LInk is broken, but I'll take your word for it. However there is no guarantee the general subset of this problem is solved because you can always run into something it can't do. Another example you could try is a glass HALF-full of wine. It just can't produce a glass that has 50% amount of wine, or another example a jar half-full of jam. It's something that if a human can draw a glass of wine, drawing it half-full is trivial.