Biautomaticity conjecture for the fundamental group of $X_2$

Let $X_2$ be the specific compact locally CAT(0) triangle-square complex constructed in the paper. Biautomaticity conjecture for $X_2$. The fundamental group $\pi_1(X_2)$ is biautomatic. The paper presents this as a conjecture after noting that the construction embeds in the universal cover of $X_2$; no proof or disproof is supplied in the given text.