NO
Non-Confluence Proof
Non-Confluence Proof
by Hakusan
Input
The rewrite relation of the following TRS is considered.
|
br(0,y,z) |
→ |
y |
|
br(s(x),y,z) |
→ |
z |
|
p(0) |
→ |
0 |
|
p(s(x)) |
→ |
x |
|
+(x,y) |
→ |
br(x,y,+(p(x),s(y))) |
|
+(x,y) |
→ |
br(y,x,+(s(x),p(y))) |
Proof
1 Non-Joinable Fork
The system is not confluent due to the following forking derivations.
| t0
|
= |
+(y1,y2) |
|
→ε
|
br(y2,y1,+(s(y1),p(y2))) |
|
= |
t1
|
| t0
|
= |
+(y1,y2) |
|
→ε
|
br(y1,y2,+(p(y1),s(y2))) |
|
= |
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