google-plex and beyond

G(1) = google = 10 ^ 100;
G(2) = goole-plex = google ^ google = G(1) ^ G(1);
G(3) = google-du-plex = google-plex ^ google-plex = G(2) ^ G(2);
G(4) = google-tri-plex = G(3) ^ G(3);
G(5) = google-quad-plex = G(4) ^ G(4);
....

G(n) = google-n-plex = G(n-1) ^ G(n-1);

G(google) = google-google-plex;
G(google-plex) = google-google-plex-plex;
G(google-google-plex-plex) = google-google-google-plex-plex-plex;
....
G(google(written a google number of times)-plex(written a google number
of times))
= G(google(written a google - 1 number of times)-plex(written a google -
1 number of times)) ^ G(google(written a google - 1 number of times)-
plex(written a google - 1 number of times))
= google-google(written a google number of times)-plex(written a google
number of times)-plex
= G(g)

G(g+1) = G(g) ^ G(g) = google-g+1-plex;
G(g+2) = G(g+1) ^ G(g+1)= google-g+2-plex;
....
G(g+google) = G(g+google-1) ^ G(g+google-1) = google-g+google-plex;
G(g+google+1) = G(g+google) ^ G(g+google) = google-g+google+1-plex;
G(g+google+2) = G(g+google+1) ^ G(g+google+1)= google-g+google+2-
plex;...
....
G(g+g) = google-g+g-plex;
....
G(g^g) = google-g^g-plex;
G(g^g+1) = google-g^g+1-plex;
G(g^g+2) = google-g^g+2-plex;
....
G(g^g + g^g) = google-g^g+g^g-plex;
....

G((g^g)^(g^g)) = google-(g^g)^(g^g)-plex;

G((g^g) raised to the (g^g) a (g^g) number of times;

G(google-g^g-plex) = google-google-g^g-plex-plex;
.