NO
Non-Confluence Proof
Non-Confluence Proof
by Hakusan
Input
The rewrite relation of the following TRS is considered.
|
s(p(x)) |
→ |
x |
|
p(s(x)) |
→ |
x |
|
+(x,0) |
→ |
x |
|
+(x,s(y)) |
→ |
s(+(x,y)) |
|
+(x,p(y)) |
→ |
p(+(x,y)) |
|
-(x,0) |
→ |
x |
|
-(x,s(y)) |
→ |
p(-(x,y)) |
|
-(x,p(y)) |
→ |
s(-(x,y)) |
|
*(x,0) |
→ |
0 |
|
*(x,s(y)) |
→ |
+(*(x,y),x) |
|
*(x,p(y)) |
→ |
-(*(x,y),x) |
Proof
1 Non-Joinable Fork
The system is not confluent due to the following forking derivations.
| t0
|
= |
*(y1,s(p(x1))) |
|
→2
|
*(y1,x1) |
|
= |
t1
|
| t0
|
= |
*(y1,s(p(x1))) |
|
→ε
|
+(*(y1,p(x1)),y1) |
|
= |
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