[![enter image description here](https://i.stack.imgur.com/WPTOU.jpg)](https://i.stack.imgur.com/WPTOU.jpg)

In the following figure, if we wanted to move the system, the minimum force we apply must overcome the static friction between the ground surface and the block of mass $m\_{1}$. Thus, $F>\mu\_{1}(m\_{1}+m\_{2})g$. In this case, the friction between the two blocks $f\_{1}=\mu\_{2}m\_{2}g$ starts acting. I'm trying to understand if this force of friction resists the motion of the block of mass $m\_{1}$ relative to the ground. The force $f\_{2}$ is certainly acting backwards on $m\_{1}$, but is it just resisting relative motion between the blocks or is it also preventing the block on the bottom from moving forwards. To put it concisely, I'm asking for the minimum force $F$ required horizontally to move the system. Is it $\mu\_{1}(m\_{1}+m\_{2})g$ or $\mu\_{1}(m\_{1}+m\_{2})g+\mu\_{2}m\_{2}g$