How did the Buddha know rebirth was ended?

I read the following in the internet: > You are right, **punarbhāva** doesn't mean "rebirth"... except in all the > dictionaries, all the Pāli instruction books, all the grammars, all > the traditional literature, and all the modern commentarial > literature. LMAO. – Based on in the above, how did the Buddha have direct knowledge and vision "this is my last rebirth; now there’ll be no more future lives” (ayamantimā jāti, natthi dāni **punabbhavo**’”ti.)? If the question is not clear, some Buddhists assert punabbhavo & jati are mental states, therefore such Buddhists assert such mental states can be directly known to arise & cease, as for example, when SN 12.20 says: "*birth is impermanent, conditioned, dependently arisen, subject to destruction, vanishing, fading away, and cessation*." But if punabbhavo means rebirth, how did the Buddha directly know this rebirth would end when craving ended? For example, when craving ends in a Buddha, the body keeps breathing, the cells of the body keep replicating, consciousness keeps arising at the six sense bases. Therefore, how did the Buddha directly know craving leads to reincarnation/rebirth? For example, if the hair of the head keeps growing after craving ends, how could the Buddha have been certain rebirth ends when craving ends?