(VAR x xs y ys )
(RULES 
        +(0, y) -> y
        +(s(x), y) -> s(+(x, y))
        ++(nil, ys) -> ys
        ++(:(x, xs), ys) -> :(x, ++(xs, ys))
        sum(:(x, nil)) -> :(x, nil)
        sum(:(x, :(y, xs))) -> sum(:(+(x, y), xs))
        sum(++(xs, :(x, :(y, ys)))) -> sum(++(xs, sum(:(x, :(y, ys)))))
        -(x, 0) -> x
        -(0, s(y)) -> 0
        -(s(x), s(y)) -> -(x, y)
        quot(0, s(y)) -> 0
        quot(s(x), s(y)) -> s(quot(-(x, y), s(y)))
        length(nil) -> 0
        length(:(x, xs)) -> s(length(xs))
        hd(:(x, xs)) -> x
        avg(xs) -> quot(hd(sum(xs)), length(xs))
        
)