MAYBE
Time: 0.034861
TRS:
 { app(app(app(app(filter2(), true()), f), x), xs) -> app(app(cons(), x), app(app(filter(), f), xs)),
  app(app(app(app(filter2(), false()), f), x), xs) -> app(app(filter(), f), xs),
                app(app(ack(), app(succ(), x)), y) -> app(app(ack(), x), app(succ(), 0())),
   app(app(ack(), app(succ(), x)), app(succ(), y)) -> app(app(ack(), x), app(app(ack(), app(succ(), x)), y)),
                           app(app(ack(), 0()), y) -> app(succ(), y),
       app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs)),
                         app(app(map(), f), nil()) -> nil(),
    app(app(filter(), f), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(f, x)), f), x), xs),
                      app(app(filter(), f), nil()) -> nil()}
 DP:
  DP:
   { app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)),
     app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs),
     app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x),
     app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f),
    app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs),
    app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f),
                  app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())),
                  app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()),
                  app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x),
     app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)),
     app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y),
     app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x),
                             app#(app(ack(), 0()), y) -> app#(succ(), y),
         app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x),
         app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs),
         app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)),
         app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)),
      app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x),
      app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs),
      app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x),
      app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f),
      app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x))}
  TRS:
  { app(app(app(app(filter2(), true()), f), x), xs) -> app(app(cons(), x), app(app(filter(), f), xs)),
   app(app(app(app(filter2(), false()), f), x), xs) -> app(app(filter(), f), xs),
                 app(app(ack(), app(succ(), x)), y) -> app(app(ack(), x), app(succ(), 0())),
    app(app(ack(), app(succ(), x)), app(succ(), y)) -> app(app(ack(), x), app(app(ack(), app(succ(), x)), y)),
                            app(app(ack(), 0()), y) -> app(succ(), y),
        app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs)),
                          app(app(map(), f), nil()) -> nil(),
     app(app(filter(), f), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(f, x)), f), x), xs),
                       app(app(filter(), f), nil()) -> nil()}
  UR:
   { app(app(app(app(filter2(), true()), f), x), xs) -> app(app(cons(), x), app(app(filter(), f), xs)),
    app(app(app(app(filter2(), false()), f), x), xs) -> app(app(filter(), f), xs),
                  app(app(ack(), app(succ(), x)), y) -> app(app(ack(), x), app(succ(), 0())),
     app(app(ack(), app(succ(), x)), app(succ(), y)) -> app(app(ack(), x), app(app(ack(), app(succ(), x)), y)),
                             app(app(ack(), 0()), y) -> app(succ(), y),
         app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs)),
                           app(app(map(), f), nil()) -> nil(),
      app(app(filter(), f), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(f, x)), f), x), xs),
                        app(app(filter(), f), nil()) -> nil(),
                                             a(z, w) -> z,
                                             a(z, w) -> w}
   EDG:
    {
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)), app#(app(ack(), 0()), y) -> app#(succ(), y))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)), app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)), app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)), app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(ack(), 0()), y) -> app#(succ(), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(ack(), 0()), y) -> app#(succ(), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(ack(), 0()), y) -> app#(succ(), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(ack(), 0()), y) -> app#(succ(), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(ack(), 0()), y) -> app#(succ(), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(ack(), 0()), y) -> app#(succ(), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(ack(), 0()), y) -> app#(succ(), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(ack(), 0()), y) -> app#(succ(), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(ack(), 0()), y) -> app#(succ(), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(ack(), 0()), y) -> app#(succ(), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(ack(), 0()), y) -> app#(succ(), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(ack(), 0()), y) -> app#(succ(), y), app#(app(ack(), 0()), y) -> app#(succ(), y))
     (app#(app(ack(), 0()), y) -> app#(succ(), y), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x))
     (app#(app(ack(), 0()), y) -> app#(succ(), y), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y))
     (app#(app(ack(), 0()), y) -> app#(succ(), y), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)))
     (app#(app(ack(), 0()), y) -> app#(succ(), y), app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x))
     (app#(app(ack(), 0()), y) -> app#(succ(), y), app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()))
     (app#(app(ack(), 0()), y) -> app#(succ(), y), app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())))
     (app#(app(ack(), 0()), y) -> app#(succ(), y), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(ack(), 0()), y) -> app#(succ(), y), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(ack(), 0()), y) -> app#(succ(), y), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(ack(), 0()), y) -> app#(succ(), y), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(ack(), 0()), y) -> app#(succ(), y), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(ack(), 0()), y) -> app#(succ(), y), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x), app#(app(ack(), 0()), y) -> app#(succ(), y))
     (app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x))
     (app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y))
     (app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)))
     (app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x), app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x))
     (app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x), app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()))
     (app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x), app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())))
     (app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
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     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(ack(), 0()), y) -> app#(succ(), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
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     (app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()), app#(app(ack(), 0()), y) -> app#(succ(), y))
     (app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x))
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     (app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)))
     (app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()), app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x))
     (app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()), app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()))
     (app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()), app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())))
     (app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(ack(), 0()), y) -> app#(succ(), y))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(ack(), 0()), y) -> app#(succ(), y))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(ack(), 0()), y) -> app#(succ(), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(ack(), 0()), y) -> app#(succ(), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(ack(), 0()), y) -> app#(succ(), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(ack(), 0()), y) -> app#(succ(), y))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())), app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())))
     (app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())), app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()))
     (app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())), app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x))
     (app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)))
     (app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y))
     (app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x))
     (app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())), app#(app(ack(), 0()), y) -> app#(succ(), y))
     (app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(ack(), 0()), y) -> app#(succ(), y))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(ack(), 0()), y) -> app#(succ(), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x), app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x), app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x), app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x), app#(app(ack(), 0()), y) -> app#(succ(), y))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(ack(), 0()), y) -> app#(succ(), y))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y), app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y), app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y), app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y), app#(app(ack(), 0()), y) -> app#(succ(), y))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(ack(), 0()), y) -> app#(succ(), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(ack(), 0()), y) -> app#(succ(), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(ack(), 0()), y) -> app#(succ(), y))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
    }
    EDG:
     {
      (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)), app#(app(ack(), 0()), y) -> app#(succ(), y))
      (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x))
      (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y))
      (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)))
      (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)), app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x))
      (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)), app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()))
      (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)), app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(ack(), 0()), y) -> app#(succ(), y))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
      (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
      (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
      (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
      (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
      (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
      (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
      (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
      (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
      (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
      (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
      (app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())), app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())))
      (app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())), app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()))
      (app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())), app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x))
      (app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)))
      (app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y))
      (app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x))
      (app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())), app#(app(ack(), 0()), y) -> app#(succ(), y))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(ack(), 0()), y) -> app#(succ(), y))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
      (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y), app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())))
      (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y), app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()))
      (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y), app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x))
      (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)))
      (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y))
      (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x))
     }
     EDG:
      {
       (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)), app#(app(ack(), 0()), y) -> app#(succ(), y))
       (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x))
       (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y))
       (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)))
       (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)), app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x))
       (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)), app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()))
       (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)), app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())))
       (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
       (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
       (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
       (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
       (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
       (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
       (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
       (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
       (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
       (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(ack(), 0()), y) -> app#(succ(), y))
       (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x))
       (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y))
       (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)))
       (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x))
       (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()))
       (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())))
       (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
       (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
       (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
       (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
       (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
       (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
       (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
       (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
       (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
       (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
       (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
       (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
       (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
       (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
       (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
       (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
       (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
       (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
       (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
       (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
       (app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())), app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())))
       (app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())), app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()))
       (app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())), app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x))
       (app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)))
       (app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y))
       (app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x))
       (app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())), app#(app(ack(), 0()), y) -> app#(succ(), y))
       (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
       (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
       (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
       (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
       (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
       (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
       (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())))
       (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()))
       (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x))
       (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)))
       (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y))
       (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x))
       (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(ack(), 0()), y) -> app#(succ(), y))
       (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
       (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
       (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
       (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
       (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
       (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
       (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
       (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
       (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
       (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y), app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())))
       (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y), app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()))
       (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y), app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x))
       (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)))
       (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y))
       (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x))
      }
      EDG:
       {
        (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)), app#(app(ack(), 0()), y) -> app#(succ(), y))
        (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x))
        (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y))
        (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)))
        (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)), app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x))
        (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)), app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()))
        (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)), app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())))
        (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
        (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
        (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
        (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
        (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
        (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
        (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
        (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
        (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
        (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(ack(), 0()), y) -> app#(succ(), y))
        (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x))
        (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y))
        (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)))
        (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x))
        (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()))
        (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())))
        (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
        (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
        (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
        (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
        (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
        (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
        (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
        (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
        (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
        (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
        (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
        (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
        (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
        (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
        (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
        (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
        (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
        (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
        (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
        (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
        (app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())), app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())))
        (app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())), app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()))
        (app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())), app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x))
        (app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)))
        (app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y))
        (app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x))
        (app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())), app#(app(ack(), 0()), y) -> app#(succ(), y))
        (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
        (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
        (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
        (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
        (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
        (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
        (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())))
        (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()))
        (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x))
        (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)))
        (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y))
        (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x))
        (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(ack(), 0()), y) -> app#(succ(), y))
        (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
        (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
        (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
        (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
        (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
        (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
        (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
        (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
        (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
        (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y), app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())))
        (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y), app#(app(ack(), app(succ(), x)), y) -> app#(succ(), 0()))
        (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y), app#(app(ack(), app(succ(), x)), y) -> app#(ack(), x))
        (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)))
        (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y))
        (app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y), app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(ack(), x))
       }
       STATUS:
        arrows: 0.838843
        SCCS (2):
         Scc:
          { app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs),
           app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs),
                app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x),
                app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs),
             app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x)}
         Scc:
          {             app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())),
           app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)),
           app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y)}
         
         SCC (5):
          Strict:
           { app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs),
            app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs),
                 app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x),
                 app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs),
              app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x)}
          Weak:
          { app(app(app(app(filter2(), true()), f), x), xs) -> app(app(cons(), x), app(app(filter(), f), xs)),
           app(app(app(app(filter2(), false()), f), x), xs) -> app(app(filter(), f), xs),
                         app(app(ack(), app(succ(), x)), y) -> app(app(ack(), x), app(succ(), 0())),
            app(app(ack(), app(succ(), x)), app(succ(), y)) -> app(app(ack(), x), app(app(ack(), app(succ(), x)), y)),
                                    app(app(ack(), 0()), y) -> app(succ(), y),
                app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs)),
                                  app(app(map(), f), nil()) -> nil(),
             app(app(filter(), f), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(f, x)), f), x), xs),
                               app(app(filter(), f), nil()) -> nil()}
          Open
         
         
         
         
         
         
         
         
         
         SCC (3):
          Strict:
           {             app#(app(ack(), app(succ(), x)), y) -> app#(app(ack(), x), app(succ(), 0())),
            app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), x), app(app(ack(), app(succ(), x)), y)),
            app#(app(ack(), app(succ(), x)), app(succ(), y)) -> app#(app(ack(), app(succ(), x)), y)}
          Weak:
          { app(app(app(app(filter2(), true()), f), x), xs) -> app(app(cons(), x), app(app(filter(), f), xs)),
           app(app(app(app(filter2(), false()), f), x), xs) -> app(app(filter(), f), xs),
                         app(app(ack(), app(succ(), x)), y) -> app(app(ack(), x), app(succ(), 0())),
            app(app(ack(), app(succ(), x)), app(succ(), y)) -> app(app(ack(), x), app(app(ack(), app(succ(), x)), y)),
                                    app(app(ack(), 0()), y) -> app(succ(), y),
                app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs)),
                                  app(app(map(), f), nil()) -> nil(),
             app(app(filter(), f), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(f, x)), f), x), xs),
                               app(app(filter(), f), nil()) -> nil()}
          Open