I have to complain to the manager about it.

But how would appeals work in a voluntary system of private law?

In a statist society such as the current United States, if someone doesn't like the ruling of a lower court, he or she can appeal it to a higher court.

In his complaint, he said that when he returned to his office after he was fired, he may not have signed out of his Yahoo account.

There is no other court of appeal.