A set of intervals A-E together with its corresponding semi-square representation. This example for c = 0.5 also shows that not all candidate cliques are maximal with respect to the set of active semi-squares: When D is born, there are two maximal cliques in the y-structure: {A, B} and {B, C}. D is intersecting with A and B. Thus, there will be one candidate clique {A, B, D}, built from clique {A, B}, and {A, D}, built from {B, C}. The latter candidate clique is thus not maximal with respect to all active cliques and should not be inserted into Q.