Certification Problem

Input (COPS 579)

We consider the TRS containing the following rules:

+(x,0) → x (1)
+(x,s(y)) → s(+(x,y)) (2)
-(0,x) → 0 (3)
-(x,0) → x (4)
-(s(x),s(y)) → -(x,y) (5)

The underlying signature is as follows:

{+/2, 0/0, s/1, -/2}

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.