# Algorithm to compute the Kruskal’s Tree function

Im talking about the tree function, the famous function whose value TREE(3) is enormous. I know it is computable. Given that the function definition is rather simple, does there exist an algorithm of non pathological size that computes the function?

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– D.W.
Commented Aug 6 at 18:40

Sure. The definition of the TREE function is "the largest $$m$$ so that... there is a sequence $$T_1,\dots,T_m$$..." So it suffices to build an algorithm to iterate over $$m:=1,2,3,\dots$$, and for each $$m$$, search over all possible combinations $$T_1,\dots,T_m$$ to see if there is any that meets the criteria, stopping at the first $$m$$ where no such combination exists. For any $$m$$, there are only finitely many combinations, so this algorithm is guaranteed to terminate. And it can be implemented fairly concisely.