def inplace$\_$quick$\_$sort$($S$,$ a$,$ b$)$:

$"""$Sort the list from S$[$a$]$ to S$[$b$]$ inclusive using the quick$-$sort algorithm."""

if a $>=$ b: return # range is trivially sorted

# $[$snip$]$ partition the array around left

# make recursive calls

inplace$\_$quick$\_$sort$($S$,$ a$,$ left $-1)$

inplace$\_$quick$\_$sort$($S$,$ left $+1,$ b$)$

The recursive calls are ALWAYS smaller than the original, meaning that we will eventually reach the base case and the recursion terminates.