Certification Problem

Input (COPS 586)

We consider the TRS containing the following rules:

+(0,y) → y (1)
+(s(0),y) → s(y) (2)
+(s(s(x)),y) → s(s(+(y,x))) (3)

The underlying signature is as follows:

{+/2, 0/0, s/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.