NO
Non-Confluence Proof
Non-Confluence Proof
by Hakusan
Input
The rewrite relation of the following TRS is considered.
|
f(g(x)) |
→ |
g(f(f(x))) |
|
f(h(x)) |
→ |
h(h(f(x))) |
|
f(x) |
→ |
x |
|
g(x) |
→ |
x |
Proof
1 Non-Joinable Fork
The system is not confluent due to the following forking derivations.
| t0
|
= |
f(h(y1)) |
|
→ε
|
h(y1) |
|
= |
t1
|
| t0
|
= |
f(h(y1)) |
|
→ε
|
h(h(f(y1))) |
|
= |
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.
Tool configuration
Hakusan