/* black box recognition procedure for Fi24'.2 */

StandardGeneratorsFi24Autm := function (G : Projective := false, Limit := 500)

   Fct := Projective select ProjectiveOrder else Order;
   
   P := RandomProcessWithWords (G); 
   g, w := ElementOfOrder (P, {34,46,54,70,78}, Limit: Fct := Fct);
   if Type (g) eq BoolElt then return false, _; end if;
   h, v := ElementOfOrder (P, 40, Limit: Fct := Fct);
   if Type (h) eq BoolElt then return false, _; end if;

   o1 := Fct (g); o2 := Fct (h);
   x := g^(o1 div 2); xw := w^(o1 div 2);
   b := h^(o2 div 8); bw := v^(o2 div 8);

   nmr := Limit;
   repeat 
      nmr -:= 1;
      c, cw := Random (P);
      a := x^c;
   until Fct (a * b) eq 29 or nmr eq 0;

   if nmr eq 0 then return false, _; end if;

   aw := xw^cw; 

   if not PresentationFi24Autm (G: UserGenerators := [a, b], Projective := Projective) then 
      return false, _; 
   end if;

   return [a, b], [aw, bw];

end function;