
     f(!cr_0,!cr_1) = g(!cr_0,!cr_0),
     f(!cr_0,!cr_0) = f(!cr_0,!cr_1),
     g(!cr_0,!cr_1) = f(!cr_1,!cr_1),
     g(!cr_1,!cr_1) = f(!cr_1,!cr_1),
     g(!cr_0,!cr_1) = g(!cr_1,!cr_1),
     f(?x,?x) = g(!cr_0,?x),
     i(b) = !cr_1,
     j(b) = !cr_1,
     i(b) = j(a),
     i(b) = j(b),
     j(b) = j(a),
     i(a) = i(b),
     j(b) = i(a),
     j(a) = i(a),
     !cr_1 = j(a),
     !cr_1 = i(a),
     g(?x,?x) = f(?x,!cr_1),
     i(?x) = j(?x),
     a = b ]
Time: 0.021 [s]

CPNF:
   [ !cr_0 … j(b),
     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: 0.022 [s]

problems/108.trs: Success(UNC)
real 0.04
user 0.03
sys 0.00