Period bound conjecture for quadratic rational maps with a rational critical 2-cycle

Let $\phi$ be a quadratic rational function defined over $\mathbb{Q}$ having a $\mathbb{Q}$-rational periodic critical point of period $2$. Period bound conjecture for a rational critical 2-cycle. The map $\phi$ has no $\mathbb{Q}$-rational periodic points of period greater than $2$. The conjecture is used to obtain a classification of the corresponding preperiodicity graphs, but the source gives no proof.