NO
Non-Confluence Proof
Non-Confluence Proof
by Hakusan
Input
The rewrite relation of the following TRS is considered.
|
f(a,f(a,x)) |
→ |
f(f(a,a),a) |
Proof
1 Non-Joinable Fork
The system is not confluent due to the following forking derivations.
| t0
|
= |
f(a,f(a,f(a,x1))) |
|
→2
|
f(a,f(f(a,a),a)) |
|
= |
t1
|
| t0
|
= |
f(a,f(a,f(a,x1))) |
|
→ε
|
f(f(a,a),a) |
|
= |
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