Certification Problem

Input (COPS 178)

We consider the TRS containing the following rules:

+(+(x,y),z) → +(x,+(y,z)) (1)
+(x,+(y,z)) → +(+(x,y),z) (2)
+(x,y) → +(y,x) (3)

The underlying signature is as follows:

{+/2}

Property / Task

Prove or disprove confluence.

Answer / Result

Yes.

Proof (by csi @ CoCo 2021)

1 Redundant Rules Transformation

To prove that the TRS is (non-)confluent, we show (non-)confluence of the following modified system:

+(x,+(y,z)) → +(+(x,y),z) (2)
+(x,y) → +(y,x) (3)

All redundant rules that were added or removed can be simulated in 4 steps .

1.1 Strongly closed

Confluence is proven since the TRS is strongly closed. The joins can be performed using 7 step(s).