Certification Problem

Input (COPS 237)

We consider the TRS containing the following rules:

a(x) g(b(x)) (1)
a(x) c(x) (2)
b(x) g(b(x)) (3)

The underlying signature is as follows:

{a/1, g/1, b/1, c/1}

Property / Task

Prove or disprove confluence.

Answer / Result

No.

Proof (by ACP @ CoCo 2022)

1 Non-Joinable Fork

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

t0 = a(c_1)
g(b(c_1))
= t1

t0 = a(c_1)
c(c_1)
= t1

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