Certification Problem
Input (COPS 1649)
We consider the TRS containing the following rules:
|
f(g(x)) |
→ |
g(f(f(x))) |
(1) |
|
f(h(x)) |
→ |
h(h(f(x))) |
(2) |
|
f(x) |
→ |
x |
(3) |
|
g(x) |
→ |
x |
(4) |
The underlying signature is as follows:
{f/1, g/1, h/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
|
= |
f(h(x26)) |
|
→
|
h(h(f(x26))) |
|
= |
t1
|
| t0
|
= |
f(h(x26)) |
|
→
|
h(x26) |
|
= |
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.