Certification Problem

Input (COPS 258)

We consider the TRS containing the following rules:

c f(c) (1)
c h(c) (2)
f(x) f(f(x)) (3)
h(x) h(h(x)) (4)

The underlying signature is as follows:

{c/0, f/1, h/1}

Property / Task

Prove or disprove confluence.

Answer / Result

No.

Proof (by csi @ CoCo 2022)

1 Non-Joinable Fork

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

t0 = c
h(c)
= t1

t0 = c
f(c)
= t1

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