Shortest Circuit Cover Conjecture

Let $G$ be a $2$-edge-connected graph, and let $scc(G)$ denote the minimum length of a circuit cover of $G$, where the length of a circuit cover is the sum of the lengths of its circuits. Shortest Circuit Cover Conjecture.

$$scc(G) \leq \frac{7}{5}|E(G)|.$$

This conjecture, proposed by Alon and Tarsi, concerns the shortest circuit cover of a $2$-edge-connected graph. The source does not provide evidence of a resolution.