Pulley system for block piled on block on an inclined plane

This article discusses a scenario/arrangement whose statics/dynamics/kinematics can be understood using the ideas of classical mechanics.
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The scenario

Consider one block placed on top of another, with the bottom block being $A$ and the block on top being $B$. $A$ is on a fixed inclined plane making an angle of $\theta$ with the horizontal and the surface of contact between $A$ and $B$ is parallel to the inclined plane, i.e., that surface also makes an angle of $\theta$ with the horizontal. There is a pulley system connecting $A$ and $B$, with both sides of the pulley rope being parallel to the inclined plane.

Consider the following conventions:

• $\mu _{s1}$ is the limiting coefficient of static friction between $A$ and the inclined plane.
• $\mu _{k1}$ is the coefficient of kinetic friction between $A$ and the inclined plane.
• $\mu _{s2}$ is the limiting coefficient of static friction between $A$ and $B$.
• $\mu _{k2}$ is the coefficient of kinetic friction between $A$ and $B$.

Assume that $\mu _{k1}\leq \mu _{s1}$ and $\mu _{k2}\leq \mu _{s2}$.

We assume the pulley and string to be massless, so that the tension at both ends of the string is equal.