Certification Problem

Input (COPS 978)

We consider the TRS containing the following rules:

b(a(a(b(b(x)))))	→	b(a(a(a(a(b(b(x)))))))	(1)
b(a(b(b(x))))	→	b(b(x))	(2)
b(a(b(a(a(a(a(b(x))))))))	→	b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))	(3)
b(a(a(b(a(a(a(a(b(x)))))))))	→	b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x)))))))))))))))	(4)
b(a(a(a(b(a(a(a(a(b(x))))))))))	→	b(x)	(5)

The underlying signature is as follows:

{b/1, a/1}

Property / Task

Prove or disprove confluence.

Answer / Result

Yes.

Proof (by ACP @ CoCo 2023)

1 Strongly closed

Confluence is proven since the TRS is strongly closed. The joins can be performed using 4 step(s).