The part of the algorithm that is repeated is called a cycle and the sequence of instructions to be repeated is

called its body.

Exercise $2\mathrm{.}2$: prove that the number of steps of $A_n$ is $4n($formally we write $T(A_n)=4n).$

Exercise $2\mathrm{.}3$: How can we change the algorithm to have $T(A_n^{\text{'}})=4n-1?$