NO
(ignored inputs)COMMENT doi:10.1006/jsco.1996.0002 [112] p. 31 ( signature extension and currying do not preserve UNR ) submitted by: Bertram Felgenhauer
Input:
   [ f(?x,?x) -> g,
     a -> b,
     a -> c,
     d -> c,
     d -> e,
     c -> c,
     f(a,?x) -> g,
     f(b,?x) -> g,
     f(c,?x) -> g,
     f(d,?x) -> g,
     f(e,?x) -> g,
     f(?x,a) -> g,
     f(?x,b) -> g,
     f(?x,c) -> g,
     f(?x,d) -> g,
     f(?x,e) -> g ]

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

Make it Complete (R^):
   [ f(?x,?x) = f(?x_1,e),
     f(?x,?x) = f(?x_1,d),
     f(?x,?x) = f(?x_1,c),
     f(?x,?x) = f(?x_1,b),
     f(?x,?x) = f(?x_1,a),
     f(?x,?x) = f(e,?x_1),
     f(?x,?x) = f(d,?x_1),
     f(?x,?x) = f(c,?x_1),
     f(?x,?x) = f(b,?x_1),
     f(?x,?x) = f(a,?x_1),
     f(?x,?x) = f(?x_1,?x_1),
     f(?x,?x) = g,
     b = c,
     b = e,
     b = d,
     a = b,
     a = d,
     a = e,
     a = c,
     c = e,
     d = c,
     d = e,
     f(a,?x) = f(?x_1,e),
     f(a,?x) = f(?x_1,d),
     f(a,?x) = f(?x_1,c),
     f(a,?x) = f(?x_1,b),
     f(a,?x) = f(?x_1,a),
     f(a,?x) = f(e,?x_1),
     f(a,?x) = f(d,?x_1),
     f(a,?x) = f(c,?x_1),
     f(a,?x) = f(b,?x_1),
     f(a,?x) = f(a,?x_1),
     f(a,?x) = g,
     f(b,?x) = f(?x_1,e),
     f(b,?x) = f(?x_1,d),
     f(b,?x) = f(?x_1,c),
     f(b,?x) = f(?x_1,b),
     f(b,?x) = f(?x_1,a),
     f(b,?x) = f(e,?x_1),
     f(b,?x) = f(d,?x_1),
     f(b,?x) = f(c,?x_1),
     f(b,?x) = f(b,?x_1),
     f(b,?x) = g,
     f(c,?x) = f(?x_1,e),
     f(c,?x) = f(?x_1,d),
     f(c,?x) = f(?x_1,c),
     f(c,?x) = f(?x_1,b),
     f(c,?x) = f(?x_1,a),
     f(c,?x) = f(e,?x_1),
     f(c,?x) = f(d,?x_1),
     f(c,?x) = f(c,?x_1),
     f(c,?x) = g,
     f(d,?x) = f(?x_1,e),
     f(d,?x) = f(?x_1,d),
     f(d,?x) = f(?x_1,c),
     f(d,?x) = f(?x_1,b),
     f(d,?x) = f(?x_1,a),
     f(d,?x) = f(e,?x_1),
     f(d,?x) = f(d,?x_1),
     f(d,?x) = g,
     f(e,?x) = f(?x_1,e),
     f(e,?x) = f(?x_1,d),
     f(e,?x) = f(?x_1,c),
     f(e,?x) = f(?x_1,b),
     f(e,?x) = f(?x_1,a),
     f(e,?x) = f(e,?x_1),
     f(e,?x) = g,
     f(?x,a) = f(?x_1,e),
     f(?x,a) = f(?x_1,d),
     f(?x,a) = f(?x_1,c),
     f(?x,a) = f(?x_1,b),
     f(?x,a) = f(?x_1,a),
     f(?x,a) = g,
     f(?x,b) = f(?x_1,e),
     f(?x,b) = f(?x_1,d),
     f(?x,b) = f(?x_1,c),
     f(?x,b) = f(?x_1,b),
     f(?x,b) = g,
     f(?x,c) = f(?x_1,e),
     f(?x,c) = f(?x_1,d),
     f(?x,c) = f(?x_1,c),
     f(?x,c) = g,
     f(?x,d) = f(?x_1,e),
     f(?x,d) = f(?x_1,d),
     f(?x,d) = g,
     f(?x,e) = f(?x_1,e),
     f(?x,e) = g ]
Time: 0.955 [s]

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

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

proof:
     b
->R^ a

     e
->R^ d
->R^ c
->R^ a
Total Time: 0.957 [s]

problems/526.trs: Success(not UNC)
real 0.97
user 0.96
sys 0.01