Infinitely Many Programs for URM Computable Function

Theorem
Let $$g: \N^k \to \N$$ be a URM computable function.

Then there is an infinite number of URM programs which compute $$g$$.

Proof
As $$g$$ is URM computable, there exists a URM programs which computes it.

Let $$Q$$ be such a program.

Let $$n \in \N$$.

Increment the Jumps in $$Q$$ by $$n$$ lines. Call this amended version $$Q'$$.

This is because, as $$Q$$ was written so as to start from line 1, we need to move all the Jumps so as to point to the same lines relative to the start of $$Q'$$.

Then we can build the following URM program:

...etc.

Each of the $$C \left({1, 1}\right)$$ instructions codes the identity function.

So adding it to the front of $$Q$$ has no effect on the behaviour of $$Q$$

It is clear that for each $$n \in \N$$ there is a different URM program which computes $$f$$.

The result follows from Infinite if Injection from Natural Numbers.