User blog comment:BlauesWasser/A function I have created (still unnamed)/@comment-35392788-20180823063358/@comment-35470197-20180823225120

I meant by "limit" an effective upperbound, and hence I did not mean that your system eventually dominates all functions with growth rate smaller than \(f_{\omega+1}\). In order to know that, you need to estimate an lower bound in a similar way.