4 problems

Coexistence conjecture. Introducing different $?$ symbols for rules a)--d) and adopting the exact symmetric rules for the backward transitions should allow the four rules to coexis…

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

Coherence-preservation conjecture. Instantiating a coherent-memory context with an incoherent process should produce an incoherent term.