Degraded performance of auto-invert-solve in OCaml 5.0.0

[MartyO256]

The t/harpoon/nats_and_bools_tps_auto_invert.input test case using the auto-invert-solve tactic takes ~80 seconds to succeed when Harpoon is compiled using OCaml 5.0.0.
That test case is reported to fail with the upgraded OCaml compiler because the TEST.sh script has a 10 seconds time limit for each test case.

With OCaml 4.14.1, that same test case succeeds in ~0.07 seconds. This seems to suggest that some optimizations done during the compilation of the Logic module with OCaml 4.14.1 are not performed in OCaml 5.0.0.

Load the signature t/harpoon/nats_and_bools_tps_auto_invert.input in Harpoon and input the commands in t/harpoon/nats_and_bools_tps_auto_invert.input.
The degraded performance happens specifically when inputting auto-invert-solve in the following Harpoon states:

Theorem: tps
intros <- split x (case e_if_then_else)
Meta-context:
  M1 : ( |- term)
  M3 : ( |- term)
  M4 : ( |- term)
  M2 : ( |- term)
  A : ( |- tp)
  S : ( |- step M1 M2)
Computational context:
  x : [ |- step (if_then_else M1 M3 M4) (if_then_else M2 M3 M4)]
  x1 : [ |- hastype (if_then_else M1 M3 M4) A]
       
--------------------------------------------------------------------------------
[ |- hastype (if_then_else M2 M3 M4) A]

Theorem: tps
intros <- split x (case e_if_false)
Meta-context:
  M1 : ( |- term)
  N : ( |- term)
  A : ( |- tp)
Computational context:
  x : [ |- step (if_then_else false M1 N) N]
  x1 : [ |- hastype (if_then_else false M1 N) A]
       
--------------------------------------------------------------------------------
[ |- hastype N A]

Theorem: tps
intros <- split x (case e_if_true)
Meta-context:
  N : ( |- term)
  M2 : ( |- term)
  A : ( |- tp)
Computational context:
  x : [ |- step (if_then_else true N M2) N]
  x1 : [ |- hastype (if_then_else true N M2) A]
       
--------------------------------------------------------------------------------
[ |- hastype N A]

[MartyO256]

During the latest attempt at publishing Beluga on the opam repository, some Linux distributions also failed this test case with OCaml 4.14.

What I think is happening here is that different environments and later versions of OCaml yield more memory-optimized compiled code.
This means that a stack overflow exception is not being raised soon enough during the proof search, so the test case times out.

Stepping through the evaluation of the test case reveals that we run into a near infinite loop that repeatedly calls the following function.

https:/Beluga-lang/Beluga/blob/e7ec039aec6607fde0acbc1dae5abbaa2ab4dda3/src/core/whnf.ml#L868C16-L871