With `Relaxed`, no such ordering is induced, so we have a data race.
To be fair, it is very unlikely that this race could lead to real misbehavior, but I am still happy to know that we now have a proof that `Arc` is mostly[^1] correctly synchronized.
-[^1]: "Mostly", you may wonder? Unfortunately it turns out that there is [one `Relaxed` access in `make_mut`](https://github.com/rust-lang/rust/blob/c0955a34bcb17f0b31d7b86522a520ebe7fa93ac/src/liballoc/sync.rs#L793) that Hai and Jacques-Henri have not yet been able to prove correct. However, this is likely fixable by making the entire proof more complicated. The version where that `Relaxed` is also replaced by `Acquire` *has* been proven correct.
+[^1]: "Mostly", you may wonder? Unfortunately it turns out that there is [one `Relaxed` access in `make_mut`](https://github.com/rust-lang/rust/blob/c0955a34bcb17f0b31d7b86522a520ebe7fa93ac/src/liballoc/sync.rs#L793) that Hai and Jacques-Henri have not yet been able to prove correct. However, this is likely fixable by making the entire proof more complicated. The version where that `Relaxed` is also replaced by `Acquire` *has* been proven correct, albeit still against a model of relaxed memory accesses that is not quite as weak as C11.
One last thing:
I have previously claimed that our [first RustBelt paper]({{ site.baseurl }}{% post_url 2017-07-08-rustbelt %}) already verified correctness of `Arc`, how can there still be bugs?