NO
Non-Confluence Proof
Non-Confluence Proof
by Hakusan
Input
The rewrite relation of the following TRS is considered.
| c |
→ |
f(f(c)) |
|
h(h(h(b,b),f(f(a))),f(f(f(a)))) |
→ |
a |
| b |
→ |
h(h(f(a),c),f(a)) |
Proof
1 Non-Joinable Fork
The system is not confluent due to the following forking derivations.
| t0
|
= |
h(h(h(b,b),f(f(a))),f(f(f(a)))) |
|
→1.1.1
|
h(h(h(h(h(f(a),c),f(a)),b),f(f(a))),f(f(f(a)))) |
|
= |
t1
|
| t0
|
= |
h(h(h(b,b),f(f(a))),f(f(f(a)))) |
|
→ε
|
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