2 problems

HHPB congruence conjecture. HHPB is equivalent to a congruence relation on terms that do not exhibit auto-conflict.

HHPB correspondence conjecture. If $R\mathrel{\sim^{\tau}}S$, then there exists a HHPB $\mathrel{\mathcal{R}}$ between $\mathcal{C}_R$ and $\mathcal{C}_S$ such that