Certification Problem

Input (COPS 739)

We consider the TRS containing the following rules:

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

The underlying signature is as follows:

{a/0, g/1, b/0}

Property / Task

Prove or disprove confluence.

Answer / Result

No.

Proof (by csi @ CoCo 2020)

1 Non-Joinable Fork

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

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

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

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