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