NO
(ignored inputs)COMMENT [111] p. 30 ( GUN & ~UN & ~GUNC )
Input:
   [ b -> a,
     b -> c,
     c -> c,
     d -> c,
     d -> e,
     f(?x,a) -> A,
     f(?x,e) -> A,
     f(?x,A) -> A,
     f(c,?x) -> A ]

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

Make it Complete (R^):
   [ a = c,
     f(a,?x) = f(d,?x_1),
     f(a,?x_2) = f(b,?x),
     a = e,
     f(a,?x_2) = f(?x_1,b),
     f(a,?x_1) = f(e,?x_3),
     f(a,?x_1) = f(?x,c),
     a = d,
     f(a,?x_1) = f(?x,d),
     f(a,?x_1) = f(?x,a),
     f(a,?x_1) = f(?x,e),
     f(a,?x_1) = f(?x,A),
     f(a,?x_1) = f(c,?x),
     f(a,?x) = f(a,?x_1),
     f(a,?x) = A,
     b = a,
     f(b,?x) = A,
     f(b,?x_1) = f(c,?x),
     f(b,?x_1) = f(?x,A),
     f(b,?x_1) = f(?x,e),
     f(b,?x_1) = f(?x,a),
     f(b,?x_1) = f(?x,d),
     b = d,
     f(?x,b) = A,
     f(?x_1,b) = f(?x,c),
     f(?x_1,b) = f(?x,e),
     f(?x,b) = f(?x_1,A),
     f(b,?x_1) = f(?x,c),
     f(?x,b) = f(c,?x_1),
     f(?x,b) = f(d,?x_1),
     f(b,?x_1) = f(e,?x_3),
     f(?x,b) = f(e,?x_1),
     f(?x_3,b) = f(?x_1,d),
     f(?x_1,b) = f(b,?x_2),
     f(?x_1,b) = f(?x_3,b),
     f(?x_1,b) = f(?x,a),
     b = e,
     f(b,?x) = f(b,?x_2),
     f(b,?x) = f(d,?x_1),
     b = c,
     f(d,?x) = A,
     f(d,?x_1) = f(c,?x),
     f(d,?x_1) = f(?x,A),
     f(d,?x_1) = f(?x,e),
     f(d,?x_1) = f(?x,a),
     f(d,?x_1) = f(?x,d),
     c = e,
     f(?x_1,c) = f(?x,a),
     f(?x_3,c) = f(?x_1,d),
     f(e,?x_1) = f(?x,c),
     f(e,?x_1) = f(e,?x_3),
     f(c,?x_1) = f(e,?x_3),
     f(e,?x_3) = A,
     f(e,?x_3) = f(?x_4,A),
     f(e,?x_3) = f(?x_4,e),
     f(e,?x_3) = f(?x_4,a),
     f(e,?x_3) = f(?x_5,d),
     f(e,?x_3) = f(d,?x_1),
     f(d,?x_1) = f(d,?x_3),
     f(d,?x_1) = f(?x,c),
     f(?x,c) = f(c,?x_1),
     f(?x,c) = f(?x_1,A),
     f(?x_1,c) = f(?x,e),
     f(?x,c) = f(?x_1,c),
     f(?x,c) = A,
     d = c,
     f(?x,d) = A,
     f(?x_1,d) = f(?x,e),
     f(?x,d) = f(?x_1,A),
     f(?x,d) = f(c,?x_1),
     f(?x_1,d) = f(?x_3,d),
     f(?x_1,d) = f(?x,a),
     d = e,
     f(?x,a) = f(c,?x_1),
     f(?x,a) = f(?x_1,A),
     f(?x,a) = f(?x_1,e),
     f(?x,a) = f(?x_1,a),
     f(?x,a) = A,
     f(?x,e) = f(c,?x_1),
     f(?x,e) = f(?x_1,A),
     f(?x,e) = f(?x_1,e),
     f(?x,e) = A,
     f(?x,A) = f(c,?x_1),
     f(?x,A) = f(?x_1,A),
     f(?x,A) = A,
     f(c,?x) = f(c,?x_1),
     f(c,?x) = A ]
Time: 0.808 [s]

CPNF:
   [ a … a,
     a … e,
     A … A ]
Time: 0.000 [s]

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

proof:
     a

     e
->R^ d
->R^ c
->R^ b
->R^ a
Total Time: 0.809 [s]

problems/511.trs: Success(not UNC)
real 0.83
user 0.81
sys 0.01