Single Instruction URM Programs/Successor Function

Theorem
The successor function $\operatorname{succ}: \N \to \N$, defined as:
 * $\forall n \in \N: \operatorname{succ} \left({n}\right) = n + 1$

is URM computable by a single-instruction URM program.

Proof
The successor function is computed by the following URM program:

The input $n$ is in $R_1$ when the program starts.

The program adds $1$ to $r_1$ and then stops.

The output $n+1$ is in $R_1$ when the program terminates.