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Is there an example of an algorithm whose time complexity is strictly larger than Ackermann's function?

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$A(n,n)$ is computable. So a trivial algorithm with complexity $O(A(n,n)^2)$ is the following:

  1. Compute $x = A(n,n)$.
  2. Loop $x^2$ times, doing nothing.
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    $\begingroup$ A(n+1, n+1) has a hugely higher time complexity. $\endgroup$ – gnasher729 Nov 25 '20 at 14:01

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