User blog comment:PsiCubed2/An example that shows why a "table of ordinals" proves nothing/@comment-35470197-20181119220314

Writing a table proves at least a single fact even if the definition of the OCF appearing in the table is not specified: The one who wrote it believes the termination the system below any terms below terms in the table.

It is very informative, because the unwritten analysis in his or her mind (if exists) will turn out to be completely incorrect if a counterexample of the termination is found.