Certification Problem

Input (COPS 99)

We consider the TRS containing the following rules:

W(W(x)) → W(x) (1)
B(I(x)) → W(x) (2)
W(B(x)) → B(x) (3)
F(H(x),y) → F(H(x),G(y)) (4)
F(x,I(y)) → F(G(x),I(y)) (5)
G(x) → x (6)

The underlying signature is as follows:

{W/1, B/1, I/1, F/2, H/1, G/1}

Property / Task

Prove or disprove confluence.

Answer / Result

Yes.

Proof (by ACP @ CoCo 2020)

1 Strongly closed

Confluence is proven since the TRS is strongly closed. The joins can be performed using 3 step(s).