Certification Problem

Input (COPS 358)

The rewrite relation of the following conditional TRS is considered.

f(x) → a | x ≈ b
a → b
a → 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 →* b
a →* c
The two resulting terms cannot be joined for the following reason: