NO
(ignored inputs)COMMENT doi:10.1016/j.ic.2016.06.011 [76] Example 28
Input:
   [ c -> f(a,b),
     c -> f(a,a),
     f(?x,?x) -> ?x,
     f(?x,?y) -> f(?y,?x),
     f(a,a) -> f(b,b),
     f(b,b) -> f(a,a) ]

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

Make it Complete (R^):
   [ c = f(a,b),
     f(b,a) = c,
     f(a,a) = f(c,c),
     c = f(b,b),
     c = a,
     f(b,c) = f(a,a),
     f(c,b) = f(a,a),
     f(b,c) = a,
     f(c,b) = a,
     f(b,c) = b,
     f(c,b) = b,
     f(a,c) = b,
     f(c,a) = b,
     f(a,c) = f(b,a),
     f(c,a) = f(a,b),
     f(b,c) = f(b,a),
     f(c,b) = f(b,a),
     f(c,a) = f(b,b),
     f(b,c) = f(a,b),
     f(c,b) = f(a,b),
     f(a,c) = f(b,b),
     f(a,c) = a,
     f(c,a) = a,
     f(a,c) = f(a,a),
     f(c,a) = f(a,a),
     a = f(c,c),
     c = f(c,c),
     f(c,c) = f(b,b),
     f(a,b) = f(a,c),
     f(c,c) = f(a,b),
     f(c,b) = f(c,a),
     f(b,c) = f(c,a),
     f(c,b) = f(c,c),
     f(c,a) = c,
     f(c,a) = f(b,a),
     f(b,c) = f(c,c),
     f(c,b) = f(a,c),
     f(b,c) = f(a,c),
     f(b,b) = f(c,b),
     f(b,b) = f(b,c),
     f(c,b) = f(b,c),
     c = f(c,b),
     f(b,c) = c,
     f(a,c) = c,
     f(a,c) = f(c,a),
     f(c,c) = f(a,c),
     f(c,a) = f(c,c),
     f(c,c) = f(b,a),
     b = f(c,c),
     c = b,
     c = f(a,a),
     b = f(a,a),
     a = f(a,a),
     f(b,a) = f(a,a),
     f(a,b) = f(a,a),
     f(b,a) = a,
     f(a,b) = a,
     f(a,b) = f(b,b),
     f(b,a) = f(b,b),
     f(b,a) = f(a,b),
     f(b,a) = b,
     f(a,b) = b,
     b = f(b,b),
     a = b,
     a = f(b,b),
     f(?x,?x) = ?x,
     f(?x,?y) = f(?y,?x),
     f(a,a) = f(b,b) ]
Time: 0.098 [s]

CPNF:
   [ a … b,
     a … a ]
Time: 0.000 [s]

The TRS doesn't have Uniqueness of Normal Forms.
Counter Example: 
     b
<->* a

proof:
     b
->R^ a

     a
Total Time: 0.099 [s]

problems/392.trs: Success(not UNC)
real 0.12
user 0.10
sys 0.01