User blog comment:GamesFan2000/Alternate Ackermann Function/@comment-35470197-20181226035430

Roughly speaking, \(A(x,y)\) is bounded by \(f_{1+x}^2(\max \{x,y\} + 2)\), and hence the limit \(A(n,n)\) is bounded by \(f_{1+\omega}^2(n+2)\), if I am correct.