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Recursionhard
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Functions PPP and QQQ satisfy the mutually recursive system: P(n)=Q(n−1),Q(n)=P(n−1)+1P(n) = Q(n-1), \quad Q(n) = P(n-1) + 1P(n)=Q(n−1),Q(n)=P(n−1)+1 with base cases P(0)=0P(0) = 0P(0)=0 and Q(0)=0Q(0) = 0Q(0)=0. Compute P(5)P(5)P(5).