Certification Problem

Input (COPS 325)

The rewrite relation of the following conditional TRS is considered.

f(x) x | xe, xe'
g(d,x,x) A
h(x,x) g(x,x,f(k))
c e'
a c
a d
b c
b d
c e
c l
k l
k m
d m

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.
k * l
k * m
The two resulting terms cannot be joined for the following reason: