What would happen if Jhin and Jinx got into some kind of psychotic rivalry?

Before starting the discussion, I want to go over some points about each character.

Jinx She's crazy, unpredictable and smart enough to constantly evade Caitlyn, Vi and maybe Camille along with the entire Piltover police force. This is even more impressive considering everyone in Piltover and Zaun knows what she looks like... and she's never been caught. Also, keep in mind that despite her chaotic nature, she is perfectly capable of making plans and falling through with them; although it is implied that this doesn't always happen.

She's pretty fit and a lot more durable than she looks considering she runs around with a rocket launcher and minigun on a regular basis and was able to survive an entire building coming down on top of her.

She has a lot of firepower. Pow Pow may not be all that powerful per bullet, but it doesn't have to be. It fires really, really fast, thus allowing it to shred things (especially people) with ease. Fishbones is obviously powerful given that its a rocket launcher. Zap can immobilize and maybe even kill people if hit enough times or in the right spot. Her Flame Chompers appear to have the power of your average grenade while possessing the capability to latch onto those she throws them at. Her weapons likely aren't the most advanced, but they do their job, and they do it well. Jinx likely has stockpiles of ammo hidden away as she will likely need it for the kind of work she does.

Jhin He's a different kind of crazy. Smart, meticulous and artistically strategic, he killed for years without anyone knowing his identity. It was only when three of the best ninjas of Iona came looking for him that he got caught.

Physically, Jhin has been shown to be able to put up with fighting those three ninjas, so he's obviously fairly capable. However, this may have its limits as he's generally the type to strike and watch from the shadows, rather than get into a fight or actively flee on a regular basis.

When it comes to firepower, Jhin's got plenty. Whisper is a hextech pistol that packs more of a magical punch than other hextech weaponry, while the same can be said for his sniper rifle (not sure what its name is, or if it even has one). The downside to these weapons, is they are only capable of holding four shots. His mines are equally as powerful as his guns and appear to immobilize their targets. Jhin may have a decent supply of ammo, but keep in mind he only ever chooses four targets and therefore doesn't generally need a whole lot.

Now discuss.

EDIT: I feel like I should clarify what I mean by rivalry, which is a scenario where Jhin is trying to kill Jinx who is aware of this and actively ressisting.