Certification Problem

Input (COPS 683)

We consider the TRS containing the following rules:

f(h(b,a)) a (1)
f(f(f(c))) c (2)
b c (3)
c c (4)
a a (5)

The underlying signature is as follows:

{f/1, h/2, b/0, a/0, c/0}

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 = f(h(b,a))
f(h(c,a))
= t1

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

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