Certification Problem

Input (COPS 1103)

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

c → f'(b) (1)
c → b (2)

and S contains the following rules:

a → f(a,b) (3)
f(a,b) → f(b,a) (4)

The underlying signature is as follows:

{a/0, b/0, c/0, f/2, f'/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).