MAYBE
Time: 0.064530
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()}
  UR:
   {     app(app(app(app(filter2(), true()), fun), x), xs) -> app(app(cons(), x), app(app(filter(), fun), xs)),
        app(app(app(app(filter2(), false()), fun), x), xs) -> app(app(filter(), fun), xs),
     app(app(app(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(),
                                                   a(z, w) -> z,
                                                   a(z, w) -> w}
   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))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(g(), x), app(c(), y)) -> app#(g(), app(s(), x)))
     (app#(app(app(app(filter2(), true()), 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(), true()), 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(), true()), fun), x), xs) -> app#(filter(), fun), 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#(s(), x))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(g(), x), app(c(), y)) -> app#(f(), x))
     (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#(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(), true()), fun), x), xs) -> app#(filter(), fun), 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(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(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(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(f(), app(s(), x)) -> app#(f(), x))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(g(), x), app(c(), y)) -> app#(g(), app(s(), x)))
     (app#(app(app(app(filter2(), true()), 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(), true()), 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(), 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#(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(filter(), fun), xs), app#(app(g(), x), app(c(), y)) -> 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#(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(), 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), 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(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(filter(), fun), xs), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(f(), app(s(), x)) -> app#(f(), x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(g(), x), app(c(), y)) -> app#(g(), app(s(), x)))
     (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(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(map(), fun), xs), 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), app#(app(g(), x), app(c(), y)) -> app#(s(), x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> 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(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(), 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), 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#(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(map(), fun), xs), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(f(), app(s(), x)) -> app#(f(), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(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#(fun, x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, 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#(g(), app(s(), 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#(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(), 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#(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#(s(), 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#(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#(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(), 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), 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(filter2(), app(fun, x)), 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#(app(app(filter2(), app(fun, x)), fun), x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(app(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(), 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#(cons(), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(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(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#(f(), app(s(), x)) -> 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(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), 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#(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(app(filter2(), app(fun, x)), 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#(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#(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#(cons(), 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#(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(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#(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(g(), x), app(c(), y)) -> app#(g(), app(s(), 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#(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#(c(), 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#(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#(s(), 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#(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#(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(), 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), 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(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(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(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#(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#(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(), true()), fun), x), xs) -> app#(cons(), 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(app(app(filter2(), true()), 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(), 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#(f(), app(s(), x)) -> app#(f(), 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#(filter2(), 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#(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(app(filter2(), app(fun, x)), 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#(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#(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#(cons(), 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#(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(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#(fun, x))
     (app#(app(g(), x), app(c(), y)) -> app#(c(), 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#(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#(c(), 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#(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(), x), y)), app#(app(g(), x), app(c(), y)) -> app#(s(), x))
     (app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), x), y)), app#(app(g(), x), app(c(), y)) -> 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#(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(), 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), 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#(c(), 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#(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(), 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(), x), y)), app#(app(app(app(filter2(), true()), 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(), true()), fun), x), xs) -> app#(cons(), x))
     (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(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#(g(), app(s(), x)), app#(f(), app(s(), x)) -> app#(f(), x))
     (app#(app(g(), x), app(c(), y)) -> app#(g(), app(s(), x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), 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#(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(app(filter2(), app(fun, x)), fun), x))
     (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(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#(g(), app(s(), x)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), 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#(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(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#(fun, x))
     (app#(app(g(), x), app(c(), y)) -> app#(g(), app(s(), x)), app#(app(g(), x), app(c(), y)) -> app#(g(), app(s(), x)))
     (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(g(), x), app(c(), y)) -> app#(g(), app(s(), x)), app#(app(g(), x), app(c(), y)) -> app#(c(), 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#(if(), app(f(), x)))
     (app#(app(g(), x), app(c(), y)) -> app#(g(), app(s(), x)), app#(app(g(), x), app(c(), y)) -> app#(s(), x))
     (app#(app(g(), x), app(c(), y)) -> app#(g(), app(s(), x)), app#(app(g(), x), app(c(), y)) -> app#(f(), x))
     (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#(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(g(), x), app(c(), y)) -> app#(g(), app(s(), x)), 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(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(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(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#(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#(filter(), fun))
     (app#(app(g(), x), app(c(), y)) -> app#(g(), app(s(), x)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
     (app#(app(g(), x), app(c(), y)) -> app#(g(), app(s(), x)), app#(app(app(app(filter2(), true()), 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(), 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#(f(), app(s(), x)) -> app#(f(), x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)), app#(app(g(), x), app(c(), y)) -> app#(g(), app(s(), x)))
     (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(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), 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#(cons(), 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#(cons(), app(fun, x)), app#(app(g(), x), app(c(), y)) -> app#(s(), x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)), app#(app(g(), x), app(c(), y)) -> 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#(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(), 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), 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#(cons(), 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#(cons(), app(fun, x)), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(f(), app(s(), x)) -> app#(f(), x))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(g(), x), app(c(), y)) -> app#(g(), app(s(), x)))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), 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#(cons(), x), app#(app(g(), x), app(c(), y)) -> app#(c(), 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#(if(), app(f(), x)))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(g(), x), app(c(), y)) -> app#(s(), x))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(g(), x), app(c(), y)) -> app#(f(), x))
     (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#(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#(cons(), x), 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(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(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(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
     (app#(app(g(), x), app(c(), y)) -> app#(s(), x), app#(f(), app(s(), x)) -> app#(f(), x))
     (app#(app(g(), x), app(c(), y)) -> app#(s(), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
     (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#(s(), 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#(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#(s(), 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(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
     (app#(app(g(), x), app(c(), y)) -> 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(g(), x), app(c(), y)) -> app#(s(), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
     (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#(s(), x), app#(app(g(), x), app(c(), y)) -> app#(g(), app(s(), x)))
     (app#(app(g(), x), app(c(), y)) -> app#(s(), 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#(s(), x), app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), x), y)))
     (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#(s(), x), app#(app(g(), x), app(c(), y)) -> app#(s(), x))
     (app#(app(g(), x), app(c(), y)) -> app#(s(), x), 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#(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(), 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), 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#(s(), 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#(s(), 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#(app(filter(), fun), xs))
     (app#(app(g(), x), app(c(), y)) -> app#(s(), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(g(), x), app(c(), y)) -> app#(s(), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
     (app#(app(g(), x), app(c(), y)) -> app#(s(), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> 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#(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#(f(), app(s(), x)) -> app#(f(), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(f(), app(s(), x)) -> app#(f(), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
     (app#(f(), app(s(), x)) -> app#(f(), x), 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(), 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#(f(), app(s(), x)) -> 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#(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#(f(), app(s(), x)) -> app#(f(), x), app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), y))
     (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#(f(), app(s(), x)) -> app#(f(), x), 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#(f(), x))
     (app#(f(), app(s(), x)) -> app#(f(), x), app#(app(g(), x), app(c(), y)) -> app#(s(), x))
     (app#(f(), app(s(), x)) -> app#(f(), x), app#(app(g(), x), app(c(), y)) -> app#(if(), app(f(), x)))
     (app#(f(), app(s(), x)) -> app#(f(), x), app#(app(g(), x), app(c(), y)) -> app#(c(), app(app(g(), x), y)))
     (app#(f(), app(s(), x)) -> app#(f(), 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#(g(), app(s(), x)))
     (app#(f(), app(s(), x)) -> app#(f(), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(f(), app(s(), x)) -> app#(f(), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
     (app#(f(), app(s(), x)) -> app#(f(), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
     (app#(f(), app(s(), x)) -> app#(f(), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
     (app#(f(), app(s(), x)) -> app#(f(), x), 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#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
     (app#(f(), app(s(), x)) -> app#(f(), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
     (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#(f(), app(s(), x)) -> app#(f(), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), 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#(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(filter(), fun), xs))
     (app#(app(g(), x), app(c(), y)) -> app#(f(), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
     (app#(app(g(), x), app(c(), y)) -> app#(f(), x), app#(app(app(app(filter2(), true()), 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#(app(filter(), fun), xs))
     (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#(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#(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#(f(), x), 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), 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(), app(s(), x)), y))
     (app#(app(g(), x), app(c(), y)) -> app#(f(), x), app#(app(g(), x), app(c(), y)) -> app#(f(), x))
     (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#(f(), x), 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#(c(), app(app(g(), x), y)))
     (app#(app(g(), x), app(c(), y)) -> 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#(f(), x), app#(app(g(), x), app(c(), y)) -> app#(g(), app(s(), 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#(f(), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> 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#(f(), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), 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#(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#(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#(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#(f(), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, 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#(filter2(), app(fun, x)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(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#(cons(), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), 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#(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#(filter2(), 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#(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#(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#(filter2(), app(fun, x)), app#(app(g(), x), app(c(), y)) -> 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#(s(), 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#(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(), 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#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), 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#(filter2(), app(fun, x)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), 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#(filter2(), app(fun, x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(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#(filter2(), app(fun, x)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(f(), app(s(), x)) -> 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(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(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))
     (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#(if(), 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#(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))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(f(), app(s(), x)) -> app#(f(), x))
     (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#(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#(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#(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#(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#(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#(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#(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(), app(s(), 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), 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(), 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#(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#(s(), 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#(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#(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#(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))
     (app#(app(g(), x), app(c(), y)) -> app#(if(), 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#(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()}
          Open
         
         
         
         
         
         
         
         
         
         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()}
          Open
         
         
         
         
         
         
         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()}
          Open