MAYBE
Trs:
 {                                    app'(min(), app'(app'(add(), n), nil())) -> n,
                    app'(min(), app'(app'(add(), n), app'(app'(add(), m), x))) -> app'(app'(if_min(), app'(app'(le(), n), m)), app'(app'(add(), n), app'(app'(add(), m), x))),
                                                      app'(app'(le(), 0()), y) -> true(),
                                           app'(app'(le(), app'(s(), x)), 0()) -> false(),
                                  app'(app'(le(), app'(s(), x)), app'(s(), y)) -> app'(app'(le(), x), y),
   app'(app'(if_min(), true()), app'(app'(add(), n), app'(app'(add(), m), x))) -> app'(min(), app'(app'(add(), n), x)),
  app'(app'(if_min(), false()), app'(app'(add(), n), app'(app'(add(), m), x))) -> app'(min(), app'(app'(add(), m), x)),
                                                    app'(app'(eq(), 0()), 0()) -> true(),
                                           app'(app'(eq(), 0()), app'(s(), x)) -> false(),
                                           app'(app'(eq(), app'(s(), x)), 0()) -> false(),
                                  app'(app'(eq(), app'(s(), x)), app'(s(), y)) -> app'(app'(eq(), x), y),
                                                    app'(app'(rm(), n), nil()) -> nil(),
                                  app'(app'(rm(), n), app'(app'(add(), m), x)) -> app'(app'(app'(if_rm(), app'(app'(eq(), n), m)), n), app'(app'(add(), m), x)),
                                                   app'(app'(app(), nil()), y) -> y,
                                 app'(app'(app(), app'(app'(add(), n), x)), y) -> app'(app'(add(), n), app'(app'(app(), x), y)),
                                           app'(app'(minsort(), nil()), nil()) -> nil(),
                             app'(app'(minsort(), app'(app'(add(), n), x)), y) -> app'(app'(app'(if_minsort(), app'(app'(eq(), n), app'(min(), app'(app'(add(), n), x)))), app'(app'(add(), n), x)), y),
                                                   app'(app'(map(), f), nil()) -> nil(),
                                app'(app'(map(), f), app'(app'(add(), x), xs)) -> app'(app'(add(), app'(f, x)), app'(app'(map(), f), xs)),
                                                app'(app'(filter(), f), nil()) -> nil(),
                             app'(app'(filter(), f), app'(app'(add(), x), xs)) -> app'(app'(app'(app'(filter2(), app'(f, x)), f), x), xs),
                 app'(app'(app'(if_rm(), true()), n), app'(app'(add(), m), x)) -> app'(app'(rm(), n), x),
                app'(app'(app'(if_rm(), false()), n), app'(app'(add(), m), x)) -> app'(app'(add(), m), app'(app'(rm(), n), x)),
            app'(app'(app'(if_minsort(), true()), app'(app'(add(), n), x)), y) -> app'(app'(add(), n), app'(app'(minsort(), app'(app'(app(), app'(app'(rm(), n), x)), y)), nil())),
           app'(app'(app'(if_minsort(), false()), app'(app'(add(), n), x)), y) -> app'(app'(minsort(), x), app'(app'(add(), n), y)),
                           app'(app'(app'(app'(filter2(), true()), f), x), xs) -> app'(app'(add(), x), app'(app'(filter(), f), xs)),
                          app'(app'(app'(app'(filter2(), false()), f), x), xs) -> app'(app'(filter(), f), xs)}
 Comment:
  We consider a duplicating trs.
  FAIL:
   Open