Certification Problem
Input (COPS 1654)
We consider the TRS containing the following rules:
|
f(g(x)) |
→ |
h(x,x) |
(1) |
|
g(a) |
→ |
b |
(2) |
|
f(x) |
→ |
h(x,x) |
(3) |
| b |
→ |
a |
(4) |
|
h(x,y) |
→ |
h(g(x),g(y)) |
(5) |
|
g(x) |
→ |
x |
(6) |
| a |
→ |
b |
(7) |
The underlying signature is as follows:
{f/1, g/1, h/2, a/0, b/0}Property / Task
Prove or disprove confluence.Answer / Result
Yes.Proof (by ACP @ CoCo 2023)
1 Development Closed
Confluence is proven since the TRS is development closed.
The joins can be performed using
1 development
step(s).