Function with space-depending computation time
By the Space Hierarchy Theorem, for every space-constructible space bound $s&gt;\log(n)$, there is a problem $L \in \mathsf{SPACE}(s)\setminus \mathsf{SPACE}(o(s))$. 

In other words, $L$ can be solved in space $s$, and thus in time $c^{s(n)}$, but not in space $o(s)$, regardless of how much extra time you allow.