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The first iteration of the repeat-loop in Refine applies NewSplit to ; it is equivalent to applying Split. The result is shown in Step 1. The next iteration of NewSplit is then applied to ; the vectors computed are This yields Step 2-1. The reordering produces Step 2-2. Finally, the last iteration of Refine produces the partitioning with every partition of size 1. This in fact mean that the problem is completely solved; for every graph isomorphic to our graph G, Refine will construct a partitioning which has all partitions of size 1. This is an ideal situation.