NO
Non-Confluence Proof
Non-Confluence Proof
by Hakusan
Input
The rewrite relation of the following TRS is considered.
|
f(h(a,c)) |
→ |
h(f(b),h(c,h(c,h(f(h(b,b)),a)))) |
|
h(h(h(f(b),c),b),h(a,h(a,c))) |
→ |
h(f(b),h(c,b)) |
| a |
→ |
h(h(b,b),b) |
| c |
→ |
a |
Proof
1 Non-Joinable Fork
The system is not confluent due to the following forking derivations.
| t0
|
= |
f(h(a,c)) |
|
→1.1
|
f(h(h(h(b,b),b),c)) |
|
= |
t1
|
| t0
|
= |
f(h(a,c)) |
|
→ε
|
h(f(b),h(c,h(c,h(f(h(b,b)),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