Conjugacy in Artin groups of extra-large type

We describe a constructive, cubic time solution to the conjugacy problem in Artin groups of extra-large type, which was proved solvable in those groups by Appel and Schupp. We use results from two of our previous papers that characterise geodesic words in those groups, as well as the description of conjugacy between elements involving three or more generators that is given by Appel and Schupp.