Problem 1: The Mysterious Function We have come through an old interesting function whose pseudo-code was defined as follows: Algorithm 1 Mysterious-Function(n) Require: n ∈ Z ∧ n ≤ 222 if n ≥ 222 then return n − 14 else return Mysterious-Function(Mysterious-Function(n + 15)) end if a) Implement the algorithm in Python b) Try various inputs, within the valid range n ≤ 222, what have you noticed of the output? c) Prove your thoughts, hypothesis, in part (b) [Hint: use your implementation to prove a property of the output at a particular input along with inductive scheme] d) Empirically, show the performance curve of the algorithm using time measurements

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