> I know that you mean a system that transfer money ....

No, cost is used in the fullest abstract meaning of the word here.

Time cost, effort cost, monetary cost, work cost, so long as there is a functional limitation that prevents resource exhaustion that is the point.

If cost can be anything, does Anubis implement such a system then, by using proof-of-work as the cost function?

Sort of. Anubis is frontloading the cost all at once and then amortizing it over a large number of subsequent requests. That detail is what's causing the issue when browsing with additional privacy measures.

That's exactly what Anubis does: https://anubis.techaro.lol/docs/design/why-proof-of-work

Can't see, that page is protected by anubis.