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(.(), x), app(i(), x)) -> 1(),
                             app(app(.(), x), 1()) -> x,
   app(app(.(), y), app(app(.(), app(i(), y)), z)) -> z,
             app(app(.(), app(app(.(), x), y)), z) ->
  app(app(.(), x), app(app(.(), y), z)),
                     app(app(.(), app(i(), x)), x) -> 1(),
   app(app(.(), app(i(), y)), app(app(.(), y), z)) -> z,
                             app(app(.(), 1()), x) -> x,
       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(i(), app(app(.(), x), y)) ->
  app(app(.(), app(i(), y)), app(i(), x)),
                             app(i(), app(i(), x)) -> x,
                                     app(i(), 1()) -> 1()
 }
 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(.(), x), app(i(), x)) -> 1(),
                               app(app(.(), x), 1()) -> x,
     app(app(.(), y), app(app(.(), app(i(), y)), z)) -> z,
               app(app(.(), app(app(.(), x), y)), z) ->
    app(app(.(), x), app(app(.(), y), z)),
                       app(app(.(), app(i(), x)), x) -> 1(),
     app(app(.(), app(i(), y)), app(app(.(), y), z)) -> z,
                               app(app(.(), 1()), x) -> x,
         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(i(), app(app(.(), x), y)) ->
    app(app(.(), app(i(), y)), app(i(), x)),
                               app(i(), app(i(), x)) -> x,
                                       app(i(), 1()) -> 1()
   }
  Fail