User blog comment:B1mb0w/Strong D Function/@comment-1605058-20150702183610

After 1,5 hours of looking for good reference, I was able to find this dissertation, results from which show upper bounds on strength of your function.

Firstly, on pages 22-25 of the file (not of the paper - PDF file has different page numeration from the paper itself due to frontmatter) have definitions required to define class Nn of functions. With a good luck, you will see that function \(D(x_1,...,x_k)\) is in Nk.

On page 67 you will find formulation of bounding lemma, using variant of FGH from page 52 (although I'm sure the conclusion of lemma 5 is true with standard FGH as well). In particular it implies that function \(D(n,...,n)\) with \(k\) n's is weaker than \(f_\alpha(n)\) for \(\alpha<\omega^k\), and thus also by \(f_{\omega^k}(n)\). In particular, \(D(n,n,n)\) is bounded by \(f_{\omega^3}(n)\). This is quite far away from \(f_{\varepsilon_0}(n)\)...