The directed degree-f arboricity conjecture

Let $D$ be a directed multigraph and let $f:V(D)\to\mathbb{Z}_{\ge 2}$ be a vertex function. A degree-$f$ branching is a branching in which every vertex $v$ has outdegree at most $f(v)-1$; let $\vec{a}_f(D)$ be the minimum number of colors needed to partition the arcs of $D$ into degree-$f$ branchings. Write $\overline{D}$ for the underlying undirected multigraph, define

$$\Delta_{f-1}^+(D)=\max_{v\in V(D)}\left\lceil\frac{d^+(v)}{f(v)-1}\right\rceil,$$

and let $\Delta^-(D)$ be the maximum indegree and $a(\overline{D})$ the arboricity of $\overline{D}$.

Directed degree-$f$ arboricity conjecture. For every directed multigraph $D$,

$$\vec{a}_f(D)\le\max\{\Delta^-(D),\Delta_{f-1}^+(D),a(\overline{D})\}+1.$$

This is proposed as a natural generalization of the updated Directed Linear Arboricity Conjecture and the preceding degree-$f$ results. The source gives no resolution.