(VAR fun u x xs y z )
(RULES 
        app(perfectp, 0) -> false
        app(perfectp, app(s, x)) -> app(app(app(app(f, x), app(s, 0)), app(s, x)), app(s, x))
        app(app(app(app(f, 0), y), 0), u) -> true
        app(app(app(app(f, 0), y), app(s, z)), u) -> false
        app(app(app(app(f, app(s, x)), 0), z), u) -> app(app(app(app(f, x), u), app(app(minus, z), app(s, x))), u)
        app(app(app(app(f, app(s, x)), app(s, y)), z), u) -> app(app(app(if, app(app(le, x), y)), app(app(app(app(f, app(s, x)), app(app(minus, y), x)), z), u)), app(app(app(app(f, x), u), z), u))
        app(app(map, fun), nil) -> nil
        app(app(map, fun), app(app(cons, x), xs)) -> app(app(cons, app(fun, x)), app(app(map, fun), xs))
        app(app(filter, fun), nil) -> nil
        app(app(filter, fun), app(app(cons, x), xs)) -> app(app(app(app(filter2, app(fun, x)), fun), x), xs)
        app(app(app(app(filter2, true), fun), x), xs) -> app(app(cons, x), app(app(filter, fun), xs))
        app(app(app(app(filter2, false), fun), x), xs) -> app(app(filter, fun), xs)
        
)