NO
Non-Confluence Proof
Non-Confluence Proof
by Hakusan
Input
The rewrite relation of the following TRS is considered.
|
F(x) |
→ |
A |
|
F(x) |
→ |
G(F(x)) |
|
G(F(x)) |
→ |
F(H(x)) |
|
G(F(x)) |
→ |
B |
Proof
1 Non-Joinable Fork
The system is not confluent due to the following forking derivations.
| t0
|
= |
G(F(y1)) |
|
→1
|
G(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