I have two problems, one of which is solved using dynamic programming. I showed that it is NP-complete (a knapsack variant), therefore having this dynamic programming solution says that this one is weakly NP-complete. Right?
Then, in the second problem I have added a new dimension to the problem which makes is more complicated. It is still NP-complete and I assume that this one is strongly NP-complete.
Is there a way to prove that it is 'strongly' NP-complete?
I can show that the second problem needs to solve $2^n$ instances of the first problem, where $n$ is the size of problem.