MAYBE
MAYBE
TRS:
 {
       app(app(app(app(filter2(), true()), fun), x), xs) ->
  app(app(cons(), x), app(app(filter(), fun), xs)),
      app(app(app(app(filter2(), false()), fun), x), xs) ->
  app(app(filter(), fun), xs),
   app(app(app(if(), true()), app(s(), x)), app(s(), y)) -> app(s(), x),
  app(app(app(if(), false()), app(s(), x)), app(s(), y)) -> app(s(), y),
                           app(app(g(), x), app(c(), y)) ->
  app(
     app(g(), x),
     app(
        app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))),
        app(c(), y)
     )
  ),
                           app(app(g(), x), app(c(), y)) ->
  app(c(), app(app(g(), x), y)),
           app(app(map(), fun), app(app(cons(), x), xs)) ->
  app(app(cons(), app(fun, x)), app(app(map(), fun), xs)),
                             app(app(map(), fun), nil()) -> nil(),
        app(app(filter(), fun), app(app(cons(), x), xs)) ->
  app(app(app(app(filter2(), app(fun, x)), fun), x), xs),
                          app(app(filter(), fun), nil()) -> nil(),
                                   app(f(), app(s(), x)) -> app(f(), x),
                                           app(f(), 0()) -> true(),
                                           app(f(), 1()) -> false()
 }
 DUP: We consider a duplicating system.
  Trs:
   {
         app(app(app(app(filter2(), true()), fun), x), xs) ->
    app(app(cons(), x), app(app(filter(), fun), xs)),
        app(app(app(app(filter2(), false()), fun), x), xs) ->
    app(app(filter(), fun), xs),
     app(app(app(if(), true()), app(s(), x)), app(s(), y)) -> app(s(), x),
    app(app(app(if(), false()), app(s(), x)), app(s(), y)) -> app(s(), y),
                             app(app(g(), x), app(c(), y)) ->
    app(
       app(g(), x),
       app(
          app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))
          ), app(c(), y)
       )
    ),
                             app(app(g(), x), app(c(), y)) ->
    app(c(), app(app(g(), x), y)),
             app(app(map(), fun), app(app(cons(), x), xs)) ->
    app(app(cons(), app(fun, x)), app(app(map(), fun), xs)),
                               app(app(map(), fun), nil()) -> nil(),
          app(app(filter(), fun), app(app(cons(), x), xs)) ->
    app(app(app(app(filter2(), app(fun, x)), fun), x), xs),
                            app(app(filter(), fun), nil()) -> nil(),
                                     app(f(), app(s(), x)) -> app(f(), x),
                                             app(f(), 0()) -> true(),
                                             app(f(), 1()) -> false()
   }
  Fail