Work of Levin and Przytycki shows that if two non-special rational functions f and g of degree > 1 over C share the same set of preperiodic points, there are m, n, and r such that f^m g^n = f^r. In other words, f and g nearly commute. One might ask if there are other sorts of relations non-special rational functions f and g over C might satisfy when they do not share the same set of preperiodic points. We will present a recent proof of Beaumont that shows that they may not, that if f and g do not share the same set of preperiodic points, then they generate a free semi-group under composition. The proof builds on work of Bell, Huang, Peng, and the speaker, and uses a ping-pong lemma similar to the one used by Tits in his proof of the Tits alternative for finitely generated linear groups.