NO
Non-Confluence Proof
Non-Confluence Proof
by Hakusan
Input
The rewrite relation of the following TRS is considered.
|
+(0,y) |
→ |
y |
|
+(s(x),y) |
→ |
s(+(x,y)) |
|
+(x,+(y,z)) |
→ |
+(+(z,y),x) |
|
s(s(x)) |
→ |
x |
Proof
1 Non-Joinable Fork
The system is not confluent due to the following forking derivations.
| t0
|
= |
+(0,+(x2,x3)) |
|
→ε
|
+(+(x3,x2),0) |
|
= |
t1
|
| t0
|
= |
+(0,+(x2,x3)) |
|
→ε
|
+(x2,x3) |
|
= |
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