Certification Problem
Input (COPS 70)
We consider the TRS containing the following rules:
|
F(x,C(x)) |
→ |
A |
(1) |
|
F(x,x) |
→ |
B |
(2) |
| a |
→ |
g(C(a)) |
(3) |
|
g(x) |
→ |
x |
(4) |
The underlying signature is as follows:
{F/2, C/1, A/0, B/0, a/0, 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(a,C(a)) |
|
→
|
F(g(C(a)),C(a)) |
|
→
|
F(C(a),C(a)) |
|
→
|
B |
|
= |
t3
|
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.