Clear Registers Program

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

Then we define the URM program $\map Z {a, b}$ to be:

where $\map Z a$ denotes the zero instruction:
 * $r_a \gets 0$

Hence this URM program zeroizes all the registers from $R_a$ through to $R_b$.

If $a > b$ then $\map Z {a, b}$ is the null URM program.

The length of $\map Z {a, b}$ is:
 * $\map \lambda {\map Z {a, b} } = \begin {cases}

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

Proof
Self-evident.