Partitioning on an element is used in a cyclical way to order the indexing of the matrix under development. In the process of partitioning, data are supplied that partially fill the matrix. Each cycle may involve several parts, and each part involves the same four steps. The firstc ycleh as only one part, and the four steps will be described shortly in describing the first cycle. The second i;yde may have as many as three parts, depending on the results of the first cycle. The thirdc yclem ay have as many as nine parts, and in general the nth cycle may have as many as 3•- 1 parts. Experience suggests that only a few cycles will normally be needed to develop a reachability matrix, and the number of parts will seldom be as high as the stated maxima.