  We compute the finite generation ideal for Daigle and Freudenburg's
counterexample to Hilbert's fourteenth problem. This ideal helps to understand
how far the ring of invariants is from being finitely generated. Our
calculations show that the finite generation ideal is the radical of an ideal
generated by three infinite families of invariants. We show that these three
families together with an additional invariant form a SAGBI-basis. We use the
properties of our SAGBI-basis in our computation of the finite generation
ideal.

Commutative Algebra;Algebraic Geometry