As was indicated, Lemma 2 is false. Here is a counterexample to lemma 2. Note that it is not a counterexample to the conjecture, since it has two sinks.

## Counterexample for the proof

As was indicated, Lemma 2 is false. Here is a counterexample to lemma 2. Note that it is not a counterexample to the conjecture, since it has two sinks.