Clique {2, 3,4} at x = 2 has a global ordering of B(2), B(3), B(4), H(2), H(3), H(4) and a global ordering of B(2), B(3), H(2), H(3), B(4), H(4) at x = 4. When an interval is added to the y-structure it can either intersect all of the bases of a clique, or only a part of the bases, and/or all of the hypotenuses, or just a part of them. If it intersects all bases and/or hypotenuses, it can simply be added to that clique, if it only intersects a part of the bases and/or hypotenuses, it will split the clique.