CMIMC 2016 Computer Science Problem 4

Given a list A, let f(A) = [A[0] + A[1], A[0] - A[1]]. Alef makes two programs to compute f(f(\ldots(f(A)))), where the function is composed n times:

\begin{array}{|l|l|} \hline \textbf{T_{1}(A, n)} & \textbf{T_{2}(A, n)} \\ \hline 1: \ \textbf{FUNCTION } T_{1}(A, n) & 1: \ \textbf{FUNCTION } T_{2}(A, n) \\ 2: \ \quad \textbf{IF } n = 0 & 2: \ \quad \textbf{IF } n = 0 \\ 3: \ \quad \quad \quad \textbf{RETURN } A & 3: \ \quad \quad \quad \textbf{RETURN } A \\ 4: \ \quad \textbf{ELSE} & 4: \ \quad \textbf{ELSE} \\ 5: \ \quad \quad \textbf{RETURN } [T_{1}(A, n - 1)[0] + T_{1}(A, n - 1)[1], & 5: \ \quad \quad B \leftarrow T_{2}(A, n - 1) \\ \quad \quad \quad \quad \quad T_{1}(A, n - 1)[0] - T_{1}(A, n - 1)[1]] & 6: \ \quad \quad \textbf{RETURN } [B[0] + B[1], B[0] - B[1]] \\ \hline \end{array}

Each time T_{1} or T_{2} is called, Alef has to pay one dollar. How much money does he save by calling T_{2}([13, 37], 4) instead of T_{1}([13, 37], 4)?