Question about fast-growing functions

The sequence that produces Graham?s number is a well-known fast-growing sequence. I want to know how it contrasts with the following: Let F(x) be the function that produces the sequence and have it be defined for natural numbers n?2. F(2)=2?2=4 F(3)=3????3=k F(4)=4?(k)4=j F(5)=5?(j)5... where ?(x) denotes the number of arrows in an expression. Clearly this is similar to the G sequence. In fact, G(1)=F(3). Given that, is G(x)>F(x) for all positive integers? If not, around what size is the input that outputs a larger number in F's sequence given the same input to G's sequence? 

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