Background: In GAP I created the DihedralGroup of an octagon as a quotient of the freegroup on 2 variables and the presentation $r^8=s^2=s*r*(r^7*s)^{-1}=e \ $ as follows:
gap> f:=FreeGroup(2);
gap> r:=f.1;
f1
gap> s:=f.2;
f2
gap> G:=f/[r^8,s^2,s*r*(r^7*s)^-1];
gap> str(G);
"D16"
gap> r^8;
f1^8
gap> Elements(G);
[ , f1, f2, f1^2, f1^4, f1*f2, f1^3, f1^5, f1^6*f2, f1^4*f2,
f1^6, f1^7*f2, f1^5*f2, f1^7, f1^2*f2, f1^3*f2 ]
gap>
I would have expected that r^8 would return the identity element, instead it leaves r^8 unevaluated.
Question: What should I do so that GAP evaluates $r^8$ to $e$?