YES
(ignored inputs)COMMENT doi:10.1006/jsco.1996.0002 [112] p. 31 ( signature extension and currying do not preserve NFP ) submitted by: Bertram Felgenhauer
Input:
   [ f(?x,?x) -> g,
     a -> b,
     a -> c,
     b -> b,
     c -> c,
     f(a,?x) -> g,
     f(b,?x) -> g,
     f(c,?x) -> g,
     f(?x,a) -> g,
     f(?x,b) -> g,
     f(?x,c) -> g ]

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

Make it Complete (R^):
   [ 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(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,
     a = b,
     a = c,
     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(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,c),
     f(b,?x) = f(?x_1,b),
     f(b,?x) = f(?x_1,a),
     f(b,?x) = f(c,?x_1),
     f(b,?x) = f(b,?x_1),
     f(b,?x) = g,
     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(c,?x_1),
     f(c,?x) = g,
     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,c),
     f(?x,b) = f(?x_1,b),
     f(?x,b) = g,
     f(?x,c) = f(?x_1,c),
     f(?x,c) = g ]
Time: 0.101 [s]

CPNF:
   [ g … g ]
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: 0.101 [s]

problems/525.trs: Success(UNC)
real 0.12
user 0.11
sys 0.00