I was going through this page related to dynamic programming. I am a big confused about the complexity given

Here in the third case the complexity is given as $O(n^2)$. I am not sure how it came to be that. Can anyone please elaborate. How the complexities were calculated here.
If i and j are both free to range from 1 to n, I can see n^2 subproblems by thinking about holding i fixed at 1 while ranging j from 1-n. Then do the same for all values of i 1-n. But the picture and set notation seem to imply j > i (a contiguous, unique set) so I think that makes it a bit confusing. I’m imagining i=2, j=1… could it be x2, x3 (interpreting j as the number of x’s we want starting at 2?) or x2, x1 (interpreting j as the index)….