[GAP Forum] elements of free groups

[rcone]

GAP,

Is there a way to find the number of generators of a free group, based on a 
word from that free group?  I.E., is there some way to "talk about" the group 
of origin of an (associative) word in GAP?

Better, can I determine the number of generators based solely on the GAP 
object "g" below?:
 
gap> G := FreeGroup("a","b");
<free group on the generators [ a, b ]>
gap> a := G.1;
a
gap> b := G.2;
b
gap> f := a*b*b*a*b;
a*b^2*a*b
gap> g := a*a;
a^2

Thanks,
Randy Cone
VT