Certification Problem

Input (COPS 5)

We consider the TRS containing the following rules:

f(g(x,a,b)) x (1)
p(a) c (2)
g(f(h(c,d)),x,y) h(p(x),q(x)) (3)
q(b) d (4)

The underlying signature is as follows:

{f/1, g/3, a/0, b/0, p/1, c/0, h/2, d/0, q/1}

Property / Task

Prove or disprove confluence.

Answer / Result

No.

Proof (by csi @ CoCo 2021)

1 Non-Joinable Fork

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

t0 = f(g(f(h(c,d)),a,b))
f(h(p(a),q(a)))
= t1

t0 = f(g(f(h(c,d)),a,b))
f(h(c,d))
= t1

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