Certification Problem

Input (COPS 737)

We consider the TRS containing the following rules:

f(a,f(a,x)) b (1)

The underlying signature is as follows:

{f/2, a/0, 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 = f(a,f(a,f(a,f3)))
f(a,b)
= t1

t0 = f(a,f(a,f(a,f3)))
b
= t1

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