Conjectura
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Convergent relation

Conjectura.Defs.ComputerScience.Rewriting.Convergent

/-
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 Conjectura.Defs.ComputerScience.Rewriting.Confluent
import Conjectura.Defs.ComputerScience.Rewriting.Terminating

/-! # Convergent relation

## 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 **convergent** when it is both `Confluent` and `Terminating`. Convergent
rewriting systems decide their own equational theory: rewrite to normal form and compare. -/
def Convergent {α : Type*} (r : α → α → Prop) : Prop :=
  Confluent r ∧ Terminating r

end Conjectura.Rewriting