On a decomposition of a $3$-connected graph into cyclically $4$-edge-connected components

A graph is called cyclically $4$-edge-connected if removing any three edges from it leads us to a graph, at most one connected component of which contains a cycle. $3$-connected graph is $4$-edge-connected iff removing any three edges from it leads us to either a connected graph or to a graph with exactly two connected components, one of which is a single-vertex one. We show, how to correspond for any $3$-connected graph a components tree, such that every component would be a $3$-connected and cyclically $4$-edge-connected graph.