(VAR f k l x xs y z )
(RULES 
        app'(app'(minus, x), 0) -> x
        app'(app'(minus, app'(s, x)), app'(s, y)) -> app'(app'(minus, x), y)
        app'(app'(minus, app'(app'(minus, x), y)), z) -> app'(app'(minus, x), app'(app'(plus, y), z))
        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'(plus, 0), y) -> y
        app'(app'(plus, app'(s, x)), y) -> app'(s, app'(app'(plus, x), y))
        app'(app'(app, nil), k) -> k
        app'(app'(app, l), nil) -> l
        app'(app'(app, app'(app'(cons, x), l)), k) -> app'(app'(cons, x), app'(app'(app, l), k))
        app'(sum, app'(app'(cons, x), nil)) -> app'(app'(cons, x), nil)
        app'(sum, app'(app'(cons, x), app'(app'(cons, y), l))) -> app'(sum, app'(app'(cons, app'(app'(plus, x), y)), l))
        app'(sum, app'(app'(app, l), app'(app'(cons, x), app'(app'(cons, y), k)))) -> app'(sum, app'(app'(app, l), app'(sum, app'(app'(cons, x), app'(app'(cons, y), k)))))
        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)
        
)