NO
Input:
   [ f(?x,?y) -> a,
     f(k(l(a1,a2),a1,a3),?y) -> a,
     f(?x,u) -> a,
     a -> g(b1,u),
     b1 -> b,
     b -> h(?x,d),
     h(?y,d) -> i(c),
     u -> j(v),
     m(?x,?x) -> n(?y) ]

Make it flat:
   [ f(!cl_1,?y) -> a,
     k(!cl_0,a1,a3) -> !cl_1,
     f(?x,u) -> a,
     a -> g(b1,u),
     b1 -> b,
     b -> h(?x,d),
     h(?y,d) -> i(c),
     u -> j(v),
     m(?x,?x) -> n(?y),
     l(a1,a2) -> !cl_0,
     f(?x,?y) -> a ]
Time: 0.000 [s]

Make it Complete (R^):
   [ f(!cl_1,?y) = f(?x_1,?y_1),
     f(!cl_1,?y) = g(b1,u),
     f(!cl_1,?y) = g(b,u),
     f(!cl_1,?y) = f(?x_1,u),
     f(!cl_1,?y) = f(!cl_1,?y_1),
     f(!cl_1,?y) = a,
     k(!cl_0,a1,a3) = !cl_1,
     f(?x,u) = f(?x_1,?y_1),
     f(?x,u) = g(b1,u),
     f(?x,u) = g(b,u),
     f(?x,u) = f(?x_1,u),
     f(?x,u) = a,
     g(b,u) = a,
     g(b,u) = g(b1,u),
     g(b,u) = f(?x_1,?y_1),
     g(b1,u) = f(?x_1,?y_1),
     a = g(b1,u),
     b1 = h(?x,d),
     b1 = i(c),
     b1 = b,
     b = i(c),
     b = h(?x,d),
     h(?y,d) = h(?y_1,d),
     h(?y,d) = i(c),
     u = j(v),
     m(?x,?x) = m(?x_1,?x_1),
     n(?y) = n(?y_1),
     m(?x,?x) = n(?y),
     l(a1,a2) = !cl_0,
     f(?x,?y) = f(?x_1,?y_1),
     f(?x,?y) = a ]
Time: 0.012 [s]

CPNF:
   [ a … g(i(c),j(v)),
     b … i(c),
     u … j(v),
     a3 … a3,
     !cl_1 … !cl_1,
     d … d,
     c … c,
     v … v,
     a2 … a2,
     a1 … a1,
     !cl_0 … !cl_0 ]
Time: 0.000 [s]

Now checking all the pairs in CW...

Time to check pairs: 0.000 [s]

The TRS doesn't have Uniqueness of Normal Forms.
Counter Example: 
     n(?y)
<->* n(?y_1)

proof:
     n(?y)
->R^ m(?!,?!)

     n(?y_1)
->R^ m(?!,?!)
Total Time: 0.013 [s]

problems/r9.trs: Success(not UNC)
real 0.03
user 0.03
sys 0.00