Certification Problem
Input (COPS 74)
We consider the TRS containing the following rules:
| a |
→ |
c |
(1) |
| b |
→ |
c |
(2) |
|
f(a,b) |
→ |
d |
(3) |
|
f(x,c) |
→ |
f(c,c) |
(4) |
|
f(c,x) |
→ |
f(c,c) |
(5) |
| d |
→ |
f(a,c) |
(6) |
| d |
→ |
f(c,b) |
(7) |
The underlying signature is as follows:
{a/0, c/0, b/0, f/2, d/0}Property / Task
Prove or disprove confluence.Answer / Result
Yes.Proof (by ACP @ CoCo 2023)
1 Strongly closed
Confluence is proven since the TRS is strongly closed.
The joins can be performed using
3
step(s).