Fig. 2.

Searching for a Segmentation. The decision tree has a height of |C|, with each layer asking the question whether segment $C_i^{*}$ can be added in the segmentation given the decisions on segments $C_j^{*}$, j < i. The blue path indicates an example solution, in which segment $C_2^{*}$ is included but $C_1^{*}\text{and}{C}_3^{*}$ are not. The subtrees rooted at $C_3^{*}\text{and}\overline{C_3^{*}}$ are shown as triagles.