Certification Problem
Input (COPS 383)
The rewrite relation of the following conditional TRS is considered.
| a |
→ |
c |
| a |
→ |
d |
| b |
→ |
c |
| b |
→ |
d |
|
f(x) |
→ |
x |
| x ≈ c
|
|
g(x,x) |
→ |
h(x,x) |
|
h(x,f(x)) |
→ |
x |
Property / Task
Prove or disprove confluence.Answer / Result
No.Proof (by ConCon @ CoCo 2020)
1 Non-Joinable Fork
The system is not confluent due to the following forking derivations.
The two resulting terms cannot be joined for the following reason:
- The terms are distinct normal forms.