User blog comment:Scorcher007/Analysis DAN up to Z2/@comment-35470197-20180828141502/@comment-31580368-20180828150552

If recursive way to compute the expression means Well-ordered ordinal notation, then no. Creating Well-ordered ordinal notation to the Z2 level is an incredibly difficult task. My analysis is based on the above two hypotheses and patterns in the expression of stable ordinals. These patterns are perfectly integrated into DAN expressions. I took this patterns from the following sources:

Arai Т. - A sneak preview of proof theory of ordinals - 1997 Barwise J. - Admissible Sets and Structures - 1975 Carlson J.T. - Patterns of Resemblance of Order 2 - 2001 Rathjen M. - An ordinal analysis of parameter free Pi-1-2-comprehension - 2005 Rathjen M. - An Ordinal Analysis of Stability - 2011 Rathjen M. - Investigations of subsystems of second order arithmetic and set theory - 2010 Rathjen M. - Recent Advances in Ordinal Analysis П12-CA and related systems - 1995 Richter W. - Inductive Definitions And Reflecting Properties Of Admissible Ordinals - 1973 Stegert J.C. - Ordinal Proof Theory of  Kripke-Platek Set Theory Augmented by Strong Reflection Principles - 2010