This alteration, however, doesn't seem to simplify the proof as the logical reasoning for the segment starting from $(0,0)$ to $P(\gamma_1 \cup \zeta_1)$ remains unique compared to subsequent segments. The discussion highlights that this approach could provide a more straightforward method for conceptualizing the problem, especially when considering horizontal line segments that decrease upon finding the optimal solution.

An example is given with three transactions, A, B, and C, each with different fees but identical sizes. Two possible sequences are proposed: $L_1$ and $L_2$. In $L_1$, transactions A and B are combined (yielding an average fee of 3/2), followed by transaction C with a fee of 1. Conversely, $L_2$ positions transaction B first (fee of 3), followed by A and C combined (average fee of 1/2). The second sequence, $L_2$, is deemed superior since the fee-size diagram indicates a higher feerate for every byte. When applying the $R(\gamma_i)$ method, the feerate for the middle byte is calculated as 3/2 for $L_1$ and 4/3 for $L_2$. The inquiry then arises whether these two sequences would be considered incomparable based on the feerate-size diagram due to this discrepancy in feerates.