That's good then. It shouldn't difficult to bootstrap that to the full Collatz conjecture.

Since the Collatz conjecture is not (known to be) finitely refutable, we cannot encode it as a program whose termination decides the conjecture. If the existence of diverging orbits were disproven though, then we could.

That's a good point & also surprising that such a simple dynamical process can not be proven one way or the other to be an instance of a terminating or non-terminating computation.