Certification Problem

Input (COPS 224)

We consider the TRS containing the following rules:

-(+(x,-(x))) → 0 (1)
+(x,-(x)) → 0 (2)
0 → -(0) (3)

The underlying signature is as follows:

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

Property / Task

Prove or disprove confluence.

Answer / Result

Yes.

Proof (by csi @ CoCo 2023)

1 Redundant Rules Transformation

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

0 → -(0) (3)
+(x,-(x)) → 0 (2)
-(+(x,-(x))) → 0 (1)
0 → -(-(0)) (4)
+(x,-(x)) → -(0) (5)
-(+(x,-(x))) → -(0) (6)

All redundant rules that were added or removed can be simulated in 2 steps .

1.1 Strongly closed

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