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