Certification Problem
Input (COPS 712)
We consider the TRS containing the following rules:
| c |
→ |
a |
(1) |
|
f(c) |
→ |
f(h(b,c)) |
(2) |
| a |
→ |
c |
(3) |
| c |
→ |
h(f(c),h(b,h(h(b,c),a))) |
(4) |
| c |
→ |
b |
(5) |
The underlying signature is as follows:
{c/0, a/0, f/1, h/2, b/0}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
|
= |
c |
|
→
|
h(f(c),h(b,h(h(b,c),a))) |
|
= |
t1
|
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.