User blog comment:Alemagno12/Quick poll/@comment-31966679-20180826025941

If it doesn't diagonalize over "repeating" (repeating in this comment means the transition from f_0(n) to f_1(n), or f_1(n) to f_2(n), etc.), I normally just calculate FGH results by evaluating f_n(x) for n within the range that I think a function F(n) stands at and comparing them to the function F(x).

If it diagonalizes over repeating I evaluate it as f_w(n)

If it repeats after something, then I evaluate it as f_currentgrowthrate + 1(n)

If it diagonalizes over repeating after diagonalizing over repeating I evaluate it as f_w2(n)

If it diagonalizes over repeating after something I evaluate it as f_currentgrowthrate + w(n)

If it diagonalizes over diagonalizing over repeating I evaluate it as f_w ^ 2(n)

And you get the idea