Certification Problem
Input (COPS 677)
We consider the TRS containing the following rules:
| b |
→ |
h(b,c) |
(1) |
| c |
→ |
a |
(2) |
| a |
→ |
f(a) |
(3) |
| b |
→ |
c |
(4) |
| b |
→ |
b |
(5) |
The underlying signature is as follows:
{b/0, h/2, c/0, a/0, f/1}Property / Task
Prove or disprove confluence.Answer / Result
No.Proof (by csi @ CoCo 2022)
1 Non-Joinable Fork
The system is not confluent due to the following forking derivations.
| t0
|
= |
b |
|
→
|
h(b,c) |
|
→
|
h(b,c) |
|
→
|
h(b,c) |
|
= |
t3
|
| t0
|
= |
b |
|
→
|
c |
|
→
|
a |
|
→
|
f(a) |
|
= |
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.