It's more than rivalry. It's more than Ash and Gary from Pokemon.
It's more than Ryu and Ken from Street Fighter.
It's an aggressive clashing of eternal friends in a competition which could nearly destroy the world but because of overusing it, the world is now used to get destroyed everytime so it takes less time to get back to the original form.
Top notch rivalry in brutal ultra deluxe.
Opponent, competitor or such pussy words can't describe the Überness of this new word.
No example. If there are two best friends who really like to beat the shit out of each other, you can call that eternal rivalment. Because they will never learn out of the situation.