2. For every clique where at least one but not all semi-squares are intersecting X, a candidate clique is built with all intersecting semi-squares together with the newborn semi-square. This operation is called the splitting of a clique. It is important to note that not all candidate cliques are really maximal, as is illustrated in Fig. 3. To maintain the y-structure invariant, it is important to insert only cliques that are maximal with respect to the set of active semi-squares. Thus, the following cases have to be checked: