Certification Problem
Input (COPS 544)
We consider the TRS containing the following rules:
|
g(x) |
→ |
h(k(x)) |
(1) |
|
g(x) |
→ |
x |
(2) |
|
h(k(x)) |
→ |
f(x) |
(3) |
|
f(x) |
→ |
x |
(4) |
|
k(c) |
→ |
c |
(5) |
|
f(c) |
→ |
g(c) |
(6) |
The underlying signature is as follows:
{g/1, h/1, k/1, f/1, c/0}Property / Task
Prove or disprove confluence.Answer / Result
No.Proof (by csi @ CoCo 2023)
1 Non-Joinable Fork
The system is not confluent due to the following forking derivations.
| t0
|
= |
f(c) |
|
→
|
g(c) |
|
→
|
h(k(c)) |
|
→
|
h(c) |
|
= |
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.