  If a rectangular diagram represents the trivial knot, then it can be deformed
into the trivial rectangular diagram with only four edges by a finite sequence
of merge operations and exchange operations, without increasing the number of
edges, which was shown by I. A. Dynnikov.
  Using this, Henrich and Kauffman gave an upper bound for the number of
Reidemeister moves needed for unknotting a knot diagram of the trivial knot.
  However, exchange or merge moves on the top and bottom pairs of edges of
rectangular diagrams are not considered in the proof.
  In this paper, we show that there is a rectangular diagram of the trivial
knot which needs such an exchange move for being unknotted, and study upper
bound of the number of Reidemeister moves needed for realizing such an exchange
or merge move.
