Certification Problem
Input (COPS 734)
We consider the TRS containing the following rules:
|
f(a,f(a,x)) |
→ |
f(f(a,a),a) |
(1) |
The underlying signature is as follows:
{f/2, a/0}Property / Task
Prove or disprove confluence.Answer / Result
No.Proof (by csi @ CoCo 2021)
1 Non-Joinable Fork
The system is not confluent due to the following forking derivations.
| t0
|
= |
f(a,f(a,f(a,x5))) |
|
→
|
f(a,f(f(a,a),a)) |
|
= |
t1
|
| t0
|
= |
f(a,f(a,f(a,x5))) |
|
→
|
f(f(a,a),a) |
|
= |
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.