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(:(), z), app(app(+(), x), app(f, y))) ->
  app(app(:(), app(app(g(), z), y)), app(app(+(), x), a())),
             app(app(:(), app(app(:(), x), y)), z) ->
  app(app(:(), x), app(app(:(), y), z)),
             app(app(:(), app(app(+(), x), y)), z) ->
  app(app(+(), app(app(:(), x), z)), app(app(:(), y), z)),
       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(:(), z), app(app(+(), x), app(f, y))) ->
    app(app(:(), app(app(g(), z), y)), app(app(+(), x), a())),
               app(app(:(), app(app(:(), x), y)), z) ->
    app(app(:(), x), app(app(:(), y), z)),
               app(app(:(), app(app(+(), x), y)), z) ->
    app(app(+(), app(app(:(), x), z)), app(app(:(), y), z)),
         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