A conjecture about Artin–Tits groups

We conjecture that the word problem of Artin–Tits groups can be solved without introducing trivial factors ss−1 or s−1s. 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.