The elementary derivation conjecture for trinomial algebras

Let $R(\mathcal{g})$ be a trinomial algebra equipped with its grading $\deg$, and let a locally nilpotent derivation be deg-homogeneous if it is homogeneous with respect to this grading. An elementary locally nilpotent derivation is one of the elementary derivations defined for trinomial algebras.

Elementary derivation conjecture. All $\deg$-homogeneous locally nilpotent derivations of a trinomial algebra are elementary.

This is posed as an open question about homogeneous locally nilpotent derivations of trinomial algebras. The surrounding discussion contrasts the claim with examples of nonzero locally nilpotent derivations that are not $\deg$-homogeneous.