Consider a list such as: $[1,2,4,1,6,8,2,3,5,4,9]$

We wish to identify the sum of the numbers in the contiguous subsequence of the list that is in non$-$decreasing order which produces the maximum sum.

Specifically, the above list has multiple contiguous subsequences that are sorted in ascending order, and for each of them we can get their respective sums. In our case, this gives:

$1,2,4$ which sums to $7$

$1,6,8$ which sums to $15$

$2,3,5$ which sums to $10$

$4,9$ which sums to $13$