Certification Problem

Input (COPS 8)

We consider the TRS containing the following rules:

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

The underlying signature is as follows:

{+/2, s/1}

Property / Task

Prove or disprove confluence.

Answer / Result

Yes.

Proof (by ACP @ CoCo 2021)

1 Strongly closed

Confluence is proven since the TRS is strongly closed. The joins can be performed using 3 step(s).