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 csi @ CoCo 2022)

1 Strongly closed

Confluence is proven since the TRS is strongly closed. The joins can be performed using 7 step(s).