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In the previous paper, we considered a link diagram invariant of Hass andNowik type using regular smoothing and unknotting number, to estimate thenumber of Reidemeister moves needed for unlinking.  In this paper, we introduce a new link diagram invariant using irregularsmoothing, and give an example of a knot diagram of the unknot for which thenew invariant gives a better estimation than the old one.

Irregular smoothing and the number of Reidemeister moves