Certification Problem

Input (COPS 548)

The rewrite relation of the following conditional TRS is considered.

g(x) → y | x ≈ y, z ≈ a

Property / Task

Prove or disprove confluence.

Answer / Result

Yes.

Proof (by ConCon @ CoCo 2020)

1 Inlining of Conditions

Inlining of conditions results in the following transformed CTRS having the same multistep rewrite relation.
g(x) → x | z ≈ a

1.1 Almost-orthogonal

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