  A locally irregular graph is a graph whose adjacent vertices have distinct
degrees. It was conjectured that every connected graph is edge decomposable to
$3$ locally irregular subgraphs, unless it belongs to a certain family of
exceptions, including graphs of small maximum degrees, which are not
decomposable to any number of such subgraphs. Recently Sedlar and
\v{S}krekovski exhibited a counterexample to the conjecture, which necessitates
a decomposition to (at least) $4$ locally irregular subgraphs. We prove that
every $d$-regular graph with $d$ large enough, i.e. $d\geq 54000$, is
decomposable to $4$ locally irregular subgraphs. Our proof relies on a mixture
of a numerically optimized application of the probabilistic method and certain
deterministic results on degree constrained subgraphs due to Addario-Berry,
Dalal, McDiarmid, Reed, and Thomason, and to Alon and Wei, introduced in the
context of related problems concerning irregular subgraphs.
