User blog:Alemagno12/Proof of termination of Pair Sequence System (BM2)

Definition
There are three cases.

Case 1: [x] = x.

Case 2:  # (0,0)[x] = #[x2] (# is the rest of the sequence).

Case 3: Otherwise...

(1) Find the bad root.
Let the rightmost element of the sequence be (x,y). Then, do the following process:
 * Start at the rightmost element.
 * Move to the element inmediately before the one you're on. Let this node be (a,b).
 * If a ≥ x, [WIP]