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Common envelope (CE) evolution is a critical but still poorly understood progenitor phase of many high-energy astrophysical phenomena. Although 3D global hydrodynamic CE simulations have become more common in recent years, those involving an asymptotic giant branch (AGB) primary are scarce, due to the high computational cost from the larger dynamical range compared to red giant branch (RGB) primaries. But CE evolution with AGB progenitors is desirable to simulate because such events are the likely progenitors of most bi-polar planetary nebulae (PNe), and prominent observational testing grounds for CE physics. Here we present a high resolution global simulation of CE evolution involving an AGB primary and $1\,\mathrm{M}_\odot$ secondary, evolved for $20$ orbital revolutions. During the last $16$ of these orbits, the envelope unbinds at an almost constant rate of about $0.1$-$0.2\,\mathrm{M}_\odot\,\mathrm{yr}^{-1}$. If this rate were maintained, the envelope would be unbound in less than $10\,\mathrm{yr}$. The dominant source of this unbinding is consistent with inspiral; we assess the influence of the ambient medium to be subdominant. We compare this run with a previous run that used an RGB phase primary evolved from the same $2\,\mathrm{M}_\odot$ main sequence star to assess the influence of the evolutionary state of the primary. When scaled appropriately, the two runs are quite similar, but with some important differences.