The reducing property for Artin–Tits presentations

Let $(\mathcal{S},\mathcal{R})$ be an Artin–Tits presentation, and let denote the reducing equivalence defined earlier in the paper. Reducing conjecture. Every Artin–Tits presentation $(\mathcal{S},\mathcal{R})$ satisfies.

This conjecture is motivated by the difficulty of constructing counterexamples of the relevant type among Artin–Tits presentations, since each Artin relation is determined by any pair of adjacent letters. Whether the reducing property holds in complete generality is left open here.