(VAR x y )
(RULES 
        half(0) -> 0
        half(s(0)) -> 0
        half(s(s(x))) -> s(half(x))
        inc(0) -> 0
        inc(s(x)) -> s(inc(x))
        zero(0) -> true
        zero(s(x)) -> false
        p(0) -> 0
        p(s(x)) -> x
        bits(x) -> bitIter(x, 0)
        bitIter(x, y) -> if(zero(x), x, inc(y))
        if(true, x, y) -> p(y)
        if(false, x, y) -> bitIter(half(x), y)
        
)