Mutual recursion and `@[specialize]` lead to `(kernel) deep recursion detected`

[TwoFX]

Prerequisites

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• [x] Check that your issue is not already filed: https://github.com/leanprover/lean4/issues
• [x] Reduce the issue to a minimal, self-contained, reproducible test case. Avoid dependencies to Mathlib or Batteries.
• [x] Test your test case against the latest nightly release, for example on https://live.lean-lang.org/#project=lean-nightly (You can also use the settings there to switch to “Lean nightly”)

Description

In the following code, applying the function g leads to the error (kernel) deep recursion detected.

def g (f : Nat → Nat) (n : Nat) : Nat :=
  inner n
where
  @[specialize] inner (n : Nat) : Nat :=
    if n = 0 then 0 else g f (n - 1)

/-- error: (kernel) deep recursion detected -/
#guard_msgs in
def x := g (fun _ => 0) 0

Steps to Reproduce

1. Copy the above code into the Lean web editor

Expected behavior: No error message

Actual behavior: (kernel) deep recursion detected

Versions

4.11.0-nightly-2024-07-10

Impact

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