Clear Registers Program

URM Program
Let $$a, b \in \N$$ be natural numbers such that $$0 < a$$.

Then we define the URM program $$Z \left({a, b}\right)$$ to be:

This program clears (that is, sets to $$0$$) all the registers from $$R_a$$ through to $$R_b$$.

If $$a > b$$ then $$Z \left({a, b}\right)$$ is the null URM program.

The length of $$Z \left({a, b}\right)$$ is:
 * $$\lambda \left({Z \left({a, b}\right)}\right) = \begin{cases}

0 & : a > b \\ b - a + 1 & : a \le b \end{cases} $$

Proof
Self-evident.