Certification Problem

Input (COPS 1072)

We consider two TRSs R and S where R contains the rules

+(x,y) +(y,x) (1)

and S contains the following rules:

-(+(x,y)) +(-(x),-(y)) (2)
+(-(x),-(y)) -(+(x,y)) (3)

The underlying signature is as follows:

{+/2, -/1}

Property / Task

Prove or disprove commutation.

Answer / Result

Yes.

Proof (by ACP @ CoCo 2023)

1 Development Closed

Commutation is proven since the TRSs are development closed. The joins can be performed using 5 step(s).