(VAR f x xs y )
(RULES 
        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, app(succ, x)), app(succ, y)) -> app(app(ack, x), app(app(ack, app(succ, x)), y))
        app(app(map, f), nil) -> nil
        app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs))
        app(app(filter, 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(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)
        
)