Problem Statement

Create a function,   or show a built-in function,   to count the number of non-overlapping occurrences of a substring inside a string. The function should take two arguments:

It should return an integer count. The matching should yield the highest number of non-overlapping matches. In general, this essentially means matching from left-to-right or right-to-left   (see proof on talk page).

Let's start with the solution: