Infinite-length conjecture for blocked wild labyrinth fractals

Let ${\cal A}$ be a wild labyrinth pattern: its graph is connected, it has at least one vertical and one horizontal exit pair, and it satisfies the stated labyrinth-pattern connectivity property. Suppose that ${\cal A}$ is horizontally and vertically blocked, meaning that every horizontal and vertical exit pair is blocked. Let $L_{\infty}$ be the self-similar wild labyrinth fractal generated by ${\cal A}$. Infinite-length conjecture. For any two distinct points $x,y\in L_{\infty}$, every arc in $L_{\infty}$ connecting them has infinite length. This concerns the metric complexity of wild labyrinth fractals; the supplied text gives no resolution or supporting result for the assertion.