User blog comment:Alemagno12/Proof of termination of Pair Sequence System (BM2)/@comment-30754445-20180709030305/@comment-25601061-20180709035046

So the bad root of (0,0)(1,1)(0,0)(1,0) is the second (0,0).
 * (0,0)(1,1)(0,0)(1,0)
 * (0,0)(1,1)(0,0)(1,0)
 * 0 < 1, so we keep the node.
 * (0,0)(1,1)(0,0)(1,0)
 * 1 > 0, so we delete the node.
 * (0,0)(0,0)(1,0)
 * (0,0)(0,0)(1,0)
 * 0 = 0, so we keep the node.
 * Final sequence: (0,0)(0,0)(1,0)
 * Bad root: (0,0)(0,0)(1,0)