The prime-factor bound for generators of full Collatz processes

Let $f$ be the Collatz function and let $\{f^{s}(a)\}_{s=1}^{\infty}$ be the corresponding Collatz process. Let $\Omega(a)$ denote the total number of prime factors of $a$, counted with multiplicity. The prime-factor bound conjecture. If the process is full, then

$$\Omega(a)\leq 2.$$

This is proposed as a structural restriction on generators of full Collatz processes. The supplied text gives no resolution evidence.