User blog:Alemagno12/A program-free definition for BM2?

Thanks to Ecl1psed276 for the sequence reduction method and for helping me test and fix the rules!

Preparation: sequence reduction
Before we begin, we need to define a transformation over sequences called sequence reduction. It works like this:

Let the rightmost element of the sequence be (x1,x2,x3,...,xn).

Start at x1. Then, do the following subprocess: Then, move to the next term of the rightmost element. Call it xm. If it's bigger than 0, repeat this subprocess again, but comparing ym and xm instead of y1 and x1, move to the next term of the rightmost element, and repeat the process; else, stop. Notice that we've kept the sequence the same, but we've labelled some nodes as discarded. These nodes will be important later. [WIP]
 * Start at the rightmost element.
 * Move to the rightmost non-discarded element to the left of the one you're on. Let this node be (y1,y2,y3,...,yn).
 * If y1 ≥ x1, label the element you're on as discarded and move to the rightmost non-discarded element element to the left of the one you're on.
 * Move to the rightmost non-discarded element to the left of the one you're on.
 * Repeat the previous two steps until you've gone through all the non-discarded elements of the sequence.