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\end{align}  \end{subequations}  For each time the size of the problem doubles, it takes $$8 $8  = 2^3$$ 2^3$  times longer for Algo1 to complete. For Algo2, it takes $$4 $4  = 2^2$$ 2^2$  times longer, and $$2 $2  = 2^1$$ 2^1$  times longer for Algo1.