Certification Problem

Input (COPS 653)

We consider the TRS containing the following rules:

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

The underlying signature is as follows:

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

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

t0 = h(a,b)
a
= t1

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