MAYBE
MAYBE
TRS:
 {
   app(app(app(app(filter2(), true()), f), x), xs) ->
  app(app(cons(), x), app(app(filter(), f), xs)),
  app(app(app(app(filter2(), false()), f), x), xs) ->
  app(app(filter(), f), xs),
                     app(app(*(), app(s(), x)), y) ->
  app(app(+(), app(app(*(), x), y)), y),
                             app(app(*(), 0()), y) -> 0(),
                     app(app(+(), x), app(s(), y)) ->
  app(s(), app(app(+(), x), y)),
                             app(app(+(), x), 0()) -> x,
       app(app(map(), f), app(app(cons(), x), xs)) ->
  app(app(cons(), app(f, x)), app(app(map(), f), xs)),
                         app(app(map(), f), nil()) -> nil(),
    app(app(filter(), f), app(app(cons(), x), xs)) ->
  app(app(app(app(filter2(), app(f, x)), f), x), xs),
                      app(app(filter(), f), nil()) -> nil(),
                             app(p(), app(s(), x)) -> x,
                          app(fact(), app(s(), x)) ->
  app(app(*(), app(s(), x)), app(fact(), app(p(), app(s(), x)))),
                                  app(fact(), 0()) -> app(s(), 0())
 }
 DUP: We consider a duplicating system.
  Trs:
   {
     app(app(app(app(filter2(), true()), f), x), xs) ->
    app(app(cons(), x), app(app(filter(), f), xs)),
    app(app(app(app(filter2(), false()), f), x), xs) ->
    app(app(filter(), f), xs),
                       app(app(*(), app(s(), x)), y) ->
    app(app(+(), app(app(*(), x), y)), y),
                               app(app(*(), 0()), y) -> 0(),
                       app(app(+(), x), app(s(), y)) ->
    app(s(), app(app(+(), x), y)),
                               app(app(+(), x), 0()) -> x,
         app(app(map(), f), app(app(cons(), x), xs)) ->
    app(app(cons(), app(f, x)), app(app(map(), f), xs)),
                           app(app(map(), f), nil()) -> nil(),
      app(app(filter(), f), app(app(cons(), x), xs)) ->
    app(app(app(app(filter2(), app(f, x)), f), x), xs),
                        app(app(filter(), f), nil()) -> nil(),
                               app(p(), app(s(), x)) -> x,
                            app(fact(), app(s(), x)) ->
    app(app(*(), app(s(), x)), app(fact(), app(p(), app(s(), x)))),
                                    app(fact(), 0()) -> app(s(), 0())
   }
  Fail