Harikae–Nakanishi $(2,2)$-move conjecture for links

A $(2,2)$-move is the local link modification shown in Figure 1.10; two links are $(2,2)$-move equivalent if they are related by such moves, their inverses, and Reidemeister moves. A trivial link is a disjoint union of unknotted, unlinked circles. Harikae–Nakanishi conjecture. Every link is $(2,2)$-move equivalent to a trivial link. The source introduces this move because a 5-move is a combination of a $(2,2)$-move and its mirror-image inverse. It supplies no resolution of the conjecture.