MAYBE

Problem:
 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()

Proof:
 Open