Certification Problem

Input (COPS 1044)

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

+(x,0) x (1)
+(x,s(y)) s(+(x,y)) (2)
-(0,x) 0 (3)
-(x,0) x (4)
-(s(x),s(y)) -(x,y) (5)

and S contains the following rules:

+(0,y) y (6)
+(s(x),y) s(+(x,y)) (7)
+(x,0) x (1)
+(x,s(y)) s(+(x,y)) (2)

The underlying signature is as follows:

{+/2, -/2, 0/0, s/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).