Half-or-full asymptotic reflection complexity conjecture

Let $\mathbf{x}$ be a sequence, and let $r_{\mathbf{x}}(n)$ and $\rho_{\mathbf{x}}(n)$ denote its reflection complexity and factor complexity, respectively. The half-or-full limit conjecture. If the limit

$$\lim_{n\to\infty}\frac{r_{\mathbf{x}}(n)}{\rho_{\mathbf{x}}(n)}$$

exists, then it is either $\frac{1}{2}$ or $1$. Results in the paper establish related asymptotic behavior in reversal-closed and uniformly recurrent cases, but the conjecture is open for general sequences.