NO
Non-Confluence Proof
Non-Confluence Proof
by Hakusan
Input
The rewrite relation of the following TRS is considered.
|
f(f(x,y),z) |
→ |
f(x,f(y,z)) |
|
f(x,1) |
→ |
x |
Proof
1 Non-Joinable Fork
The system is not confluent due to the following forking derivations.
| t0
|
= |
f(f(y1,1),y3) |
|
→1
|
f(y1,y3) |
|
= |
t1
|
| t0
|
= |
f(f(y1,1),y3) |
|
→ε
|
f(y1,f(1,y3)) |
|
= |
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