Certification Problem

Input (COPS 368)

The rewrite relation of the following conditional TRS is considered.

a → c
a → d
f(x) → x | x ≈ c

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: