Vernitski's conjecture on knot semigroups of 2-bridge knots

A knot semigroup is a cancellative semigroup whose defining relations arise in pairs of the form $xy=yx$ and $yx=zy$ from the crossing points of a knot diagram. An alternating sum semigroup is the semigroup associated with the alternating-sum construction. A 2-bridge knot is a knot in the class containing torus knots and twist knots.

Vernitski's conjecture. The knot semigroup of every 2-bridge knot is isomorphic to an alternating sum semigroup.

Vernitski proved the claim for torus knots and twist knots. The paper proves it for double twist knots, but the general 2-bridge case remains open in the supplied text.