Certification Problem

Input (COPS 526)

We consider the TRS containing the following rules:

f(x,x) g (1)
a b (2)
a c (3)
d c (4)
d e (5)
c c (6)
f(a,x) g (7)
f(b,x) g (8)
f(c,x) g (9)
f(d,x) g (10)
f(e,x) g (11)
f(x,a) g (12)
f(x,b) g (13)
f(x,c) g (14)
f(x,d) g (15)
f(x,e) g (16)

The underlying signature is as follows:

{f/2, g/0, a/0, b/0, c/0, d/0, e/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 = d
e
= t1

t0 = d
c
= t1

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