overview of finiteness proof Gerog comment "not helpful", adding more intuitions of "closed forms"
\usepackage{tikz}
%\usepackage{pgf}
%\usetikzlibrary{positioning}
%\usetikzlibrary{calc}
%\usetikzlibrary{automata}
%\usetikzlibrary{arrows}
%\usetikzlibrary{backgrounds}
%\usetikzlibrary{fit}
%\usepackage{tikz-qtree}
\usepackage{pgfplots}
%\pgfplotsset{compat=1.15}