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(head(X)) -> head(active(X)),
        active(head(cons(X, XS))) -> mark(X),
                   active(2nd(X)) -> 2nd(active(X)),
         active(2nd(cons(X, XS))) -> mark(head(XS)),
             active(take(X1, X2)) -> take(X1, active(X2)),
             active(take(X1, X2)) -> take(active(X1), X2),
  active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS))),
            active(take(0(), XS)) -> mark(nil()),
              active(sel(X1, X2)) -> sel(X1, active(X2)),
              active(sel(X1, X2)) -> sel(active(X1), X2),
   active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)),
    active(sel(0(), cons(X, XS))) -> mark(X),
                    head(mark(X)) -> mark(head(X)),
                      head(ok(X)) -> ok(head(X)),
                     2nd(mark(X)) -> mark(2nd(X)),
                       2nd(ok(X)) -> ok(2nd(X)),
               take(X1, mark(X2)) -> mark(take(X1, X2)),
               take(mark(X1), X2) -> mark(take(X1, X2)),
             take(ok(X1), ok(X2)) -> ok(take(X1, X2)),
                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(head(X)) -> head(proper(X)),
                   proper(2nd(X)) -> 2nd(proper(X)),
                    proper(nil()) -> ok(nil()),
             proper(take(X1, X2)) -> take(proper(X1), proper(X2)),
                      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)),
                      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(head(X)) -> head(active(X)),
          active(head(cons(X, XS))) -> mark(X),
                     active(2nd(X)) -> 2nd(active(X)),
           active(2nd(cons(X, XS))) -> mark(head(XS)),
               active(take(X1, X2)) -> take(X1, active(X2)),
               active(take(X1, X2)) -> take(active(X1), X2),
    active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS))),
              active(take(0(), XS)) -> mark(nil()),
                active(sel(X1, X2)) -> sel(X1, active(X2)),
                active(sel(X1, X2)) -> sel(active(X1), X2),
     active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)),
      active(sel(0(), cons(X, XS))) -> mark(X),
                      head(mark(X)) -> mark(head(X)),
                        head(ok(X)) -> ok(head(X)),
                       2nd(mark(X)) -> mark(2nd(X)),
                         2nd(ok(X)) -> ok(2nd(X)),
                 take(X1, mark(X2)) -> mark(take(X1, X2)),
                 take(mark(X1), X2) -> mark(take(X1, X2)),
               take(ok(X1), ok(X2)) -> ok(take(X1, X2)),
                  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(head(X)) -> head(proper(X)),
                     proper(2nd(X)) -> 2nd(proper(X)),
                      proper(nil()) -> ok(nil()),
               proper(take(X1, X2)) -> take(proper(X1), proper(X2)),
                        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