Apologies, perhaps I could have been more clear. "Rivalry" is a word which here means "treating the other as a rival, as opposed to an associate". That is DC and Marvel have proven in the past that they can work together and work together magnificently with their joint venture: Amalgam Comics. They also showed a certain level of respect for each other by introducing the idea that one company exists in the others' universe in their comic book form. However, in 2019, Amalgam Comics has been stated to have no chance of ever releasing another issue and the idea that Marvel exists in comic form in the DC Universe has not been brought up in some time.