While doing global sequence alignment, Is it a fact that the right-down corner of the matrix will ALWAYS have the highest value? Is it possible for another cell of the matrix to have higher value than the last one?

I know it presents the score and the Needleman-Wunsch algorithm behind it
F(i,j) = max { F(i-1,j-1) + s(xi,yj) , F(i-1,j) -d , F(i,j-1) - d . }

but that only doesn't seem clear to me if the score cell traceback is always the highest one.

If you were to write this question in a reasonable way, such that the average interested biologist knew what you were describing, it might trigger you to think about it more clearly, and the answer might present itself. It would be enlightening for you, as well as anyone who stumbled upon it. As is, your words are like an esoteric non-sequitur which means almost nothing to most people. Yet, could be interesting and informative.

When using the Needleman-Wunsch algorithm to align two sequences, the right-down cell in the matrix may not have the highest value compared to all the other cells in the matrix. However, the value in this cell represents the overall alignment score between the two sequences. The traceback step always starts from this bottom-down cell. On the other hand, in the Smith-Waterman algorithm, which is a local alignment algorithm, traceback starts from the cell with the highest score, which may not be the bottom-right corner cell and can be anywhere in the matrix.

If you were to write this question in a reasonable way, such that the average interested biologist knew what you were describing, it might trigger you to think about it more clearly, and the answer might present itself. It would be enlightening for you, as well as anyone who stumbled upon it. As is, your words are like an esoteric non-sequitur which means almost nothing to most people. Yet, could be interesting and informative.

I tried to write it in a more reasonable way. Thank you.