Termination

Conjectura.Defs.ComputerScience.Rewriting.Terminating

/-
Copyright (c) 2025 Fabrizio Montesi and Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi, Thomas Waring, Chris Henson
-/

import Mathlib.Order.WellFounded

/-! # Termination

## Source

Adapted for Conjectura from [cslib](https://github.com/leanprover/cslib), `Cslib/Foundations/Relation/Defs.lean`, split into one concept per module. Released by its authors under Apache 2.0.
-/

namespace Conjectura.Rewriting

/-- A relation is **terminating** (strongly normalizing) when it admits no infinite rewrite
sequence — formally, when the reversed relation is well-founded. -/
def Terminating {α : Type*} (r : α → α → Prop) : Prop :=
  WellFounded (fun a b => r b a)

end Conjectura.Rewriting