Certification Problem

Input (COPS 357)

The rewrite relation of the following conditional TRS is considered.

a c
a d
b c
b d
c e
c l
d m
k l
k m
h(x,x) g(x,x,f(k))
g(d,x,x) A
A h(f(a),f(b))
f(x) x | xe

Property / Task

Prove or disprove confluence.

Answer / Result

No.

Proof (by ConCon @ CoCo 2020)

1 Non-Joinable Fork

The system is not confluent due to the following forking derivations.
a * e
a * l
The two resulting terms cannot be joined for the following reason: