User blog comment:Ynought/The degree function/@comment-33713741-20181231052946/@comment-35470197-20181231064141

Is the following interpretation helpful for you?

A term means an expression of the form \((a)_b\) for numral numbers \(a\) and \(b\). For a term \(t = (a)_b\), I call \(a\) the upper value of \(t\).

For a finite array \(B = ((a_1)_{b_1},\ldots,(a_L)_{b_L})\) of terms and a natural number \(n\), I denote by \(B + n\) the finite array of terms given by adding \(n\) to the upper value of each entry of \(B\), i.e. \(((a_1+n)_{b_1},\ldots,(a_L+n)_{b_L})\).

For a natural number \(k\) and a finite array \(B\) of terms, I define a natural number \([k] B\) in the following recursive way:


 * 1) Put \(f(k) = k^3\).
 * 2) Suppose that \(B\) is the empty array.
 * 3) Return \([k] B = f(k)\).
 * 4) Denote by \(L\) the length of \(B\).
 * 5) For each \(1 \leq i \leq L\), denote by \((a_i)_{b_i}\) the \(i\)-th entry of \(B\).
 * 6) Suppose that there is an entry of \(B\) of the form \((n)_0\) or \((0)_n\) for some natural number \(n\).
 * 7) Let \(N\) denote the minimum of such an \(n\) above.
 * 8) Denote by \(C\) the finite array of terms obtained by removing from \(B\) all entries of the form \((N)_0\) or \((0)_N\).
 * 9) Return \([k] B = [f(k)] (C + k + a_1)\).
 * 10) Denote by \(C\) the finite array \((\underbrace{(a_1)_{b_1-1},\ldots,(a_1)_{b_1-1}}_{a_1+1},(a_2)_{b_2},\ldots,(a_L)_{b_L})\) of terms.
 * 11) Return \([k] B = [f(k)] (C + k + a_k)\).