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(ack(), app(succ(), x)), y) ->
  app(app(ack(), x), app(succ(), 0())),
   app(app(ack(), app(succ(), x)), app(succ(), y)) ->
  app(app(ack(), x), app(app(ack(), app(succ(), x)), y)),
                           app(app(ack(), 0()), y) -> app(succ(), y),
       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()
 }
 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(ack(), app(succ(), x)), y) ->
    app(app(ack(), x), app(succ(), 0())),
     app(app(ack(), app(succ(), x)), app(succ(), y)) ->
    app(app(ack(), x), app(app(ack(), app(succ(), x)), y)),
                             app(app(ack(), 0()), y) -> app(succ(), y),
         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()
   }
  Fail