(COMMENT harder variant of AG01 3.8a)
(VAR x y b)
(RULES
le(0,y) -> true
le(s(x),0) -> false
le(s(x),s(y)) -> le(x,y)
inc(0) -> 0
inc(s(x)) -> s(inc(x))
minus(0,y) -> 0
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)))
log(x) -> log2(x,0)
log2(x,y) -> if(le(x,0),le(x,s(0)),x,inc(y))
if(true,b,x,y) -> log_undefined
if(false,b,x,y) -> if2(b,x,y)
if2(true,x,s(y)) -> y
if2(false,x,y) -> log2(quot(x,s(s(0))),y)
)