(VAR f m n x xs y )
(RULES 
        app'(app'(minus, x), 0) -> x
        app'(app'(minus, app'(s, x)), app'(s, y)) -> app'(app'(minus, x), y)
        app'(app'(quot, 0), app'(s, y)) -> 0
        app'(app'(quot, app'(s, x)), app'(s, y)) -> app'(s, app'(app'(quot, app'(app'(minus, x), y)), app'(s, y)))
        app'(app'(le, 0), y) -> true
        app'(app'(le, app'(s, x)), 0) -> false
        app'(app'(le, app'(s, x)), app'(s, y)) -> app'(app'(le, x), y)
        app'(app'(app, nil), y) -> y
        app'(app'(app, app'(app'(add, n), x)), y) -> app'(app'(add, n), app'(app'(app, x), y))
        app'(app'(low, n), nil) -> nil
        app'(app'(low, n), app'(app'(add, m), x)) -> app'(app'(app'(if_low, app'(app'(le, m), n)), n), app'(app'(add, m), x))
        app'(app'(app'(if_low, true), n), app'(app'(add, m), x)) -> app'(app'(add, m), app'(app'(low, n), x))
        app'(app'(app'(if_low, false), n), app'(app'(add, m), x)) -> app'(app'(low, n), x)
        app'(app'(high, n), nil) -> nil
        app'(app'(high, n), app'(app'(add, m), x)) -> app'(app'(app'(if_high, app'(app'(le, m), n)), n), app'(app'(add, m), x))
        app'(app'(app'(if_high, true), n), app'(app'(add, m), x)) -> app'(app'(high, n), x)
        app'(app'(app'(if_high, false), n), app'(app'(add, m), x)) -> app'(app'(add, m), app'(app'(high, n), x))
        app'(quicksort, nil) -> nil
        app'(quicksort, app'(app'(add, n), x)) -> app'(app'(app, app'(quicksort, app'(app'(low, n), x))), app'(app'(add, n), app'(quicksort, app'(app'(high, n), x))))
        app'(app'(map, f), nil) -> nil
        app'(app'(map, f), app'(app'(add, x), xs)) -> app'(app'(add, app'(f, x)), app'(app'(map, f), xs))
        app'(app'(filter, f), nil) -> nil
        app'(app'(filter, f), app'(app'(add, x), xs)) -> app'(app'(app'(app'(filter2, app'(f, x)), f), x), xs)
        app'(app'(app'(app'(filter2, true), f), x), xs) -> app'(app'(add, x), app'(app'(filter, f), xs))
        app'(app'(app'(app'(filter2, false), f), x), xs) -> app'(app'(filter, f), xs)
        
)