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\label{def:greedy-peel}
Given $X \in \tau\text{-Idx}$ with $X \geq \underline{2}$,
the \textbf{greedy peel-off} extracts the ABCD coordinates
as follows:
\begin{enumerate}
    \item \textbf{Find $A$ (largest prime divisor):}
          Let $\underline{A}$ be the largest prime
          dividing $X$.
    \item \textbf{Find $C$ (maximal tetration height):}
          Let $\underline{C}$ be the largest
          $\underline{c} \geq \underline{1}$ such that
          $(\underline{A} \uparrow\uparrow \underline{c})
          \mid X$.
    \item \textbf{Find $B$ (maximal exponent):}
          Let $\underline{B}$ be the largest
          $\underline{b} \geq \underline{1}$ such that
          $(\underline{A} \uparrow\uparrow \underline{C})^{\underline{b}}
          \mid X$.
    \item \textbf{Compute $D$ (remainder):}
          Set $\underline{D} = X \;/\;
          (\underline{A} \uparrow\uparrow \underline{C})^{\underline{B}}$.
\end{enumerate}
The output is the tuple
$\Phi(X) = (\underline{A}, \underline{B},
\underline{C}, \underline{D})$.