2 problems

Ternary Gröbner-basis finiteness conjecture. For each $d\in\mathbb{N}$, the reduced Gröbner basis for the nonsymmetric operad encoding the identity $w_{2d+1}^{(3)}=0$ is finite.

Ternary multiplication nilpotence conjecture. The associative algebras $L(A)$ and $R(A)$ are nilpotent; in both cases, the nilpotence is of index $13$ and is not less in general.