Consider the Quicksort algorithm. Suppose there is a procedure for finding a pivot element which splits the list into two sublists each of which contains at least onefifth of the elements. Let $T(n)$ be the number of comparisons required to sort $n$ elements. Then

$T(n) \leq 2T(n/5) + n$

$T(n) \leq T(n/5) + T(4n/5) + n$

$T(n) \leq 2T(4n/5) + n$

$T(n) \leq 2T(n/2) + n$