Why did you spend it as you did, then? You cannot answer, ever, without your answer invoking something on the boundary.
It seems like if the O(N^(n-1)) algorithm (algorithm 2) is better than the O(N^n) algorithm (algorithm 1), then there is an amount of time, such that, after that time has elapsed (after adapting the new algorithm), the reduction in resource consumption will equal the cost spent finding the new algorithm. This might be called “breaking even”, and doesn’t seem to invoke something on the boundary.
It seems like if the O(N^(n-1)) algorithm (algorithm 2) is better than the O(N^n) algorithm (algorithm 1), then there is an amount of time, such that, after that time has elapsed (after adapting the new algorithm), the reduction in resource consumption will equal the cost spent finding the new algorithm. This might be called “breaking even”, and doesn’t seem to invoke something on the boundary.