MAYBE
MAYBE
TRS:
 {
             cons(mark(X1), X2) -> mark(cons(X1, X2)),
           cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)),
                     f(mark(X)) -> mark(f(X)),
                       f(ok(X)) -> ok(f(X)),
                     g(mark(X)) -> mark(g(X)),
                       g(ok(X)) -> ok(g(X)),
           active(cons(X1, X2)) -> cons(active(X1), X2),
                   active(f(X)) -> mark(cons(X, f(g(X)))),
                   active(f(X)) -> f(active(X)),
                   active(g(X)) -> g(active(X)),
                active(g(s(X))) -> mark(s(s(g(X)))),
                 active(g(0())) -> mark(s(0())),
                   active(s(X)) -> s(active(X)),
            active(sel(X1, X2)) -> sel(X1, active(X2)),
            active(sel(X1, X2)) -> sel(active(X1), X2),
  active(sel(s(X), cons(Y, Z))) -> mark(sel(X, Z)),
   active(sel(0(), cons(X, Y))) -> mark(X),
                     s(mark(X)) -> mark(s(X)),
                       s(ok(X)) -> ok(s(X)),
              sel(X1, mark(X2)) -> mark(sel(X1, X2)),
              sel(mark(X1), X2) -> mark(sel(X1, X2)),
            sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)),
           proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)),
                   proper(f(X)) -> f(proper(X)),
                   proper(g(X)) -> g(proper(X)),
                   proper(s(X)) -> s(proper(X)),
                    proper(0()) -> ok(0()),
            proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)),
                   top(mark(X)) -> top(proper(X)),
                     top(ok(X)) -> top(active(X))
 }
 DUP: We consider a duplicating system.
  Trs:
   {
               cons(mark(X1), X2) -> mark(cons(X1, X2)),
             cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)),
                       f(mark(X)) -> mark(f(X)),
                         f(ok(X)) -> ok(f(X)),
                       g(mark(X)) -> mark(g(X)),
                         g(ok(X)) -> ok(g(X)),
             active(cons(X1, X2)) -> cons(active(X1), X2),
                     active(f(X)) -> mark(cons(X, f(g(X)))),
                     active(f(X)) -> f(active(X)),
                     active(g(X)) -> g(active(X)),
                  active(g(s(X))) -> mark(s(s(g(X)))),
                   active(g(0())) -> mark(s(0())),
                     active(s(X)) -> s(active(X)),
              active(sel(X1, X2)) -> sel(X1, active(X2)),
              active(sel(X1, X2)) -> sel(active(X1), X2),
    active(sel(s(X), cons(Y, Z))) -> mark(sel(X, Z)),
     active(sel(0(), cons(X, Y))) -> mark(X),
                       s(mark(X)) -> mark(s(X)),
                         s(ok(X)) -> ok(s(X)),
                sel(X1, mark(X2)) -> mark(sel(X1, X2)),
                sel(mark(X1), X2) -> mark(sel(X1, X2)),
              sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)),
             proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)),
                     proper(f(X)) -> f(proper(X)),
                     proper(g(X)) -> g(proper(X)),
                     proper(s(X)) -> s(proper(X)),
                      proper(0()) -> ok(0()),
              proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)),
                     top(mark(X)) -> top(proper(X)),
                       top(ok(X)) -> top(active(X))
   }
  Fail