you don't need recursion, you just need a closed loop.
Police A and Police B who police each other besides the ordinary citizens. Add incentives so that they look extra closely at the other side.
Police A and Police B who police each other besides the ordinary citizens. Add incentives so that they look extra closely at the other side.
The alternative is two sides fighting a war of escalation which would likely encourage scary corrupt behavior. "Those guys busted Johnny for some minor offense, so lets go get some dirt on one of their guys, or plant it. Can't let them think they can just mess with us"
This is going by the current us vs them mentality of the police forces.
If that is so, then at least if both "us" and "them" are heavily armed cops with warrior mentalities, they'd focus less of their aggression on the general public.
/s