Normalised Paths

Given a path P we can manipulate it using the commutativity relation. Any consecutive symbols a and b such that $a\sim b$ can be swapped, to produce another path. The set of paths produced by all such manipulations of P is the set of aliases for P . Using the ordering on the paths in the alias set we can choose the unique smallest member. This is the normalised path for P. The remaining problem is then to find an efficient algorithm for finding the normalised version of any path.