  A conjecture of Dehornoy claims that, given a presentation of an Artin-Tits
group, every word that represents the identity can be transformed into the
trivial word using the braid relations, together with certain rules (between
pairs of words that are not both positive) that can be derived directly from
the braid relations, as well as free reduction, but without introducing trivial
factors $ss^{-1} $ or $s^{-1} s$. This conjecture is known to be true for
Artin-Tits groups of spherical type or of FC type. We prove the conjecture for
Artin--Tits groups of sufficiently large type.
