YES
(ignored inputs)COMMENT handcrafted "UNC & ~NFP" submitted by: Franziska Rapp
Input:
   [ if(true,a,?x) -> a,
     if(true,b,?x) -> b,
     if(true,g(a),?x) -> g(a),
     if(true,g(b),?x) -> g(b),
     if(false,?x,a) -> a,
     if(false,?x,b) -> b,
     if(false,?x,g(a)) -> g(a),
     if(false,?x,g(b)) -> g(b),
     g(a) -> g(g(a)),
     g(b) -> a,
     f(a,b) -> b,
     f(g(g(a)),?x) -> b ]

Make it flat:
   [ f(!cl_2,?x) -> b,
     f(a,b) -> b,
     !cl_1 -> a,
     !cl_0 -> g(!cr_0),
     !cr_0 -> g(a),
     if(false,?x,!cl_1) -> g(b),
     if(false,?x,!cl_0) -> g(a),
     if(false,?x,b) -> b,
     if(false,?x,a) -> a,
     if(true,!cl_1,?x) -> g(b),
     !cl_2 -> !cl_2,
     g(!cl_0) -> !cl_2,
     if(true,!cl_0,?x) -> g(a),
     if(true,b,?x) -> b,
     if(true,a,?x) -> a,
     !cl_0 -> !cl_0,
     g(a) -> !cl_0,
     g(b) -> !cl_1,
     !cl_1 -> !cl_1 ]
Time: 0.000 [s]

Make it Complete (R^):
   [ f(!cr_0,?x) = b,
     f(!cl_0,?x) = b,
     f(!cl_2,?x) = if(true,b,?x_1),
     f(!cl_2,?x) = if(false,?x_1,b),
     f(!cl_2,?x) = f(a,b),
     f(!cr_0,?x) = f(!cl_1,b),
     f(a,b) = f(!cl_0,?x),
     f(!cl_0,?x) = if(false,?x_2,b),
     f(!cr_0,?x) = if(false,?x_5,b),
     f(!cr_0,?x) = f(a,b),
     f(!cr_0,?x) = if(true,b,?x_4),
     f(!cl_0,?x) = if(true,b,?x_4),
     f(!cl_0,?x) = f(!cl_1,b),
     f(!cl_2,?x) = f(!cl_1,b),
     f(!cr_0,?x_1) = f(!cl_2,?x),
     f(!cr_0,?x_1) = f(!cr_0,?x),
     f(!cr_0,?x) = f(!cl_0,?x_1),
     f(!cl_0,?x) = f(!cl_0,?x_1),
     f(!cl_0,?x_1) = f(!cl_2,?x),
     f(!cl_2,?x) = f(!cl_2,?x_1),
     f(!cl_2,?x) = b,
     f(!cl_1,b) = b,
     f(a,b) = if(true,b,?x_1),
     f(!cl_1,b) = if(true,b,?x_3),
     f(!cl_1,b) = f(a,b),
     f(!cl_1,b) = if(false,?x_1,b),
     f(a,b) = if(false,?x_1,b),
     f(a,b) = b,
     g(!cl_1) = !cl_0,
     !cl_1 = if(true,a,?x),
     if(true,!cl_1,?x) = a,
     if(true,!cl_1,?x_1) = if(true,a,?x),
     g(!cl_1) = if(true,!cl_0,?x),
     !cl_1 = if(false,?x,a),
     if(false,?x,!cl_1) = a,
     if(false,?x_1,!cl_1) = if(false,?x,a),
     if(true,!cl_1,?x_1) = if(false,?x,a),
     if(false,?x,!cl_1) = if(true,a,?x_1),
     g(!cl_1) = if(false,?x,!cl_0),
     g(!cl_1) = !cr_0,
     g(!cl_1) = if(false,?x,!cr_0),
     g(!cl_1) = if(true,!cr_0,?x),
     g(!cl_1) = !cl_2,
     g(!cl_1) = g(!cl_0),
     g(!cl_1) = g(!cl_2),
     g(!cl_1) = if(true,!cl_2,?x),
     g(!cl_1) = if(false,?x,!cl_2),
     g(!cl_1) = g(a),
     g(!cl_1) = g(!cr_0),
     a = g(b),
     if(true,a,?x) = g(b),
     if(false,?x,a) = g(b),
     !cl_1 = a,
     g(!cl_0) = !cl_0,
     !cr_0 = g(!cr_0),
     !cl_0 = !cl_2,
     g(!cr_0) = g(a),
     g(!cr_0) = if(true,!cl_0,?x_1),
     g(!cr_0) = if(false,?x_1,!cl_0),
     g(!cr_0) = if(false,?x_1,!cr_0),
     g(!cl_0) = if(true,!cr_0,?x_1),
     if(true,!cl_0,?x_1) = !cl_2,
     if(true,!cl_2,?x_1) = !cr_0,
     if(true,!cl_2,?x_3) = if(true,!cr_0,?x_1),
     if(false,?x_1,!cl_2) = !cr_0,
     if(false,?x_3,!cl_2) = if(false,?x_1,!cr_0),
     if(true,!cl_2,?x_3) = if(false,?x_1,!cr_0),
     if(false,?x_1,!cl_2) = if(true,!cr_0,?x_3),
     if(false,?x,!cl_2) = !cl_0,
     if(false,?x,!cl_2) = if(true,!cl_0,?x_1),
     if(true,!cl_2,?x_1) = if(false,?x,!cl_0),
     if(false,?x_1,!cl_2) = if(false,?x,!cl_0),
     if(false,?x,!cl_2) = g(a),
     g(!cl_2) = !cl_2,
     g(!cl_2) = g(!cl_0),
     if(true,!cl_2,?x) = !cl_0,
     if(true,!cl_2,?x_1) = if(true,!cl_0,?x),
     if(true,!cl_2,?x) = g(a),
     g(!cl_2) = !cl_0,
     if(true,!cl_2,?x_1) = g(!cr_0),
     g(!cl_2) = if(true,!cr_0,?x_1),
     if(true,!cl_2,?x_1) = g(!cl_0),
     if(true,!cl_2,?x_1) = g(!cl_2),
     if(true,!cl_2,?x_1) = if(false,?x_5,!cl_2),
     if(true,!cl_2,?x_1) = if(true,!cl_2,?x_3),
     if(true,!cl_2,?x_1) = !cl_2,
     if(false,?x_1,!cl_2) = g(!cl_0),
     if(false,?x_3,!cl_0) = g(!cl_2),
     g(!cl_2) = !cr_0,
     g(!cl_2) = if(true,!cl_0,?x_5),
     g(!cl_2) = g(a),
     if(false,?x_3,!cr_0) = g(!cl_2),
     g(!cl_2) = g(!cr_0),
     g(!cl_2) = if(false,?x_3,!cl_2),
     if(false,?x_3,!cl_2) = g(!cr_0),
     if(false,?x_3,!cl_2) = if(false,?x_7,!cl_2),
     if(false,?x_3,!cl_2) = !cl_2,
     !cl_2 = !cr_0,
     !cl_2 = if(false,?x_3,!cr_0),
     !cl_2 = if(false,?x_2,!cl_0),
     g(!cl_0) = if(true,!cl_0,?x_1),
     g(!cl_0) = if(false,?x_1,!cl_0),
     g(!cl_0) = !cr_0,
     g(!cl_0) = if(false,?x_1,!cr_0),
     g(a) = g(!cl_0),
     !cl_2 = g(a),
     if(true,!cr_0,?x_1) = !cl_2,
     g(!cr_0) = if(true,!cr_0,?x_1),
     !cl_0 = g(!cr_0),
     if(true,!cr_0,?x) = g(a),
     if(true,!cr_0,?x_1) = if(true,!cl_0,?x),
     if(true,!cr_0,?x) = !cl_0,
     g(!cr_0) = g(!cl_0),
     g(!cr_0) = !cl_2,
     if(false,?x,!cr_0) = g(a),
     if(false,?x_1,!cr_0) = if(false,?x,!cl_0),
     if(true,!cr_0,?x_1) = if(false,?x,!cl_0),
     if(false,?x,!cr_0) = if(true,!cl_0,?x_1),
     if(false,?x,!cr_0) = !cl_0,
     if(false,?x_1,!cr_0) = if(true,!cr_0,?x_3),
     if(false,?x_1,!cr_0) = if(false,?x_3,!cr_0),
     if(false,?x_1,!cr_0) = !cr_0,
     if(true,!cr_0,?x_1) = if(true,!cr_0,?x_3),
     if(true,!cr_0,?x_1) = !cr_0,
     !cr_0 = !cl_0,
     !cr_0 = if(true,!cl_0,?x_1),
     !cr_0 = if(false,?x_1,!cl_0),
     !cr_0 = g(a),
     if(false,?x,!cl_1) = !cl_1,
     if(false,?x,!cl_1) = if(true,!cl_1,?x_1),
     if(false,?x,!cl_1) = if(false,?x_1,!cl_1),
     if(false,?x,!cl_1) = g(b),
     if(false,?x,!cl_0) = !cl_0,
     if(false,?x,!cl_0) = if(true,!cl_0,?x_1),
     if(false,?x,!cl_0) = if(false,?x_1,!cl_0),
     if(false,?x,!cl_0) = g(a),
     if(false,?x,b) = if(true,b,?x_1),
     if(false,?x,b) = if(false,?x_1,b),
     if(false,?x,b) = b,
     if(false,?x,a) = if(true,a,?x_1),
     if(false,?x,a) = if(false,?x_1,a),
     if(false,?x,a) = a,
     if(true,!cl_1,?x) = !cl_1,
     if(true,!cl_1,?x) = if(true,!cl_1,?x_1),
     if(true,!cl_1,?x) = g(b),
     g(!cl_0) = !cl_2,
     if(true,!cl_0,?x) = !cl_0,
     if(true,!cl_0,?x) = if(true,!cl_0,?x_1),
     if(true,!cl_0,?x) = g(a),
     if(true,b,?x) = if(true,b,?x_1),
     if(true,b,?x) = b,
     if(true,a,?x) = if(true,a,?x_1),
     if(true,a,?x) = a,
     g(a) = !cl_0,
     g(b) = !cl_1 ]
Time: 0.386 [s]

CPNF:
   [ false … false,
     true … true,
     !cl_1 … a,
     b … b ]
Time: 0.000 [s]

Now checking all the pairs in CW...

Time to check pairs: 0.001 [s]

The TRS has Uniqueness of Normal Forms.
Total Time: 0.393 [s]

problems/741.trs: Success(UNC)
real 0.43
user 0.40
sys 0.01