Certification Problem

Input (COPS 92)

We consider the TRS containing the following rules:

W(B(x)) W(x) (1)
B(I(x)) J(x) (2)
W(I(x)) W(J(x)) (3)

The underlying signature is as follows:

{W/1, B/1, I/1, J/1}

Property / Task

Prove or disprove confluence.

Answer / Result

Yes.

Proof (by ACP @ CoCo 2022)

1 Strongly closed

Confluence is proven since the TRS is strongly closed. The joins can be performed using 2 step(s).