Certification Problem

Input (COPS 1127)

We consider the TRS containing the following rules:

-(0,x) → 0 (1)
-(x,0) → x (2)
-(s(x),s(y)) → -(x,y) (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 2020)

1 Redundant Rules Transformation

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

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

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

1.1 Critical Pair Closing System

Confluence is proven using the following terminating critical-pair-closing-system R:

There are no rules.

1.1.1 R is empty

There are no rules in the TRS. Hence, it is terminating.