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At least one in five of all planetary nebulae are the product of a common envelope (CE) interaction, where the companion in-spirals into the envelope of an asymptotic giant branch (AGB) star ejecting the nebula and leaving behind a compact binary. In this work we carry out 3D smoothed particle hydrodynamics simulations of the CE interaction between a 1.7 $M_{\odot}$ AGB star and a 0.6 $M_{\odot}$ companion. We model the AGB structure using a 1D stellar model taken at the seventh thermal pulse. The interaction takes place when the giant is on the expanding phase of the seventh thermal pulse and has a radius of 250 $R_{\odot}$. The post-CE orbital separations varies between 20 and 31 $R_{\odot}$, with the inclusion of recombination energy resulting in wider separations. Based on the observed short in-spiral time-scales, we suggest that thermal pulses can trigger CEs, extending the ability of AGB stars to capture companions into CEs, that would lead to the prediction of a larger population of post-AGB, post-CE binaries. Simulations that include a tabulated equation of state unbind a great deal more gas, likely unbinding the entire envelope on short time-scales. The shape of the CE after the in-spiral is more spherical for AGB than red giant branch stars, and even more so if recombination energy is included. We expect that the planetary nebula formed from this CE will have different features from those predicted by Zou et al. 2020.