YES
Time: 0.205800
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(if(), true()), app(s(), x)), app(s(), y)) -> app(s(), x),
  app(app(app(if(), false()), app(s(), x)), app(s(), y)) -> app(s(), y),
                           app(app(g(), x), app(c(), y)) -> app(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))),
                           app(app(g(), x), app(c(), y)) -> app(c(), app(app(g(), x), y)),
           app(app(map(), fun), app(app(cons(), x), xs)) -> app(app(cons(), app(fun, x)), app(app(map(), fun), xs)),
                             app(app(map(), fun), nil()) -> nil(),
        app(app(filter(), fun), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(fun, x)), fun), x), xs),
                          app(app(filter(), fun), nil()) -> nil(),
                                   app(f(), app(s(), x)) -> app(f(), x),
                                           app(f(), 0()) -> true(),
                                           app(f(), 1()) -> false()}
 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(g(), x), app(c(), y)) -> app#(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y)),
                         app#(app(g(), x), app(c(), y)) -> app#(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))),
                         app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y),
                         app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))),
                         app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y),
                         app#(app(g(), x), app(c(), y)) -> app#(f(), x),
                         app#(app(g(), x), app(c(), y)) -> app#(s(), x),
                         app#(app(g(), x), app(c(), y)) -> app#(if(), app(f(), x)),
                         app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), x), y)),
                         app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), app(s(), x)), y)),
                         app#(app(g(), x), app(c(), y)) -> app#(g(), app(s(), 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#(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#(f(), app(s(), x)) -> app#(f(), 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(if(), true()), app(s(), x)), app(s(), y)) -> app(s(), x),
   app(app(app(if(), false()), app(s(), x)), app(s(), y)) -> app(s(), y),
                            app(app(g(), x), app(c(), y)) -> app(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))),
                            app(app(g(), x), app(c(), y)) -> app(c(), app(app(g(), x), y)),
            app(app(map(), fun), app(app(cons(), x), xs)) -> app(app(cons(), app(fun, x)), app(app(map(), fun), xs)),
                              app(app(map(), fun), nil()) -> nil(),
         app(app(filter(), fun), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(fun, x)), fun), x), xs),
                           app(app(filter(), fun), nil()) -> nil(),
                                    app(f(), app(s(), x)) -> app(f(), x),
                                            app(f(), 0()) -> true(),
                                            app(f(), 1()) -> false()}
  EDG:
   {
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(f(), app(s(), x)) -> app#(f(), x))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(g(), x), app(c(), y)) -> app#(g(), app(s(), x)))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), app(s(), x)), y)))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), x), y)))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(g(), x), app(c(), y)) -> app#(if(), app(f(), x)))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(g(), x), app(c(), y)) -> app#(s(), x))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(g(), x), app(c(), y)) -> app#(f(), x))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(g(), x), app(c(), y)) -> app#(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(g(), x), app(c(), y)) -> app#(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y)))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), 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#(f(), app(s(), x)) -> app#(f(), 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(g(), x), app(c(), y)) -> app#(g(), app(s(), x)))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), app(s(), x)), y)))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), x), y)))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(if(), app(f(), x)))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(s(), x))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(f(), x))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y)))
    (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(g(), x), app(c(), y)) -> app#(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app#(f(), app(s(), x)) -> app#(f(), x))
    (app#(app(g(), x), app(c(), y)) -> app#(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
    (app#(app(g(), x), app(c(), y)) -> app#(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
    (app#(app(g(), x), app(c(), y)) -> app#(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
    (app#(app(g(), x), app(c(), y)) -> app#(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
    (app#(app(g(), x), app(c(), y)) -> app#(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(g(), x), app(c(), y)) -> app#(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
    (app#(app(g(), x), app(c(), y)) -> app#(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
    (app#(app(g(), x), app(c(), y)) -> app#(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
    (app#(app(g(), x), app(c(), y)) -> app#(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(g(), x), app(c(), y)) -> app#(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app#(app(g(), x), app(c(), y)) -> app#(g(), app(s(), x)))
    (app#(app(g(), x), app(c(), y)) -> app#(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), app(s(), x)), y)))
    (app#(app(g(), x), app(c(), y)) -> app#(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), x), y)))
    (app#(app(g(), x), app(c(), y)) -> app#(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app#(app(g(), x), app(c(), y)) -> app#(if(), app(f(), x)))
    (app#(app(g(), x), app(c(), y)) -> app#(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app#(app(g(), x), app(c(), y)) -> app#(s(), x))
    (app#(app(g(), x), app(c(), y)) -> app#(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app#(app(g(), x), app(c(), y)) -> app#(f(), x))
    (app#(app(g(), x), app(c(), y)) -> app#(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y))
    (app#(app(g(), x), app(c(), y)) -> app#(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))))
    (app#(app(g(), x), app(c(), y)) -> app#(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y))
    (app#(app(g(), x), app(c(), y)) -> app#(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app#(app(g(), x), app(c(), y)) -> app#(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))))
    (app#(app(g(), x), app(c(), y)) -> app#(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app#(app(g(), x), app(c(), y)) -> app#(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y)))
    (app#(app(g(), x), app(c(), y)) -> app#(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(g(), x), app(c(), y)) -> app#(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(app(g(), x), app(c(), y)) -> app#(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(g(), x), app(c(), y)) -> app#(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
    (app#(app(g(), x), app(c(), y)) -> app#(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(app(g(), x), app(c(), y)) -> app#(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), 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#(f(), app(s(), x)) -> app#(f(), 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))
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    (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(g(), x), app(c(), y)) -> app#(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y)))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(g(), x), app(c(), y)) -> app#(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(g(), x), app(c(), y)) -> app#(f(), x))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(g(), x), app(c(), y)) -> app#(s(), x))
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    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), x), y)))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), app(s(), x)), y)))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(g(), x), app(c(), y)) -> app#(g(), app(s(), 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))
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    (app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), app(s(), x)), y)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
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    (app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), app(s(), x)), y)), app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y))
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    (app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), app(s(), x)), y)), app#(app(g(), x), app(c(), y)) -> app#(f(), x))
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    (app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), app(s(), x)), y)), app#(app(g(), x), app(c(), y)) -> app#(g(), app(s(), x)))
    (app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), app(s(), x)), y)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), app(s(), x)), y)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
    (app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), app(s(), x)), y)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
    (app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), app(s(), x)), y)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
    (app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), app(s(), x)), y)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), app(s(), x)), y)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
    (app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), app(s(), x)), y)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
    (app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), app(s(), x)), y)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
    (app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), app(s(), x)), y)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
    (app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), app(s(), x)), y)), app#(f(), app(s(), x)) -> app#(f(), x))
    (app#(app(g(), x), app(c(), y)) -> app#(if(), app(f(), x)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
    (app#(app(g(), x), app(c(), y)) -> app#(if(), app(f(), x)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(app(g(), x), app(c(), y)) -> app#(if(), app(f(), x)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
    (app#(app(g(), x), app(c(), y)) -> app#(if(), app(f(), x)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(g(), x), app(c(), y)) -> app#(if(), app(f(), x)), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(app(g(), x), app(c(), y)) -> app#(if(), app(f(), x)), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(g(), x), app(c(), y)) -> app#(if(), app(f(), x)), app#(app(g(), x), app(c(), y)) -> app#(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y)))
    (app#(app(g(), x), app(c(), y)) -> app#(if(), app(f(), x)), app#(app(g(), x), app(c(), y)) -> app#(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))))
    (app#(app(g(), x), app(c(), y)) -> app#(if(), app(f(), x)), app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y))
    (app#(app(g(), x), app(c(), y)) -> app#(if(), app(f(), x)), app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))))
    (app#(app(g(), x), app(c(), y)) -> app#(if(), app(f(), x)), app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y))
    (app#(app(g(), x), app(c(), y)) -> app#(if(), app(f(), x)), app#(app(g(), x), app(c(), y)) -> app#(f(), x))
    (app#(app(g(), x), app(c(), y)) -> app#(if(), app(f(), x)), app#(app(g(), x), app(c(), y)) -> app#(s(), x))
    (app#(app(g(), x), app(c(), y)) -> app#(if(), app(f(), x)), app#(app(g(), x), app(c(), y)) -> app#(if(), app(f(), x)))
    (app#(app(g(), x), app(c(), y)) -> app#(if(), app(f(), x)), app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), x), y)))
    (app#(app(g(), x), app(c(), y)) -> app#(if(), app(f(), x)), app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), app(s(), x)), y)))
    (app#(app(g(), x), app(c(), y)) -> app#(if(), app(f(), x)), app#(app(g(), x), app(c(), y)) -> app#(g(), app(s(), x)))
    (app#(app(g(), x), app(c(), y)) -> app#(if(), app(f(), x)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(g(), x), app(c(), y)) -> app#(if(), app(f(), x)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
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    (app#(app(g(), x), app(c(), y)) -> app#(if(), app(f(), x)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
    (app#(app(g(), x), app(c(), y)) -> app#(if(), app(f(), x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(g(), x), app(c(), y)) -> app#(if(), app(f(), x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
    (app#(app(g(), x), app(c(), y)) -> app#(if(), app(f(), x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
    (app#(app(g(), x), app(c(), y)) -> app#(if(), app(f(), x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
    (app#(app(g(), x), app(c(), y)) -> app#(if(), app(f(), x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
    (app#(app(g(), x), app(c(), y)) -> app#(if(), app(f(), x)), app#(f(), app(s(), x)) -> app#(f(), 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(g(), x), app(c(), y)) -> app#(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y)))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(g(), x), app(c(), y)) -> app#(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(g(), x), app(c(), y)) -> app#(f(), x))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(g(), x), app(c(), y)) -> app#(s(), x))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(g(), x), app(c(), y)) -> app#(if(), app(f(), x)))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), x), y)))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), app(s(), x)), y)))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(g(), x), app(c(), y)) -> app#(g(), app(s(), 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(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#(f(), app(s(), x)) -> app#(f(), 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#(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(g(), x), app(c(), y)) -> app#(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y)))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(g(), x), app(c(), y)) -> app#(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(g(), x), app(c(), y)) -> app#(f(), x))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(g(), x), app(c(), y)) -> app#(s(), x))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(g(), x), app(c(), y)) -> app#(if(), app(f(), x)))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), x), y)))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), app(s(), x)), y)))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(g(), x), app(c(), y)) -> app#(g(), app(s(), 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(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#(f(), app(s(), x)) -> app#(f(), 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(g(), x), app(c(), y)) -> app#(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y)))
    (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(g(), x), app(c(), y)) -> app#(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))))
    (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y))
    (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))))
    (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y))
    (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(g(), x), app(c(), y)) -> app#(f(), x))
    (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(g(), x), app(c(), y)) -> app#(s(), x))
    (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(g(), x), app(c(), y)) -> app#(if(), app(f(), x)))
    (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), x), y)))
    (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), app(s(), x)), y)))
    (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(g(), x), app(c(), y)) -> app#(g(), app(s(), 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#(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#(f(), app(s(), x)) -> app#(f(), 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(g(), x), app(c(), y)) -> app#(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y)))
    (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun), app#(app(g(), x), app(c(), y)) -> app#(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))))
    (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun), app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y))
    (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun), app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))))
    (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun), app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y))
    (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun), app#(app(g(), x), app(c(), y)) -> app#(f(), x))
    (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun), app#(app(g(), x), app(c(), y)) -> app#(s(), x))
    (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun), app#(app(g(), x), app(c(), y)) -> app#(if(), app(f(), x)))
    (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun), app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), x), y)))
    (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun), app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), app(s(), x)), y)))
    (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun), app#(app(g(), x), app(c(), y)) -> app#(g(), app(s(), 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(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#(f(), app(s(), x)) -> app#(f(), x))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))), app#(app(g(), x), app(c(), y)) -> app#(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y)))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))), app#(app(g(), x), app(c(), y)) -> app#(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))), app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))), app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))), app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))), app#(app(g(), x), app(c(), y)) -> app#(f(), x))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))), app#(app(g(), x), app(c(), y)) -> app#(s(), x))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))), app#(app(g(), x), app(c(), y)) -> app#(if(), app(f(), x)))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))), app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), x), y)))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))), app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), app(s(), x)), y)))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))), app#(app(g(), x), app(c(), y)) -> app#(g(), app(s(), x)))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))), app#(f(), app(s(), x)) -> app#(f(), 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(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(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#(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#(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(), 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(g(), x), app(c(), y)) -> app#(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y)))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun), app#(app(g(), x), app(c(), y)) -> app#(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun), app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun), app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun), app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun), app#(app(g(), x), app(c(), y)) -> app#(f(), x))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun), app#(app(g(), x), app(c(), y)) -> app#(s(), x))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun), app#(app(g(), x), app(c(), y)) -> app#(if(), app(f(), x)))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun), app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), x), y)))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun), app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), app(s(), x)), y)))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun), app#(app(g(), x), app(c(), y)) -> app#(g(), app(s(), 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#(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#(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#(cons(), 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(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#(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(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#(filter2(), app(fun, x)))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun), app#(f(), app(s(), x)) -> app#(f(), 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(g(), x), app(c(), y)) -> app#(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y)))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(f(), x))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(s(), x))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(if(), app(f(), x)))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), x), y)))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), app(s(), x)), y)))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(g(), app(s(), 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#(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#(f(), app(s(), x)) -> app#(f(), x))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(g(), x), app(c(), y)) -> app#(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y)))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(g(), x), app(c(), y)) -> app#(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(g(), x), app(c(), y)) -> app#(f(), x))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(g(), x), app(c(), y)) -> app#(s(), x))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(g(), x), app(c(), y)) -> app#(if(), app(f(), x)))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), x), y)))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), app(s(), x)), y)))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(g(), x), app(c(), y)) -> app#(g(), app(s(), x)))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(f(), app(s(), x)) -> app#(f(), x))
   }
   EDG:
    {
     (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(g(), x), app(c(), y)) -> app#(g(), app(s(), x)))
     (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), app(s(), x)), y)))
     (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), x), y)))
     (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(g(), x), app(c(), y)) -> app#(if(), app(f(), x)))
     (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(g(), x), app(c(), y)) -> app#(s(), x))
     (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(g(), x), app(c(), y)) -> app#(f(), x))
     (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y))
     (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))))
     (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y))
     (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(g(), x), app(c(), y)) -> app#(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))))
     (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(g(), x), app(c(), y)) -> app#(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(f(), app(s(), x)) -> app#(f(), 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(g(), x), app(c(), y)) -> app#(g(), app(s(), x)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), app(s(), x)), y)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), x), y)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(if(), app(f(), x)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(s(), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(f(), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y)))
     (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#(f(), app(s(), x)) -> app#(f(), x), app#(f(), app(s(), x)) -> app#(f(), x))
     (app#(app(g(), x), app(c(), y)) -> app#(f(), x), app#(f(), app(s(), x)) -> app#(f(), 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#(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(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(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(g(), x), app(c(), y)) -> app#(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(f(), x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(s(), x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(if(), app(f(), x)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), x), y)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), app(s(), x)), y)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(g(), app(s(), 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#(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#(f(), app(s(), x)) -> app#(f(), x))
     (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(g(), x), app(c(), y)) -> app#(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y)))
     (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(g(), x), app(c(), y)) -> app#(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))))
     (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y))
     (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))))
     (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y))
     (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(g(), x), app(c(), y)) -> app#(f(), x))
     (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(g(), x), app(c(), y)) -> app#(s(), x))
     (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(g(), x), app(c(), y)) -> app#(if(), app(f(), x)))
     (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), x), y)))
     (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), app(s(), x)), y)))
     (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(g(), x), app(c(), y)) -> app#(g(), app(s(), x)))
    }
    EDG:
     {
      (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(g(), x), app(c(), y)) -> app#(g(), app(s(), x)))
      (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), app(s(), x)), y)))
      (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), x), y)))
      (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(g(), x), app(c(), y)) -> app#(if(), app(f(), x)))
      (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(g(), x), app(c(), y)) -> app#(s(), x))
      (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(g(), x), app(c(), y)) -> app#(f(), x))
      (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y))
      (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))))
      (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y))
      (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(g(), x), app(c(), y)) -> app#(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))))
      (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(g(), x), app(c(), y)) -> app#(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y)))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(f(), app(s(), x)) -> app#(f(), 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(g(), x), app(c(), y)) -> app#(g(), app(s(), x)))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), app(s(), x)), y)))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), x), y)))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(if(), app(f(), x)))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(s(), x))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(f(), x))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y)))
      (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#(f(), app(s(), x)) -> app#(f(), x), app#(f(), app(s(), x)) -> app#(f(), x))
      (app#(app(g(), x), app(c(), y)) -> app#(f(), x), app#(f(), app(s(), x)) -> app#(f(), 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#(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(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(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(g(), x), app(c(), y)) -> app#(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y)))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(f(), x))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(s(), x))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(if(), app(f(), x)))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), x), y)))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), app(s(), x)), y)))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(g(), app(s(), 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#(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#(f(), app(s(), x)) -> app#(f(), x))
      (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(g(), x), app(c(), y)) -> app#(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y)))
      (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(g(), x), app(c(), y)) -> app#(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))))
      (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y))
      (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))))
      (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y))
      (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(g(), x), app(c(), y)) -> app#(f(), x))
      (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(g(), x), app(c(), y)) -> app#(s(), x))
      (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(g(), x), app(c(), y)) -> app#(if(), app(f(), x)))
      (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), x), y)))
      (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), app(s(), x)), y)))
      (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(g(), x), app(c(), y)) -> app#(g(), app(s(), x)))
     }
     EDG:
      {
       (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(g(), x), app(c(), y)) -> app#(g(), app(s(), x)))
       (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), app(s(), x)), y)))
       (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), x), y)))
       (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(g(), x), app(c(), y)) -> app#(if(), app(f(), x)))
       (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(g(), x), app(c(), y)) -> app#(s(), x))
       (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(g(), x), app(c(), y)) -> app#(f(), x))
       (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y))
       (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))))
       (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y))
       (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(g(), x), app(c(), y)) -> app#(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))))
       (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y), app#(app(g(), x), app(c(), y)) -> app#(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y)))
       (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(f(), app(s(), x)) -> app#(f(), 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(g(), x), app(c(), y)) -> app#(g(), app(s(), x)))
       (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), app(s(), x)), y)))
       (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), x), y)))
       (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(if(), app(f(), x)))
       (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(s(), x))
       (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(f(), x))
       (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y))
       (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))))
       (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y))
       (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))))
       (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y)))
       (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#(f(), app(s(), x)) -> app#(f(), x), app#(f(), app(s(), x)) -> app#(f(), x))
       (app#(app(g(), x), app(c(), y)) -> app#(f(), x), app#(f(), app(s(), x)) -> app#(f(), 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#(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(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(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(g(), x), app(c(), y)) -> app#(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y)))
       (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))))
       (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y))
       (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))))
       (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y))
       (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(f(), x))
       (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(s(), x))
       (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(if(), app(f(), x)))
       (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), x), y)))
       (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), app(s(), x)), y)))
       (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(g(), app(s(), 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#(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#(f(), app(s(), x)) -> app#(f(), x))
       (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(g(), x), app(c(), y)) -> app#(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y)))
       (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(g(), x), app(c(), y)) -> app#(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))))
       (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y))
       (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))))
       (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y))
       (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(g(), x), app(c(), y)) -> app#(f(), x))
       (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(g(), x), app(c(), y)) -> app#(s(), x))
       (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(g(), x), app(c(), y)) -> app#(if(), app(f(), x)))
       (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), x), y)))
       (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), app(s(), x)), y)))
       (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y), app#(app(g(), x), app(c(), y)) -> app#(g(), app(s(), x)))
      }
      STATUS:
       arrows: 0.865569
       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),
            app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs)}
        Scc:
         {app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y),
          app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y)}
        Scc:
         {app#(f(), app(s(), x)) -> app#(f(), x)}
        
        SCC (6):
         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),
             app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs)}
         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(if(), true()), app(s(), x)), app(s(), y)) -> app(s(), x),
          app(app(app(if(), false()), app(s(), x)), app(s(), y)) -> app(s(), y),
                                   app(app(g(), x), app(c(), y)) -> app(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))),
                                   app(app(g(), x), app(c(), y)) -> app(c(), app(app(g(), x), y)),
                   app(app(map(), fun), app(app(cons(), x), xs)) -> app(app(cons(), app(fun, x)), app(app(map(), fun), xs)),
                                     app(app(map(), fun), nil()) -> nil(),
                app(app(filter(), fun), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(fun, x)), fun), x), xs),
                                  app(app(filter(), fun), nil()) -> nil(),
                                           app(f(), app(s(), x)) -> app(f(), x),
                                                   app(f(), 0()) -> true(),
                                                   app(f(), 1()) -> false()}
         POLY:
          Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
          Interpretation:
           [app](x0, x1) = x0 + x1,
           
           [true] = 0,
           
           [f] = 0,
           
           [0] = 0,
           
           [false] = 0,
           
           [1] = 0,
           
           [s] = 0,
           
           [if] = 0,
           
           [c] = 1,
           
           [g] = 1,
           
           [nil] = 0,
           
           [map] = 0,
           
           [cons] = 1,
           
           [filter] = 0,
           
           [filter2] = 0,
           
           [app#](x0, x1) = x0
          Strict:
           app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs)
           1 + 1x + 0fun + 1xs >= 0 + 0x + 0fun + 1xs
           app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x)
           1 + 1x + 0fun + 1xs >= 0 + 1x + 0fun
           app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs)
           1 + 1x + 0fun + 1xs >= 0 + 0fun + 1xs
           app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x)
           1 + 1x + 0fun + 1xs >= 0 + 1x + 0fun
           app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs)
           0 + 0x + 0fun + 1xs >= 0 + 0fun + 1xs
           app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs)
           0 + 0x + 0fun + 1xs >= 0 + 0fun + 1xs
          Weak:
           app(f(), 1()) -> false()
           0 >= 0
           app(f(), 0()) -> true()
           0 >= 0
           app(f(), app(s(), x)) -> app(f(), x)
           0 + 1x >= 0 + 1x
           app(app(filter(), fun), nil()) -> nil()
           0 + 1fun >= 0
           app(app(filter(), fun), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(fun, x)), fun), x), xs)
           1 + 1x + 1fun + 1xs >= 0 + 2x + 2fun + 1xs
           app(app(map(), fun), nil()) -> nil()
           0 + 1fun >= 0
           app(app(map(), fun), app(app(cons(), x), xs)) -> app(app(cons(), app(fun, x)), app(app(map(), fun), xs))
           1 + 1x + 1fun + 1xs >= 1 + 1x + 2fun + 1xs
           app(app(g(), x), app(c(), y)) -> app(c(), app(app(g(), x), y))
           2 + 1x + 1y >= 2 + 1x + 1y
           app(app(g(), x), app(c(), y)) -> app(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y)))
           2 + 1x + 1y >= 4 + 3x + 2y
           app(app(app(if(), false()), app(s(), x)), app(s(), y)) -> app(s(), y)
           0 + 1x + 1y >= 0 + 1y
           app(app(app(if(), true()), app(s(), x)), app(s(), y)) -> app(s(), x)
           0 + 1x + 1y >= 0 + 1x
           app(app(app(app(filter2(), false()), fun), x), xs) -> app(app(filter(), fun), xs)
           0 + 1x + 1fun + 1xs >= 0 + 1fun + 1xs
           app(app(app(app(filter2(), true()), fun), x), xs) -> app(app(cons(), x), app(app(filter(), fun), xs))
           0 + 1x + 1fun + 1xs >= 1 + 1x + 1fun + 1xs
         SCCS (0):
          
          
          
       
       
       
       
       
       
       
       
       
       SCC (2):
        Strict:
         {app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y),
          app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y)}
        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(if(), true()), app(s(), x)), app(s(), y)) -> app(s(), x),
         app(app(app(if(), false()), app(s(), x)), app(s(), y)) -> app(s(), y),
                                  app(app(g(), x), app(c(), y)) -> app(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))),
                                  app(app(g(), x), app(c(), y)) -> app(c(), app(app(g(), x), y)),
                  app(app(map(), fun), app(app(cons(), x), xs)) -> app(app(cons(), app(fun, x)), app(app(map(), fun), xs)),
                                    app(app(map(), fun), nil()) -> nil(),
               app(app(filter(), fun), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(fun, x)), fun), x), xs),
                                 app(app(filter(), fun), nil()) -> nil(),
                                          app(f(), app(s(), x)) -> app(f(), x),
                                                  app(f(), 0()) -> true(),
                                                  app(f(), 1()) -> false()}
        POLY:
         Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
         Interpretation:
          [app](x0, x1) = x0 + x1,
          
          [true] = 0,
          
          [f] = 1,
          
          [0] = 1,
          
          [false] = 0,
          
          [1] = 1,
          
          [s] = 1,
          
          [if] = 1,
          
          [c] = 1,
          
          [g] = 0,
          
          [nil] = 0,
          
          [map] = 0,
          
          [cons] = 0,
          
          [filter] = 0,
          
          [filter2] = 0,
          
          [app#](x0, x1) = x0
         Strict:
          app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), x)), y)
          1 + 0x + 1y >= 0 + 0x + 1y
          app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y)
          1 + 0x + 1y >= 0 + 0x + 1y
         Weak:
          app(f(), 1()) -> false()
          2 >= 0
          app(f(), 0()) -> true()
          2 >= 0
          app(f(), app(s(), x)) -> app(f(), x)
          2 + 1x >= 1 + 1x
          app(app(filter(), fun), nil()) -> nil()
          0 + 1fun >= 0
          app(app(filter(), fun), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(fun, x)), fun), x), xs)
          0 + 1x + 1fun + 1xs >= 0 + 2x + 2fun + 1xs
          app(app(map(), fun), nil()) -> nil()
          0 + 1fun >= 0
          app(app(map(), fun), app(app(cons(), x), xs)) -> app(app(cons(), app(fun, x)), app(app(map(), fun), xs))
          0 + 1x + 1fun + 1xs >= 0 + 1x + 2fun + 1xs
          app(app(g(), x), app(c(), y)) -> app(c(), app(app(g(), x), y))
          1 + 1x + 1y >= 1 + 1x + 1y
          app(app(g(), x), app(c(), y)) -> app(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y)))
          1 + 1x + 1y >= 5 + 3x + 2y
          app(app(app(if(), false()), app(s(), x)), app(s(), y)) -> app(s(), y)
          3 + 1x + 1y >= 1 + 1y
          app(app(app(if(), true()), app(s(), x)), app(s(), y)) -> app(s(), x)
          3 + 1x + 1y >= 1 + 1x
          app(app(app(app(filter2(), false()), fun), x), xs) -> app(app(filter(), fun), xs)
          0 + 1x + 1fun + 1xs >= 0 + 1fun + 1xs
          app(app(app(app(filter2(), true()), fun), x), xs) -> app(app(cons(), x), app(app(filter(), fun), xs))
          0 + 1x + 1fun + 1xs >= 0 + 1x + 1fun + 1xs
        Qed
       
       
       
       
       
       
       SCC (1):
        Strict:
         {app#(f(), app(s(), x)) -> app#(f(), 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(if(), true()), app(s(), x)), app(s(), y)) -> app(s(), x),
         app(app(app(if(), false()), app(s(), x)), app(s(), y)) -> app(s(), y),
                                  app(app(g(), x), app(c(), y)) -> app(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y))),
                                  app(app(g(), x), app(c(), y)) -> app(c(), app(app(g(), x), y)),
                  app(app(map(), fun), app(app(cons(), x), xs)) -> app(app(cons(), app(fun, x)), app(app(map(), fun), xs)),
                                    app(app(map(), fun), nil()) -> nil(),
               app(app(filter(), fun), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(fun, x)), fun), x), xs),
                                 app(app(filter(), fun), nil()) -> nil(),
                                          app(f(), app(s(), x)) -> app(f(), x),
                                                  app(f(), 0()) -> true(),
                                                  app(f(), 1()) -> false()}
        POLY:
         Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
         Interpretation:
          [app](x0, x1) = x0 + x1,
          
          [true] = 0,
          
          [f] = 1,
          
          [0] = 1,
          
          [false] = 0,
          
          [1] = 1,
          
          [s] = 1,
          
          [if] = 1,
          
          [c] = 0,
          
          [g] = 0,
          
          [nil] = 0,
          
          [map] = 0,
          
          [cons] = 0,
          
          [filter] = 0,
          
          [filter2] = 0,
          
          [app#](x0, x1) = x0 + x1
         Strict:
          app#(f(), app(s(), x)) -> app#(f(), x)
          2 + 1x >= 1 + 1x
         Weak:
          app(f(), 1()) -> false()
          2 >= 0
          app(f(), 0()) -> true()
          2 >= 0
          app(f(), app(s(), x)) -> app(f(), x)
          2 + 1x >= 1 + 1x
          app(app(filter(), fun), nil()) -> nil()
          0 + 1fun >= 0
          app(app(filter(), fun), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(fun, x)), fun), x), xs)
          0 + 1x + 1fun + 1xs >= 0 + 2x + 2fun + 1xs
          app(app(map(), fun), nil()) -> nil()
          0 + 1fun >= 0
          app(app(map(), fun), app(app(cons(), x), xs)) -> app(app(cons(), app(fun, x)), app(app(map(), fun), xs))
          0 + 1x + 1fun + 1xs >= 0 + 1x + 2fun + 1xs
          app(app(g(), x), app(c(), y)) -> app(c(), app(app(g(), x), y))
          0 + 1x + 1y >= 0 + 1x + 1y
          app(app(g(), x), app(c(), y)) -> app(app(g(), x), app(app(app(if(), app(f(), x)), app(c(), app(app(g(), app(s(), x)), y))), app(c(), y)))
          0 + 1x + 1y >= 3 + 3x + 2y
          app(app(app(if(), false()), app(s(), x)), app(s(), y)) -> app(s(), y)
          3 + 1x + 1y >= 1 + 1y
          app(app(app(if(), true()), app(s(), x)), app(s(), y)) -> app(s(), x)
          3 + 1x + 1y >= 1 + 1x
          app(app(app(app(filter2(), false()), fun), x), xs) -> app(app(filter(), fun), xs)
          0 + 1x + 1fun + 1xs >= 0 + 1fun + 1xs
          app(app(app(app(filter2(), true()), fun), x), xs) -> app(app(cons(), x), app(app(filter(), fun), xs))
          0 + 1x + 1fun + 1xs >= 0 + 1x + 1fun + 1xs
        Qed