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