Certification Problem
Input (COPS 1132)
We consider the TRS containing the following rules:
|
b(x) |
→ |
c(d(x)) |
(1) |
|
d(x) |
→ |
c(b(x)) |
(2) |
|
c(x) |
→ |
b(d(x)) |
(3) |
|
b(x) |
→ |
c(d(x)) |
(1) |
|
a(x) |
→ |
a(b(x)) |
(4) |
|
a(x) |
→ |
b(c(x)) |
(5) |
The underlying signature is as follows:
{b/1, c/1, d/1, a/1}Property / Task
Prove or disprove confluence.Answer / Result
No.Proof (by ACP @ CoCo 2023)
1 Non-Joinable Fork
The system is not confluent due to the following forking derivations.
| t0
|
= |
a(c_1) |
|
→
|
a(b(c_1)) |
|
→
|
b(c(b(c_1))) |
|
= |
t2
|
| t0
|
= |
a(c_1) |
|
→
|
b(c(c_1)) |
|
= |
t1
|
The two resulting terms cannot be joined for the following reason: