MAYBE
MAYBE
TRS:
 {
                  app(app(app(app(f(), 0()), y), 0()), u) -> true(),
          app(app(app(app(f(), 0()), y), app(s(), z)), u) -> false(),
          app(app(app(app(f(), app(s(), x)), 0()), z), u) ->
  app(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u),
  app(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) ->
  app(
     app(
        app(if(), app(app(le(), x), y)),
        app(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u)
     ), app(app(app(app(f(), x), u), z), u)
  ),
        app(app(app(app(filter2(), true()), fun), x), xs) ->
  app(app(cons(), x), app(app(filter(), fun), xs)),
       app(app(app(app(filter2(), false()), fun), x), xs) ->
  app(app(filter(), fun), xs),
                        app(app(app(if(), true()), x), y) -> x,
                       app(app(app(if(), false()), x), y) -> y,
                                app(app(minus(), 0()), y) -> 0(),
                      app(app(minus(), app(s(), x)), 0()) -> app(s(), x),
              app(app(minus(), app(s(), x)), app(s(), y)) ->
  app(app(minus(), x), y),
                                   app(app(le(), 0()), y) -> true(),
                         app(app(le(), app(s(), x)), 0()) -> false(),
                 app(app(le(), app(s(), x)), app(s(), y)) ->
  app(app(le(), x), y),
            app(app(map(), fun), app(app(cons(), x), xs)) ->
  app(app(cons(), app(fun, x)), app(app(map(), fun), xs)),
                              app(app(map(), fun), nil()) -> nil(),
         app(app(filter(), fun), app(app(cons(), x), xs)) ->
  app(app(app(app(filter2(), app(fun, x)), fun), x), xs),
                           app(app(filter(), fun), nil()) -> nil(),
                                     app(perfectp(), 0()) -> false(),
                             app(perfectp(), app(s(), x)) ->
  app(app(app(app(f(), x), app(s(), 0())), app(s(), x)), app(s(), x))
 }
 DUP: We consider a duplicating system.
  Trs:
   {
                    app(app(app(app(f(), 0()), y), 0()), u) -> true(),
            app(app(app(app(f(), 0()), y), app(s(), z)), u) -> false(),
            app(app(app(app(f(), app(s(), x)), 0()), z), u) ->
    app(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u),
    app(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) ->
    app(
       app(
          app(if(), app(app(le(), x), y)),
          app(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u)
       ), app(app(app(app(f(), x), u), z), u)
    ),
          app(app(app(app(filter2(), true()), fun), x), xs) ->
    app(app(cons(), x), app(app(filter(), fun), xs)),
         app(app(app(app(filter2(), false()), fun), x), xs) ->
    app(app(filter(), fun), xs),
                          app(app(app(if(), true()), x), y) -> x,
                         app(app(app(if(), false()), x), y) -> y,
                                  app(app(minus(), 0()), y) -> 0(),
                        app(app(minus(), app(s(), x)), 0()) -> app(s(), x),
                app(app(minus(), app(s(), x)), app(s(), y)) ->
    app(app(minus(), x), y),
                                     app(app(le(), 0()), y) -> true(),
                           app(app(le(), app(s(), x)), 0()) -> false(),
                   app(app(le(), app(s(), x)), app(s(), y)) ->
    app(app(le(), x), y),
              app(app(map(), fun), app(app(cons(), x), xs)) ->
    app(app(cons(), app(fun, x)), app(app(map(), fun), xs)),
                                app(app(map(), fun), nil()) -> nil(),
           app(app(filter(), fun), app(app(cons(), x), xs)) ->
    app(app(app(app(filter2(), app(fun, x)), fun), x), xs),
                             app(app(filter(), fun), nil()) -> nil(),
                                       app(perfectp(), 0()) -> false(),
                               app(perfectp(), app(s(), x)) ->
    app(app(app(app(f(), x), app(s(), 0())), app(s(), x)), app(s(), x))
   }
  Fail