  We conjecture that the word problem of Artin-Tits groups can be solved
without introducing trivial factors ss^{-1} or s^{-1}s. Here we make this
statement precise and explain how it can be seen as a weak form of
hyperbolicity. We prove the conjecture in the case of Artin-Tits groups of type
FC, and we discuss various possible approaches for further extensions, in
particular a syntactic argument that works at least in the right-angled case.
