YES
(ignored inputs)COMMENT [8] TRS R_1
Input:
   [ f(?x,?x) -> a,
     c -> g(c),
     g(?x) -> f(?x,?x) ]

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

Make it Complete (R^):
   [ f(?x,?x) = f(?x_1,?x_1),
     a = g(?x),
     g(a) = c,
     f(c,a) = c,
     f(a,c) = c,
     g(a) = f(c,c),
     f(c,a) = g(c),
     f(a,c) = g(c),
     g(a) = a,
     g(a) = f(?x_1,?x_1),
     f(c,a) = g(?x_1),
     f(a,c) = g(?x_1),
     f(c,a) = f(?x_1,?x_1),
     f(a,c) = f(?x_1,?x_1),
     g(a) = g(?x_1),
     f(c,a) = a,
     f(a,a) = a,
     f(c,a) = f(a,c),
     f(c,a) = f(a,a),
     f(a,c) = f(a,a),
     f(c,a) = f(c,c),
     f(a,c) = g(a),
     f(c,a) = g(a),
     g(a) = f(a,a),
     g(c) = g(a),
     f(a,a) = g(c),
     f(a,a) = c,
     f(a,a) = g(?x_2),
     f(a,a) = f(?x_2,?x_2),
     f(a,a) = f(c,c),
     f(a,c) = f(c,c),
     f(a,c) = a,
     a = c,
     a = f(c,c),
     g(c) = g(?x_1),
     f(?x_1,?x_1) = f(c,c),
     g(?x_1) = f(c,c),
     g(?x_1) = f(?x_3,?x_3),
     g(?x_1) = g(?x_3),
     c = g(?x_1),
     f(?x_1,?x_1) = c,
     g(c) = f(?x_1,?x_1),
     a = g(c),
     f(?x,?x) = a,
     f(c,c) = g(c),
     c = f(c,c),
     c = g(c),
     g(?x) = f(?x,?x) ]
Time: 0.086 [s]

The number of normal forms that must be checked: 605
Time: 0.127 [s]

Now checking all the pairs...

Time to check pairs: 0.153 [s]

The TRS has Uniqueness of Normal Forms.
Total Time: 0.366 [s]

problems/218.trs: Success(UNC)
real 0.40
user 0.38
sys 0.01