1. R ← 0. .

2. While R < Rmax

3.  For each

4.  Perform one reticulation on each lineage of and obtain new configurations .

5.  For each , recursively try all ways of coalescences of two lineages in to create new configurations ; then discard if it is incompatible (defined later in this section); otherwise, .

6.  If a final configuration is found, construct the optimal network by trace-back and stop.

7.  R ← R + 1

8. Report there is no solution with less than Rmax reticulations.