KIRBY-PARIS HYDRA step: 0
Click any leaf (top node) to cut a head. The hydra always dies — but it takes a while.
Choose a head to cut
Hercules vs the Hydra: cut a head at depth d, and d-1 copies of the parent subtree regrow. By the Kirby-Paris theorem, Hercules always wins — but the number of steps is not provable in Peano arithmetic.
Kirby & Paris, 1982 · Goodstein sequences · independence from PA