Let be the rank two free group and be a subgroup.
Observe that , then .
Clearly , because it is not difficult to convince oneself that consists on words of even length and implies .
Technically, that is attending to the Schreier’s recipe, having as a set of transversals and being the free generators for .
Set and take , then we get
So according to Schreier’s language the set in our case, is
Hence are the free generator for .
Note that this three word are the first three length-two-words in the alphabetical order, start by and continuing to