The complexity bound conjecture for S(e,23,e)-adic languages

Let $\mathcal{L}$ be an $S(e,23,e)$-adic language, and let $p_\mathcal{L}(n)$ denote its factor-complexity function.

Complexity bound conjecture. The complexity function $p_\mathcal{L}$ for any $S(e,23,e)$-adic language $\mathcal{L}$ satisfies

$$p_\mathcal{L}(n) \leq 3n.$$

This would extend the paper's classification of TRIP maps whose associated $S$-adic languages have complexity bounded above by $3n$ to the remaining map family $S(e,23,e)$ and its twins and conjugates.