'Cooperate' or 'Cooperate with each other'?

I would like to know if it is necessary to add "with each other" after the word "Cooperate’. Grammarly suggests that ‘with each other’ be removed because it is tautologous. However, I am not so sure because in some websites I see ‘with each other’ added.

So which one is better?

Different parts cooperate with each other.

OR

Different parts cooperate.