Hang when resolving complex type alias constraints

The bug is found by a fuzzer.
I tried this code:

trait PrivateSquareRoot {}
pub trait Mul<Rhs = Self> {
    type Output: Mul;
}
pub trait IsGreaterOrEqual<Rhs> {
    type Output;
}
pub type Square<A: PrivateSquareRoot> = <A as Mul>::Output;
pub type GrEq<A, B> = <A as IsGreaterOrEqual<B>>::Output;
impl<A, B: PrivateSquareRoot> IsGreaterOrEqual<B> for A {
    type Output = ();
}
impl<U> PrivateSquareRoot for U
where
    U: Mul,
    Square<U>: Mul,
    GrEq<Self, Square<Square<U>>>: Sized,
    U: PrivateSquareRoot,
{}
fn main() {}

The compiler behavior differs depending on the release channel and trait solver used:

The compiler hangs. Fixed by next solver.

Meta

rustc --version --verbose:

rustc 1.94.0-nightly (f57eac1bf 2026-01-10)
binary: rustc
commit-hash: f57eac1bf98cb5d578e3364b64365ec398c137df
commit-date: 2026-01-10
host: x86_64-unknown-linux-gnu
release: 1.94.0-nightly
LLVM version: 21.1.8

 The compiler hangs;

Start with the Rust reproducer in the issue and compare compilation with the default solver against nightly with -Znext-solver=globally. Trace the trait-solver handling of the nested type aliases and constraints; done means the default solver no longer hangs and produces a terminating result consistent with the next solver.