Type classification conjecture for complex reflection triangle groups

Let $(p,q,r)$ be a triple with $p\leq q\leq r$, and let $\rho_t(p,q,r)$ be the associated one-parameter family. Call $(p,q,r)$ type A when the endpoints of the critical interval occur when $W_A=I_pI_rI_qI_r$ is parabolic, and call it type B otherwise. Type classification conjecture. The triple $(p,q,r)$ has type A if $p<10$ and type B if $p>13$. The intermediate cases $p\in\{10,11,12,13\}$ are described as complicated and are not settled by this assertion.