Certification Problem

Input (COPS 214)

We consider the TRS containing the following rules:

a b (1)
a f(a) (2)
b f(f(b)) (3)
f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) b (4)

The underlying signature is as follows:

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

Property / Task

Prove or disprove confluence.

Answer / Result

No.

Proof (by csi @ CoCo 2023)

1 Non-Joinable Fork

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

t0 = a
b
= t1

t0 = a
f(a)
f(b)
= t2

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