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 $e$?