(VAR x y)
(RULES
lt(0, s(x)) -> true
lt(x, 0) -> false
lt(s(x), s(y)) -> lt(x, y)

logarithm(x) -> ifa(lt(0, x), x)

ifa(true, x) -> help(x, 1)
ifa(false, x) -> logZeroError

help(x, y) -> ifb(lt(y, x), x, y)

ifb(true, x, y) -> help(half(x), s(y))
ifb(false, x, y) -> y

half(0) -> 0
half(s(0)) -> 0
half(s(s(x))) -> s(half(x))
)