Certification Problem
Input (COPS 63)
We consider the TRS containing the following rules:
|
-(0,0) |
→ |
0 |
(1) |
|
-(s(x),0) |
→ |
s(x) |
(2) |
|
-(x,s(y)) |
→ |
-(d(x),y) |
(3) |
|
d(s(x)) |
→ |
x |
(4) |
|
-(s(x),s(y)) |
→ |
-(x,y) |
(5) |
|
-(d(x),y) |
→ |
-(x,s(y)) |
(6) |
The underlying signature is as follows:
{-/2, 0/0, s/1, d/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).