Increase of in backbone tips due to topology conflicts. At first (left) an initial backbone exists (thick branches), all inner nodes are labelled as inside (I) and each tip node has a cluster id. Upon completion of the post-order traversal (right), each inner node has been relabelled accordingly. Here, cluster 2 is not monophyletic. Hence, an additional virtual tip is created, that is, cluster 2 generates 2 boundary tips.