Certification Problem

Input (COPS 411)

The rewrite relation of the following conditional TRS is considered.

f(x,y) g(x) | ad
f(x,y) h(x) | bd
g(s(x)) x
h(s(x)) x
a d
b d
e e

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(__N3,__N4) * g(__N3)
f(__N3,__N4) * h(__N3)
The two resulting terms cannot be joined for the following reason: