User blog comment:Alemagno12/Proof of termination of Pair Sequence System (BM2)/@comment-30754445-20180709030305

Your "find the bad root" section gives the definition for BM1 rather than BM2.

Example where they are different:

(0,0)(1,1)(2,1)(3,1)(2,0)(1,1)(2,1)(3,1)

The bad root in BM1 and according to your definition here is (2,0)

The bad root in BM2 (according to the online Bashicu Matrix Calculator) is (0,0)