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(minus(), x), 0()) -> x,
       app(app(minus(), app(s(), x)), app(s(), y)) -> app(app(minus(), x), y),
                  app(app(plus(), app(s(), x)), y) ->
  app(app(plus(), x), app(s(), y)),
                  app(app(plus(), app(s(), x)), y) ->
  app(s(), app(app(plus(), x), y)),
                  app(app(plus(), app(s(), x)), y) ->
  app(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))),
                          app(app(plus(), 0()), y) -> 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(),
                        app(double(), app(s(), x)) ->
  app(s(), app(s(), app(double(), x))),
                                app(double(), 0()) -> 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(minus(), x), 0()) -> x,
         app(app(minus(), app(s(), x)), app(s(), y)) ->
    app(app(minus(), x), y),
                    app(app(plus(), app(s(), x)), y) ->
    app(app(plus(), x), app(s(), y)),
                    app(app(plus(), app(s(), x)), y) ->
    app(s(), app(app(plus(), x), y)),
                    app(app(plus(), app(s(), x)), y) ->
    app(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))),
                            app(app(plus(), 0()), y) -> 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(),
                          app(double(), app(s(), x)) ->
    app(s(), app(s(), app(double(), x))),
                                  app(double(), 0()) -> 0()
   }
  Fail