(VAR x y b)
(RULES
half(0) -> 0
half(s(0)) -> 0
half(s(s(x))) -> s(half(x))

le(0,y) -> true
le(s(x),0) -> false
le(s(x),s(y)) -> le(x,y)

inc(s(x)) -> s(inc(x))
inc(0) -> s(0)

logarithm(x) -> logIter(x,0)
logIter(x,y) -> if(le(s(0),x), le(s(s(0)),x), half(x), inc(y))
if(false, b, x, y) -> logZeroError
if(true, false,x,s(y)) -> y
if(true, true, x, y) -> logIter(x, y)

f -> g
f -> h
)