Certification Problem

Input (COPS 257)

We consider the TRS containing the following rules:

c f(c,d) (1)
c h(c,d) (2)
f(x,y) h(g(y),x) (3)
h(x,y) f(g(y),x) (4)

The underlying signature is as follows:

{c/0, f/2, d/0, h/2, g/1}

Property / Task

Prove or disprove confluence.

Answer / Result

No.

Proof (by ACP @ CoCo 2023)

1 Non-Joinable Fork

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

t0 = c
h(c,d)
h(f(c,d),d)
= t2

t0 = c
f(c,d)
= t1

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