Certification Problem

Input (COPS 1090)

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

b c (1)
b f(c) (2)
c c (3)

and S contains the following rules:

b f(b) (4)
f(a) f(h(h(h(h(c,b),a),f(c)),c)) (5)
c h(f(c),f(h(c,a))) (6)
c f(b) (7)

The underlying signature is as follows:

{a/0, b/0, c/0, f/1, h/2}

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).