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A computer program computes a function $\: f \: \{0, 1\}^* \times \{0, 1\}^* \rightarrow \{0, 1\}^*$. Suppose $f(a, b)$ ahs length $\mid b \mid ^2$, where $\mid a \mid$ and $\mid b \mid$ are the lengths of $a$ and $b$. Suppose, using this program, the following computation is performed.

x="01"
for i=1, ... , n do
x=f("01", x)