The bounded-degree decomposition conjecture for 4-edge-connected graphs

Let $G$ be a $4$-edge-connected graph with maximum degree at most $5$. The bounded-degree decomposition conjecture. The graph $G$ can be decomposed into two connected factors $G_1$ and $G_2$ such that

$$\Delta(G_2)\le 3.$$

The source proposes this as the special case $m_1=m_2=1$ of a decomposition problem, and notes that it would improve a lower bound for connected factors at odd-degree vertices. No resolution is given.