Certification Problem
Input (COPS 43)
We consider the TRS containing the following rules:
|
F(x) |
→ |
A |
(1) |
|
F(x) |
→ |
G(F(x)) |
(2) |
|
G(F(x)) |
→ |
F(H(x)) |
(3) |
|
G(F(x)) |
→ |
B |
(4) |
The underlying signature is as follows:
{F/1, A/0, G/1, H/1, B/0}Property / Task
Prove or disprove confluence.Answer / Result
No.Proof (by csi @ CoCo 2020)
1 Non-Joinable Fork
The system is not confluent due to the following forking derivations.
| t0
|
= |
F(F(x17)) |
|
→
|
F(A) |
|
→
|
G(F(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.