User blog comment:C7X/CNF Comparison Algorithm/@comment-32213734-20200106184503/@comment-35470197-20200107151317

If you are talking about the second method, the domain of < is T. It is useful to define OT without circular logic, and its restriction to OT is useful to characterise the ordering of ordinals.

For example, consider the relation a < (a,b) in the computation of (a,b)∈OT. In this case, you do not known whether (a,b)∈OT or not before you check a < (a,b). Therefore you actually need to use < on T.