Certification Problem

Input (COPS 1116)

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

h(f'(f'(f'(h(c,h(b,c))))),h(f'(f'(b)),b)) f'(h(b,f'(a))) (1)
f'(c) b (2)

and S contains the following rules:

a b (3)
f(x,a) b (4)
f(b,b) b (5)

The underlying signature is as follows:

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