Let a binary counter with the operations INCREMENT and DECREMENT.
I need to show that you can't implement this kind of counter with constant amortized time per operation.
Hence, I need to show that there's a series of $N$ operations with amortized time of $\omega(N)$.
Let's assume we made $2^k-1$ INCREMENT operations. Hence, our counter is a sequence with $k$ 1's. Now, Let's consider a sequence of $N$ operations alternating between DECREMENT and INCREMENT (DEC,INC,DEC,INC,DEC...)
Each operation must be $\Theta(k)$. Somehow, I need to figure out that it has to be that the amortize time is $\omega(N)$. How?