Certification Problem
Input (COPS 363)
The rewrite relation of the following conditional TRS is considered.
|
f(x) |
→ |
y |
| a ≈ h(y) |
|
g(x,b) |
→ |
g(f(c),x) |
| f(b) ≈ x, x ≈ c
|
| a |
→ |
h(b) |
| a |
→ |
h(c) |
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:
- When applying the cap-function on both terms (where variables may be treated like constants)
then the resulting terms do not unify.