I tried to watch this last month, as the final film in my 2022-2023 Letterboxd Challenge. I didn't give it a proper review at the time:
I'm afraid I can't do the film justice ... it has a confusing structure and I was on the verge of falling asleep (which is on me, not Elio Petri). So I'll have to give it an incomplete and hope to watch it again sometime when I am awake.
This will be brief. I made it through this time without getting too sleepy. It won the Oscar for Best Foreign Language Film, beating out Tristana, which I much preferred. The structure is still confusing. I'm not prepared to take that confusion totally on myself ... I may not have noticed when I was falling asleep, but Petri knew his film was confusing when he made it. I will accept that I don't always appreciate confusion in movies, and that, at least, is on me. Wikipedia tells me that most of the ending scenes are part of a dream sequence, which is news to me. I guess this is a Your Mileage May Vary movie. I'll finish by quoting Kael:
Elio Petri's indirect way of telling a story - which gradually takes the form of a paranoid fantasy - makes the viewer apprehensive. His purpose is ostensibly political, but sometimes he becomes so sophisticated and nasty and perverse that you don't trust his purposes.... The queasy, tense atmosphere derives not from the horror of the proposition itself but from the kinkiness of the details, such as Ennio Morricone's jangly music when the cop slits the throat of his mistress (Florinda Bolkan). The film is extremely dislikable. Petri is a highly skilled director but he doesn't use suspense pleasurably; he doesn't resolve the tensions, and so you're left in a rather foul mood.