MAYBE
Time: 1.043953
TRS:
 { 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(f(), app(g(), x)), app(s(), 0())), y) -> app(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x)),
       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(g(), app(s(), x)) -> app(s(), app(g(), x)),
                                       app(g(), 0()) -> 0()}
 DP:
  DP:
   { app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)),
     app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs),
     app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x),
     app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun),
    app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs),
    app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun),
     app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x)),
     app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(f(), app(g(), app(s(), 0()))), y),
     app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(f(), app(g(), app(s(), 0()))),
     app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(g(), app(s(), 0())),
         app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x),
         app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs),
         app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)),
         app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)),
      app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x),
      app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs),
      app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x),
      app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun),
      app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)),
                                 app#(g(), app(s(), x)) -> app#(g(), x),
                                 app#(g(), app(s(), x)) -> app#(s(), app(g(), x))}
  TRS:
  { 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(f(), app(g(), x)), app(s(), 0())), y) -> app(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x)),
        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(g(), app(s(), x)) -> app(s(), app(g(), x)),
                                        app(g(), 0()) -> 0()}
  UR:
   { 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(f(), app(g(), x)), app(s(), 0())), y) -> app(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x)),
         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(g(), app(s(), x)) -> app(s(), app(g(), x)),
                                         app(g(), 0()) -> 0()}
   EDG:
    {
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x)), app#(g(), app(s(), x)) -> app#(s(), app(g(), x)))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x)), app#(g(), app(s(), x)) -> app#(g(), x))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x)), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(g(), app(s(), 0())))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x)), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(f(), app(g(), app(s(), 0()))))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x)), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(f(), app(g(), app(s(), 0()))), y))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x)), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x)))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x)), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x)), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)), app#(g(), app(s(), x)) -> app#(s(), app(g(), x)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)), app#(g(), app(s(), x)) -> app#(g(), x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(g(), app(s(), 0())))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(f(), app(g(), app(s(), 0()))))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(f(), app(g(), app(s(), 0()))), y))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(g(), app(s(), x)) -> app#(s(), app(g(), x)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(g(), app(s(), x)) -> app#(g(), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(g(), app(s(), 0())))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(f(), app(g(), app(s(), 0()))))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(f(), app(g(), app(s(), 0()))), y))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(g(), app(s(), x)) -> app#(s(), app(g(), x)))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(g(), app(s(), x)) -> app#(g(), x))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(g(), app(s(), 0())))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(f(), app(g(), app(s(), 0()))))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(f(), app(g(), app(s(), 0()))), y))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x)))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(g(), app(s(), x)) -> app#(s(), app(g(), x)))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(g(), app(s(), x)) -> app#(g(), x))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(g(), app(s(), 0())))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(f(), app(g(), app(s(), 0()))))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(f(), app(g(), app(s(), 0()))), y))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x)))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun), app#(g(), app(s(), x)) -> app#(s(), app(g(), x)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun), app#(g(), app(s(), x)) -> app#(g(), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(g(), app(s(), 0())))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(f(), app(g(), app(s(), 0()))))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(f(), app(g(), app(s(), 0()))), y))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(g(), app(s(), x)) -> app#(s(), app(g(), x)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(g(), app(s(), x)) -> app#(g(), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(g(), app(s(), 0())))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(f(), app(g(), app(s(), 0()))))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(f(), app(g(), app(s(), 0()))), y))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(f(), app(g(), app(s(), 0()))), app#(g(), app(s(), x)) -> app#(s(), app(g(), x)))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(f(), app(g(), app(s(), 0()))), app#(g(), app(s(), x)) -> app#(g(), x))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(f(), app(g(), app(s(), 0()))), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(f(), app(g(), app(s(), 0()))), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(f(), app(g(), app(s(), 0()))), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(f(), app(g(), app(s(), 0()))), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(f(), app(g(), app(s(), 0()))), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(f(), app(g(), app(s(), 0()))), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(f(), app(g(), app(s(), 0()))), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(f(), app(g(), app(s(), 0()))), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(f(), app(g(), app(s(), 0()))), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(f(), app(g(), app(s(), 0()))), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(g(), app(s(), 0())))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(f(), app(g(), app(s(), 0()))), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(f(), app(g(), app(s(), 0()))))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(f(), app(g(), app(s(), 0()))), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(f(), app(g(), app(s(), 0()))), y))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(f(), app(g(), app(s(), 0()))), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x)))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(f(), app(g(), app(s(), 0()))), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(f(), app(g(), app(s(), 0()))), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(f(), app(g(), app(s(), 0()))), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(f(), app(g(), app(s(), 0()))), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(f(), app(g(), app(s(), 0()))), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(f(), app(g(), app(s(), 0()))), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(g(), app(s(), x)) -> app#(s(), app(g(), x)))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(g(), app(s(), x)) -> app#(g(), x))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(g(), app(s(), 0())))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(f(), app(g(), app(s(), 0()))))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(f(), app(g(), app(s(), 0()))), y))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x)))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(g(), app(s(), x)) -> app#(s(), app(g(), x)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(g(), app(s(), x)) -> app#(g(), x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(g(), app(s(), 0())))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(f(), app(g(), app(s(), 0()))))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(f(), app(g(), app(s(), 0()))), y))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(f(), app(g(), app(s(), 0()))), y))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(f(), app(g(), app(s(), 0()))))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(g(), app(s(), 0())))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(g(), app(s(), x)) -> app#(g(), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(g(), app(s(), x)) -> app#(s(), app(g(), x)))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), 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(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x)))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(f(), app(g(), app(s(), 0()))), y))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(f(), app(g(), app(s(), 0()))))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(g(), app(s(), 0())))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(g(), app(s(), x)) -> app#(g(), x))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(g(), app(s(), x)) -> app#(s(), app(g(), x)))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(f(), app(g(), app(s(), 0()))), y), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(f(), app(g(), app(s(), 0()))), y), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(f(), app(g(), app(s(), 0()))), y), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(f(), app(g(), app(s(), 0()))), y), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(f(), app(g(), app(s(), 0()))), y), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(f(), app(g(), app(s(), 0()))), y), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(f(), app(g(), app(s(), 0()))), y), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x)))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(f(), app(g(), app(s(), 0()))), y), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(f(), app(g(), app(s(), 0()))), y))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(f(), app(g(), app(s(), 0()))), y), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(f(), app(g(), app(s(), 0()))))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(f(), app(g(), app(s(), 0()))), y), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(g(), app(s(), 0())))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(f(), app(g(), app(s(), 0()))), y), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(f(), app(g(), app(s(), 0()))), y), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(f(), app(g(), app(s(), 0()))), y), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(f(), app(g(), app(s(), 0()))), y), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(f(), app(g(), app(s(), 0()))), y), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(f(), app(g(), app(s(), 0()))), y), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(f(), app(g(), app(s(), 0()))), y), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(f(), app(g(), app(s(), 0()))), y), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(f(), app(g(), app(s(), 0()))), y), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(f(), app(g(), app(s(), 0()))), y), app#(g(), app(s(), x)) -> app#(g(), x))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(f(), app(g(), app(s(), 0()))), y), app#(g(), app(s(), x)) -> app#(s(), app(g(), x)))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(g(), app(s(), 0())), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(g(), app(s(), 0())), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(g(), app(s(), 0())), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(g(), app(s(), 0())), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(g(), app(s(), 0())), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(g(), app(s(), 0())), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(g(), app(s(), 0())), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x)))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(g(), app(s(), 0())), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(f(), app(g(), app(s(), 0()))), y))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(g(), app(s(), 0())), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(f(), app(g(), app(s(), 0()))))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(g(), app(s(), 0())), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(g(), app(s(), 0())))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(g(), app(s(), 0())), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(g(), app(s(), 0())), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(g(), app(s(), 0())), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(g(), app(s(), 0())), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(g(), app(s(), 0())), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(g(), app(s(), 0())), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(g(), app(s(), 0())), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(g(), app(s(), 0())), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(g(), app(s(), 0())), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(g(), app(s(), 0())), app#(g(), app(s(), x)) -> app#(g(), x))
     (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(g(), app(s(), 0())), app#(g(), app(s(), x)) -> app#(s(), app(g(), x)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(f(), app(g(), app(s(), 0()))), y))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(f(), app(g(), app(s(), 0()))))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(g(), app(s(), 0())))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(g(), app(s(), x)) -> app#(g(), x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(g(), app(s(), x)) -> app#(s(), app(g(), x)))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun), 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#(filter(), fun), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x)))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(f(), app(g(), app(s(), 0()))), y))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(f(), app(g(), app(s(), 0()))))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(g(), app(s(), 0())))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun), app#(g(), app(s(), x)) -> app#(g(), x))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun), app#(g(), app(s(), x)) -> app#(s(), app(g(), x)))
     (app#(g(), app(s(), x)) -> app#(g(), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
     (app#(g(), app(s(), x)) -> app#(g(), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(g(), app(s(), x)) -> app#(g(), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
     (app#(g(), app(s(), x)) -> app#(g(), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
     (app#(g(), app(s(), x)) -> app#(g(), x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(g(), app(s(), x)) -> app#(g(), x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
     (app#(g(), app(s(), x)) -> app#(g(), x), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x)))
     (app#(g(), app(s(), x)) -> app#(g(), x), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(f(), app(g(), app(s(), 0()))), y))
     (app#(g(), app(s(), x)) -> app#(g(), x), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(f(), app(g(), app(s(), 0()))))
     (app#(g(), app(s(), x)) -> app#(g(), x), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(g(), app(s(), 0())))
     (app#(g(), app(s(), x)) -> app#(g(), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(g(), app(s(), x)) -> app#(g(), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
     (app#(g(), app(s(), x)) -> app#(g(), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
     (app#(g(), app(s(), x)) -> app#(g(), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
     (app#(g(), app(s(), x)) -> app#(g(), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(g(), app(s(), x)) -> app#(g(), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
     (app#(g(), app(s(), x)) -> app#(g(), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
     (app#(g(), app(s(), x)) -> app#(g(), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
     (app#(g(), app(s(), x)) -> app#(g(), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
     (app#(g(), app(s(), x)) -> app#(g(), x), app#(g(), app(s(), x)) -> app#(g(), x))
     (app#(g(), app(s(), x)) -> app#(g(), x), app#(g(), app(s(), x)) -> app#(s(), app(g(), x)))
     (app#(g(), app(s(), x)) -> app#(s(), app(g(), x)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
     (app#(g(), app(s(), x)) -> app#(s(), app(g(), x)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(g(), app(s(), x)) -> app#(s(), app(g(), x)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
     (app#(g(), app(s(), x)) -> app#(s(), app(g(), x)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
     (app#(g(), app(s(), x)) -> app#(s(), app(g(), x)), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(g(), app(s(), x)) -> app#(s(), app(g(), x)), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
     (app#(g(), app(s(), x)) -> app#(s(), app(g(), x)), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x)))
     (app#(g(), app(s(), x)) -> app#(s(), app(g(), x)), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(f(), app(g(), app(s(), 0()))), y))
     (app#(g(), app(s(), x)) -> app#(s(), app(g(), x)), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(f(), app(g(), app(s(), 0()))))
     (app#(g(), app(s(), x)) -> app#(s(), app(g(), x)), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(g(), app(s(), 0())))
     (app#(g(), app(s(), x)) -> app#(s(), app(g(), x)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(g(), app(s(), x)) -> app#(s(), app(g(), x)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
     (app#(g(), app(s(), x)) -> app#(s(), app(g(), x)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
     (app#(g(), app(s(), x)) -> app#(s(), app(g(), x)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
     (app#(g(), app(s(), x)) -> app#(s(), app(g(), x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(g(), app(s(), x)) -> app#(s(), app(g(), x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
     (app#(g(), app(s(), x)) -> app#(s(), app(g(), x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
     (app#(g(), app(s(), x)) -> app#(s(), app(g(), x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
     (app#(g(), app(s(), x)) -> app#(s(), app(g(), x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
     (app#(g(), app(s(), x)) -> app#(s(), app(g(), x)), app#(g(), app(s(), x)) -> app#(g(), x))
     (app#(g(), app(s(), x)) -> app#(s(), app(g(), x)), app#(g(), app(s(), x)) -> app#(s(), app(g(), x)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(f(), app(g(), app(s(), 0()))), y))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(f(), app(g(), app(s(), 0()))))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(g(), app(s(), 0())))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(g(), app(s(), x)) -> app#(g(), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(g(), app(s(), x)) -> app#(s(), app(g(), x)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(f(), app(g(), app(s(), 0()))), y))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(f(), app(g(), app(s(), 0()))))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(g(), app(s(), 0())))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(g(), app(s(), x)) -> app#(g(), x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(g(), app(s(), x)) -> app#(s(), app(g(), x)))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
     (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(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#(filter(), fun))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x)))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(f(), app(g(), app(s(), 0()))), y))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(f(), app(g(), app(s(), 0()))))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(g(), app(s(), 0())))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(g(), app(s(), x)) -> app#(g(), x))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(g(), app(s(), x)) -> app#(s(), app(g(), x)))
    }
    EDG:
     {(app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x)), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(g(), app(s(), 0())))
      (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x)), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(f(), app(g(), app(s(), 0()))))
      (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x)), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(f(), app(g(), app(s(), 0()))), y))
      (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x)), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x)))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(g(), app(s(), x)) -> app#(s(), app(g(), x)))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(g(), app(s(), x)) -> app#(g(), x))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(g(), app(s(), 0())))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(f(), app(g(), app(s(), 0()))))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(f(), app(g(), app(s(), 0()))), y))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x)))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
      (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
      (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
      (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
      (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
      (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
      (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
      (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
      (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
      (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
      (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
      (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(g(), app(s(), 0())), app#(g(), app(s(), x)) -> app#(g(), x))
      (app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(g(), app(s(), 0())), app#(g(), app(s(), x)) -> app#(s(), app(g(), x)))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x)))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(f(), app(g(), app(s(), 0()))), y))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(f(), app(g(), app(s(), 0()))))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(g(), app(s(), 0())))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(g(), app(s(), x)) -> app#(g(), x))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(g(), app(s(), x)) -> app#(s(), app(g(), x)))
      (app#(g(), app(s(), x)) -> app#(g(), x), app#(g(), app(s(), x)) -> app#(g(), x))
      (app#(g(), app(s(), x)) -> app#(g(), x), app#(g(), app(s(), x)) -> app#(s(), app(g(), x)))}
     STATUS:
      arrows: 0.854875
      SCCS (3):
       Scc:
        { app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs),
         app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs),
              app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x),
              app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs),
           app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x)}
       Scc:
        {app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x))}
       Scc:
        {app#(g(), app(s(), x)) -> app#(g(), x)}
       
       SCC (5):
        Strict:
         { app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs),
          app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs),
               app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x),
               app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs),
            app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x)}
        Weak:
        { 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(f(), app(g(), x)), app(s(), 0())), y) -> app(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x)),
              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(g(), app(s(), x)) -> app(s(), app(g(), x)),
                                              app(g(), 0()) -> 0()}
        Open
       
       
       
       
       
       
       
       
       
       SCC (1):
        Strict:
         {app#(app(app(f(), app(g(), x)), app(s(), 0())), y) -> app#(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x))}
        Weak:
        { 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(f(), app(g(), x)), app(s(), 0())), y) -> app(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x)),
              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(g(), app(s(), x)) -> app(s(), app(g(), x)),
                                              app(g(), 0()) -> 0()}
        Open
       
       SCC (1):
        Strict:
         {app#(g(), app(s(), x)) -> app#(g(), x)}
        Weak:
        { 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(f(), app(g(), x)), app(s(), 0())), y) -> app(app(app(f(), app(g(), app(s(), 0()))), y), app(g(), x)),
              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(g(), app(s(), x)) -> app(s(), app(g(), x)),
                                              app(g(), 0()) -> 0()}
        Open