Certification Problem
Input (COPS 95)
We consider the TRS containing the following rules:
|
W(B(x)) |
→ |
I(x) |
(1) |
|
B(S(x)) |
→ |
S(x) |
(2) |
|
W(x) |
→ |
I(x) |
(3) |
The underlying signature is as follows:
{W/1, B/1, I/1, S/1}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
|
= |
W(B(W(B(x10)))) |
|
→
|
W(B(I(x10))) |
|
→
|
I(B(I(x10))) |
|
= |
t2
|
| t0
|
= |
W(B(W(B(x10)))) |
|
→
|
I(W(B(x10))) |
|
→
|
I(I(B(x10))) |
|
= |
t2
|
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.