Certification Problem

Input (COPS 377)

The rewrite relation of the following conditional TRS is considered.

a c
a d
b c
b d
g(x,x) h(x,x)
f(x) x | xc

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 * c
a * d
The two resulting terms cannot be joined for the following reason: