NO
Non-Confluence Proof
Non-Confluence Proof
by Hakusan
Input
The rewrite relation of the following TRS is considered.
| c |
→ |
a |
|
f(c) |
→ |
f(h(b,c)) |
| a |
→ |
c |
| c |
→ |
h(f(c),h(b,h(h(b,c),a))) |
| c |
→ |
b |
Proof
1 Non-Joinable Fork
The system is not confluent due to the following forking derivations.
| t0
|
= |
f(c) |
|
→ε
|
f(h(b,c)) |
|
= |
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