Certification Problem

Input (COPS 527)

The rewrite relation of the following conditional TRS is considered.

f(cons(x,nil)) pair(x,nil)
f(cons(x,cons(y,l))) pair(z,cons(x,l1)) | f(cons(y,l)) ≈ pair(z,l1)

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.