The inverse relationship between Zeroing Algorithm runtime and $Q_0(r)$

Let $Q_0(r)$ be the quantity associated with the initial polynomial in the Zeroing Algorithm, and let the run-time denote the number of steps taken by that algorithm.

Inverse-relationship conjecture. $Q_0(r)$ and the run-time have an inverse relationship.

This conjecture is motivated by simulations and by the preceding theorem, which suggests that the run-time becomes unbounded as $Q_0(r)\to 0^-$. The source does not specify a precise functional meaning of “inverse relationship” or provide a proved bound.