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), app(s(), y)) ->
  app(pred(), app(app(minus(), x), y)),
                         app(app(minus(), x), 0()) -> x,
        app(app(quot(), app(s(), x)), app(s(), y)) ->
  app(s(), app(app(quot(), app(app(minus(), x), y)), app(s(), y))),
                app(app(quot(), 0()), app(s(), y)) -> 0(),
       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(pred(), app(s(), x)) -> x
 }
 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), app(s(), y)) ->
    app(pred(), app(app(minus(), x), y)),
                           app(app(minus(), x), 0()) -> x,
          app(app(quot(), app(s(), x)), app(s(), y)) ->
    app(s(), app(app(quot(), app(app(minus(), x), y)), app(s(), y))),
                  app(app(quot(), 0()), app(s(), y)) -> 0(),
         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(pred(), app(s(), x)) -> x
   }
  Fail