Certification Problem

Input (COPS 268)

The rewrite relation of the following conditional TRS is considered.

p(q(x)) 0
c c
a(x) b | p(x) ≈ 0

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.