題組內容

一、The Ackermann function A(x,y) is defined for integer x and y by

\[ A(x, y) = \begin{cases} y+1 & \text{if } x=0 \\ A(x-1, 1) & \text{if } x>0 \text{ and } y=0 \\ A(x-1, A(x, y-1)) & \text{if } x>0 \text{ and } y>0 \end{cases} \]

(b) What is the value of A(2,2)? (10 Points)