Certification Problem

Input (COPS 390)

The rewrite relation of the following conditional TRS is considered.

f(x) → g(y) | x ≈ y

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.
f(x) → g(x)

1.1 Almost-orthogonal

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