The power tower of order k is defined as a↑↑k congruent a^(a^(·^(·^(·^a)))) _︸_k, where ↑ is Knuth up-arrow notation, which in turn is defined by a↑^n k = a↑^(n - 1)[a↑^n(k - 1)] together with a↑k | = | a^k a↑^n 1 | = | a.
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