Our overall approach should be to consider each possible substring of $S$, check whether or not it's redundant, assemble a list of distinct substrings which are, and output the number of substrings in this list at the end.

We can do so by iterating over all pairs of indices $(i,j)$, such that $1\le i<j\le |S|$. Each such pair corresponds to the substring $S_{i\dots j}$, with a length of $L=j-i+1$. We can then consider each index $k$ between $i+1$ and $j$ (inclusive), and check if the substring $S_{k\dots (k+L-1)}$ is equal to $S_{i\dots j}$ (note that $k$ should also be capped at $|S|-L+1$ to avoid considering substrings which would go past the end of $S$). If such an index $k$ is found, then a pair of overlapping equal substrings has also been found, meaning that $S_{i\dots j}$ must be redundant.

What remains is maintaining the list of distinct redundant substrings, and being able to add $S_{i\dots j}$ to it if not already present. One option is to maintain this list as an array, and loop over all of its existing entries to check if $S_{i\dots j}$ is equal to any of them. A more elegant option is to use a built-in data structure such as a C++ set, which will automatically ensure that its entries are all distinct.

The time complexity of the solution described above is $\mathcal{O}(N^4)$, which is comfortably fast enough, though it's also possible to optimize it to $\mathcal{O}(N^3)$.