The hare–tortoise fertility comparison conjecture

Let $w$ be a word, and let $\langle w\rangle_{\operatorname{\mathsf{hare}}}$ and $\langle w\rangle_{\operatorname{\mathsf{tortoise}}}$ denote its hare- and tortoise-fertilities. The hare–tortoise fertility comparison conjecture.

$$\langle w\rangle_{\operatorname{\mathsf{hare}}}\leq 2\langle w\rangle_{\operatorname{\mathsf{tortoise}}}-2.$$

This is proposed alongside the conjectured sharp bound on the difference between the two fertilities.