User blog comment:GamesFan2000/The second part of my attempt at an ordinal notation/@comment-34422464-20190213012140/@comment-37246647-20190213070740

I've just analyzed the second system myself, and I've found that T_1(1) is much stronger than psi(W^W). According to my analysis, it's actually psi(W^^^W), whatever that would be equivalent to.