Nothing wrong with tabs. They don't presume the existence of money
Yeah, they kind of do.
They certainly presume eventual payment of some
kind, maybe not in cash, but yes payment. Running up a tab means the samething as running up a bill.
Tab: account, invoice, statement, bill.
But still no money. There maybe "debt" of some kind, defined in some cultural or social way, but no debt-tokens nor medium of exchange as we currently understand it.