Certification Problem

Input (COPS 799)

The rewrite relation of the following conditional TRS is considered.

g(a) c(b)
b f(a)
f(x) x | g(x) ≈ c(y)

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.