The necessity of all generalized Reidemeister moves for virtual-knot diagrams

Let $K$ be a virtual knot, and let $D$ and $D'$ be diagrams of $K$. The generalized Reidemeister-move conjecture. There exist two diagrams $D$ and $D'$ such that every sequence of generalized Reidemeister moves transforming $D$ into $D'$ contains all of the generalized Reidemeister moves. This would establish that, for virtual knots, no generalized Reidemeister move can be omitted in general when relating diagrams of the same knot; the preceding discussion notes that the claim is known for several individual move types, while the remaining cases motivate the conjecture.