Didn't read the paper, but it was easy for me to derive constants 0, 1, e and functions x + y, x - y, exp(x), ln(x), x * y, x / y. So seems to be enough for everything. Very elegant.
Although x + y is surprisingly more complicated than you'd expect at first. The construction first goes for exp(x) and ln(x) then to x - y and finally uses -y to get to x + y.