Reversify any sequential algorithm

To reversify an arbitrary sequential algorithm $A$, we gently instrument $A$ with bookkeeping machinery. The result is a step-for-step reversible algorithm that mimics $A$ step-for-step and stops exactly when $A$ does. Without loss of generality, we presume that algorithm $A$ is presented as an abstract state machine that is behaviorally identical to $A$. The existence of such representation has been proven theoretically, and the practicality of such representation has been amply demonstrated.