User blog comment:LittlePeng9/SCG(1)/@comment-6768393-20130311223753/@comment-5529393-20130312001402

I conjecture that forest(n) grows at least at the rate of F_epsilon_0 (n). For a provable lower bound, we know for a fact that the longest sequence of rooted binary trees grows at the rate of F_epsilon_0 (n) or higher. We can make a nonrooted subcubic tree into a rooted binary tree just by identifying a vertex to be the root;  for example, we can attach the prospective root to another vertex that has a loop. So you can use the construction I described on the SCG talk page, except the final sequence of forests doesn't apply since you can't have any loops anymore. So you get SCG(1) > binarytree^3 (n) ~ (F_epsilon_0) ^3 (n). This is far greater than Chained arrow notation, and goes (barely) beyond tetrational arrays in BEAF.

Of course, we can probably do much better based on the LittlePeng9's ideas;  I haven't examined them carefully yet.