The braid relations

The braid group on 4 strands has a presentation with generators s1, s2, s3 and relations s1 s2 s1 = s2 s1 s2, s2 s3 s2 = s3 s2 s3, s1 s3 = s3 s1. In the movie a braid is "simplified" using the relations and the free reduction.