Certification Problem
Input (COPS 158)
We consider the TRS containing the following rules:
|
+(0,y) |
→ |
y |
(1) |
|
+(x,0) |
→ |
x |
(2) |
|
+(s(x),y) |
→ |
s(+(x,y)) |
(3) |
|
+(x,s(y)) |
→ |
s(+(x,y)) |
(4) |
|
+(x,y) |
→ |
+(y,x) |
(5) |
The underlying signature is as follows:
{+/2, 0/0, s/1}Property / Task
Prove or disprove confluence.Answer / Result
Yes.Proof (by ACP @ CoCo 2022)
1 Strongly closed
Confluence is proven since the TRS is strongly closed.
The joins can be performed using
3
step(s).