One of the most used simple examples of application of Communication Complexity is the $\Omega(n^2)$ lower bound for recognizing palindromes of length $2n$ on a single tape Turing machine.
Is there a similarly simple example that
- proves a lower bound of $\Omega(n^3)$ for another problem
- that can be decided in time $O(n^3)$
- on a single tape Turing machine
- using arguments from communication complexity?