Certification Problem

Input (COPS 524)

The rewrite relation of the following conditional TRS is considered.

a → x | f(x) ≈ k
f(b) → k
f(c) → k

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: