  We describe the restriction of the Dehornoy ordering of braids to the dual
braid monoids introduced by Birman, Ko and Lee: we give an inductive
characterization of the ordering of the dual braid monoids and compute the
corresponding ordinal type. The proof consists in introducing a new ordering on
the dual braid monoid using the rotating normal form of arXiv:0811.3902
[math.GR], and then proving that this new ordering coincides with the standard
ordering of braids.
