Certification Problem

Input (COPS 23)

We consider the TRS containing the following rules:

from(x) → :(x,from(s(x))) (1)
sel(0,:(y,z)) → y (2)
sel(s(x),:(y,z)) → sel(x,z) (3)

The underlying signature is as follows:

{from/1, :/2, s/1, sel/2, 0/0}

Property / Task

Prove or disprove confluence.

Answer / Result

Yes.

Proof (by csi @ CoCo 2022)

1 Critical Pair Closing System

Confluence is proven using the following terminating critical-pair-closing-system R:

There are no rules.

1.1 R is empty

There are no rules in the TRS. Hence, it is terminating.