Certification Problem

Input (COPS 95)

We consider the TRS containing the following rules:

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

The underlying signature is as follows:

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

Property / Task

Prove or disprove confluence.

Answer / Result

No.

Proof (by ACP @ CoCo 2021)

1 Non-Joinable Fork

The system is not confluent due to the following forking derivations.

t0 = W(B(c_1))
I(B(c_1))
= t1

t0 = W(B(c_1))
I(c_1)
= t1

The two resulting terms cannot be joined for the following reason: