The proof that it stops instead of going on forever is here: https://arxiv.org/abs/0908.3724 https://arxiv.org/abs/0908.3724 It’s more than 200 pages of pretty

The proof that it stops instead of going on forever is here: https://arxiv.org/abs/0908.3724 https://arxiv.org/abs/0908.3724 It’s more than 200 pages of pretty technical mathematics, so I’m reasonably confident that there is no description a layperson might understand.