A conjectured upper and diagonal bound for R-Wythoff Sprague–Grundy values

Let $a$ and $b$ be integers with $4\leq a\leq b$, and let $\mathcal{G}_{\mathcal{R}}(a,b)$ denote the Sprague–Grundy value of the position $(a,b)$ in R-Wythoff. R-Wythoff bounds conjecture. If $a<b$, then

$$\mathcal{G}_{\mathcal{R}}(a,b)\leq b+\lfloor b/3\rfloor-1,$$

and on the diagonal

$$\lfloor 3b/4\rfloor\leq\mathcal{G}_{\mathcal{R}}(b,b)\leq b+\lfloor b/3\rfloor.$$

These bounds would constrain the growth of Sprague–Grundy values both off and on the main diagonal of R-Wythoff; the source gives no resolution, so the conjecture remains open.