Certification Problem

Input (COPS 945)

We consider the TRS containing the following rules:

a(a(b(b(x)))) → b(b(b(b(b(a(a(a(a(a(x)))))))))) (1)

The underlying signature is as follows:

{a/1, b/1}

Property / Task

Prove or disprove confluence.

Answer / Result

Yes.

Proof (by csi @ CoCo 2023)

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.