Certification Problem
Input (COPS 73)
We consider the TRS containing the following rules:
|
f(g(g(x))) |
→ |
a |
(1) |
|
f(g(h(x))) |
→ |
b |
(2) |
|
f(h(g(x))) |
→ |
b |
(3) |
|
f(h(h(x))) |
→ |
c |
(4) |
|
g(x) |
→ |
h(x) |
(5) |
| a |
→ |
b |
(6) |
| b |
→ |
c |
(7) |
The underlying signature is as follows:
{f/1, g/1, a/0, h/1, b/0, c/0}Property / Task
Prove or disprove confluence.Answer / Result
Yes.Proof (by ACP @ CoCo 2020)
1 Strongly closed
Confluence is proven since the TRS is strongly closed.
The joins can be performed using
3
step(s).