MAYBE
MAYBE
TRS:
 {
             cons(mark(X1), X2) -> mark(cons(X1, X2)),
           cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)),
                  from(mark(X)) -> mark(from(X)),
                    from(ok(X)) -> ok(from(X)),
                     s(mark(X)) -> mark(s(X)),
                       s(ok(X)) -> ok(s(X)),
           active(cons(X1, X2)) -> cons(active(X1), X2),
                active(from(X)) -> mark(cons(X, from(s(X)))),
                active(from(X)) -> from(active(X)),
                   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),
              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(from(X)) -> from(proper(X)),
                   proper(s(X)) -> s(proper(X)),
            proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)),
                    proper(0()) -> ok(0()),
                   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)),
                    from(mark(X)) -> mark(from(X)),
                      from(ok(X)) -> ok(from(X)),
                       s(mark(X)) -> mark(s(X)),
                         s(ok(X)) -> ok(s(X)),
             active(cons(X1, X2)) -> cons(active(X1), X2),
                  active(from(X)) -> mark(cons(X, from(s(X)))),
                  active(from(X)) -> from(active(X)),
                     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),
                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(from(X)) -> from(proper(X)),
                     proper(s(X)) -> s(proper(X)),
              proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)),
                      proper(0()) -> ok(0()),
                     top(mark(X)) -> top(proper(X)),
                       top(ok(X)) -> top(active(X))
   }
  Fail