Certification Problem

Input (COPS 803)

We consider the TRS containing the following rules:

g(a,y) → y (1)
f(x,a) → f(x,g(x,b)) (2)
g(h(x),y) → g(x,h(y)) (3)

The underlying signature is as follows:

{g/2, a/0, f/2, b/0, h/1}

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.