YES
(ignored inputs)COMMENT doi:10.1007/3-540-62950-5_71 [6] p. 209 submitted by: Takahito Aoto , Junichi Yoshida , and Yoshihito Toyama
Input:
   [ f(?x) -> g(a),
     g(?x) -> ?x,
     h(?x,?x) -> 0,
     a -> 1 ]

Make it flat:
   [ f(?x) -> g(a),
     g(?x) -> ?x,
     h(?x,?x) -> 0,
     a -> 1 ]
Time: 0.000 [s]

Make it Complete (R^):
   [ g(1) = f(?x),
     f(?x) = a,
     f(?x) = 1,
     f(?x) = f(?x_1),
     f(?x) = g(a),
     a = g(1),
     g(1) = 1,
     a = g(a),
     g(a) = g(1),
     1 = g(a),
     g(0) = 0,
     h(?x,?x) = g(0),
     g(?x) = ?x,
     h(?x,?x) = h(?x_1,?x_1),
     h(?x,?x) = 0,
     a = 1 ]
Time: 0.003 [s]

CPNF:
   [ 0 … 0,
     1 … 1 ]
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: 0.003 [s]

problems/18.trs: Success(UNC)
real 0.02
user 0.01
sys 0.01