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(:(), app(app(:(), app(app(:(), app(app(:(), C()), x)), y)), z)), u)
  ->
  app(
     app(:(), app(app(:(), x), z)),
     app(app(:(), app(app(:(), app(app(:(), x), y)), z)), u)
  ),
                                  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(:(), app(app(:(), app(app(:(), app(app(:(), C()), x)), y)), z)), u
    ) ->
    app(
       app(:(), app(app(:(), x), z)),
       app(app(:(), app(app(:(), app(app(:(), x), y)), z)), u)
    ),
                                    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