 This exponential blowup is inevitable, because there exist families of DFAs for which any equivalent regular expression must be of exponential size.In practice, the size of the regular expression obtained by running the algorithm can be very different depending on the order in which the states are considered by the procedure, i.e., the order in which they are numbered from 0 to "n".The automaton shown in the picture can be described as "M" = ("Q", Σ, δ, "q"0, "F") with

Kleene's algorithm computes the initial regular expressions as

After that, the "R" are computed from the "R" step by step for "k" = 0, 1, 2.