Certification Problem
Input (COPS 39)
We consider the TRS containing the following rules:
|
f(b) |
→ |
a |
(1) |
|
f(b) |
→ |
f(c) |
(2) |
|
f(c) |
→ |
f(b) |
(3) |
|
f(c) |
→ |
d |
(4) |
| b |
→ |
e |
(5) |
| c |
→ |
e' |
(6) |
|
f(e) |
→ |
a |
(7) |
|
f(e') |
→ |
d |
(8) |
The underlying signature is as follows:
{f/1, b/0, a/0, c/0, d/0, e/0, e'/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(b) |
|
→
|
f(c) |
|
→
|
f(e') |
|
→
|
d |
|
= |
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.