(COMMENT
AG01 3.1 + hard logarithm rules
)
(VAR x y z b)
(RULES
minus(x,0) -> x
minus(s(x),s(y)) -> minus(x,y)
quot(0,s(y)) -> 0
quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))

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)


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