Certification Problem

Input (COPS 796)

The rewrite relation of the following conditional TRS is considered.

a → b
f(a) → b
g(x) → g(a) | f(x) ≈ x

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.
f(a) →* f(b)
f(a) →* b
The two resulting terms cannot be joined for the following reason: