User blog comment:B1mb0w/The S Function Version 2/@comment-5529393-20160628040514

This looks interesting - if you would expand on your analysis, giving more concrete examples and more explanation, that would be very helpful. For example, your first example is already at $$f_{\varepsilon_0}(n)$$ - it would be better to give examples for $$\omega, \omega 2, \omega^2, \ldots $$ and so on, so that we can see the patterns.

Also, there are some things that could use proving, first and foremost that repeatedly applying the sub procedure always terminates, and next that repeatedly applying the dec procedure always terminates.