NO
Non-Confluence Proof
Non-Confluence Proof
by Hakusan
Input
The rewrite relation of the following TRS is considered.
| a |
→ |
h(a,f(b)) |
|
f(f(h(a,a))) |
→ |
f(f(f(a))) |
|
f(h(a,h(a,a))) |
→ |
f(a) |
|
f(h(h(b,a),h(f(c),c))) |
→ |
c |
Proof
1 Non-Joinable Fork
The system is not confluent due to the following forking derivations.
| t0
|
= |
f(h(h(b,a),h(f(c),c))) |
|
→1.1.2
|
f(h(h(b,h(a,f(b))),h(f(c),c))) |
|
= |
t1
|
| t0
|
= |
f(h(h(b,a),h(f(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