No, said Mises, for if taken back far enough, there comes a point at which money first emerges as a medium of exchange out of a pure barter economy Prior to this, it is valued only for its non-monetary uses as a commodity The demand for money is therefore pushed back to the last day of barter, where goods are traded only in direct exchange, and where the temporal element of the regression theorem ends It is in this way that all charges of circularity are obviated.
In his analysis of barter between coastal and inland villages in the Trobriand Islands, Keith Hart highlighted the difference between highly ceremonial gift exchange between community leaders, and the barter that occurs between individual households. The haggling that takes place between strangers is possible because of the larger temporary political order established by the gift exchanges of leaders. From this he concludes that barter is "an atomized interaction predicated upon the presence of society" (i.e. that social order established by gift exchange), and not typical between complete strangers.
On paper, this sounds a bit like delayed barter, but it bears some significant differences. For one thing, it’s much more efficient than Smith’s idea of a barter system, since it doesn’t depend on each person simultaneously having what the other wants. It’s also not tit for tat: No one ever assigns a specific value to the meat or cake or house-building labor, meaning debts can’t be transferred.