Certification Problem
Input (COPS 9)
We consider the TRS containing the following rules:
The underlying signature is as follows:
{f/1, g/1}Property / Task
Prove or disprove confluence.Answer / Result
No.Proof (by csi @ CoCo 2023)
1 Non-Joinable Fork
The system is not confluent due to the following forking derivations.
| t0
|
= |
f(g(f(g(f(x4))))) |
|
→
|
f(g(g(x4))) |
|
= |
t1
|
| t0
|
= |
f(g(f(g(f(x4))))) |
|
→
|
g(g(f(x4))) |
|
= |
t1
|
The two resulting terms cannot be joined for the following reason:
- When applying the cap-function on both terms (where variables may be treated like constants)
then the resulting terms do not unify.