Originating from the work of Navarro and Thankanchan [TCS 2016], the problem of consecutive pattern matching is a variant of the fundamental pattern matching problem, where one is given a text and a pair of patterns $p_1,p_2$, and must compute consecutive occurrences of $p_1,p_2$ in the text. Assuming that the text is given as a straight-line program of size $g$, we develop an algorithm that computes all consecutive occurrences of $p_{1}, p_{2}$ in optimal $O(g+|p_1|+|p_2|+output)$ time. As a corollary, we also derive an algorithm that reports all co-occurrences separated by a distance $d \in [a,b]$ in $O(g+|p_1|+|p_2|+\occ)$ time and an algorithm that reports the top-$k$ closest co-occurrences in $O(g+|p_1|+|p_2|+k)$ time.