Certification Problem
Input (COPS 88)
We consider the TRS containing the following rules:
|
p(x) |
→ |
q(x) |
(1) |
|
p(x) |
→ |
r(x) |
(2) |
|
q(x) |
→ |
s(p(x)) |
(3) |
|
r(x) |
→ |
s(p(x)) |
(4) |
|
s(x) |
→ |
f(p(x)) |
(5) |
The underlying signature is as follows:
{p/1, q/1, r/1, s/1, f/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
2
step(s).