Certification Problem

Input (COPS 266)

The rewrite relation of the following conditional TRS is considered.

App(App(App(S,a),b),c) → App(App(a,c),App(b,c)) | a ≈ I, b ≈ I, c ≈ I
App(App(K,a),b) → a | a ≈ I, b ≈ I
App(I,a) → a | a ≈ I

Property / Task

Prove or disprove confluence.

Answer / Result

Yes.

Proof (by ConCon @ CoCo 2020)

1 Almost-orthogonal

The given (extended) properly oriented, right-stable, oriented 3-CTRS is almost-orthogonal, since there are no conditional critical pairs.