I'd probably prefer a minimalist Encounter Point variant. Here I've tried to cut down rules language to a minimum.
Gaining Encounter Points
Your DM will award you Encounter Points after each encounter, regardless of outcome. Either the DM or the players track these in a Short Rest Pool and a Long Rest Pool. Both pools reset to zero after a long rest is completed.
Easy Encounter - 0 short rest points and 0 long rest points
Medium Encounter - 1 short rest points and 1 long rest points
Hard Encounter - 2 short rest points and 2 long rest points
Deadly Encounter - 3 short rest points and 3 long rest points
Spending Encounter Points
You spend encounter points when you wish to gain the benefits of a rest. You can still rest without spending encounter points, but this will then not give you the benefits of that rest (but see below). When a rest is interrupted for combat, it must be restarted, but you only need to spend the points when you successfully finish the rest and gain the benefits.
A short rest costs 3 short rest points and requires one hour.
A long rest costs 9 long rest points and requires 8 hours.
Resting without Encounter Points
Even if you don't have encounter points to spend, you can still gain the benefit of a short rest by resting for 8 hours uninterrupted by combat.
Even if you don't have encounter points to spend, you can still gain the benefit of a long rest by resting for 7 days uninterrupted by combat.