[handoflixue]

> Can the number of beans ever reach zero?

Well, the article disagrees, but the answer is obviously yes: if you have two beans left, regardless of whether they match, the first step is to discard them. Then you have zero beans. After that, you then add 1 additional bean.

So already we can see that the problem is underspecified: are we considering the entire action to be a single atomic "transaction" (in which case it never hits zero), or are these individual steps?

But also, I feel like if you needed TLA+ to answer that question, you're probably not capable of evaluating the TLA+ script? In particular, the TLA+ script doesn't address the "underspecified" aspect at all.