Certification Problem
Input (COPS 372)
The rewrite relation of the following conditional TRS is considered.
| a |
→ |
c |
| a |
→ |
d |
| b |
→ |
c |
| b |
→ |
d |
|
s(k) |
→ |
t(a) |
|
s(l) |
→ |
t(a) |
|
g(x,x) |
→ |
h(x,x) |
|
f(x,y) |
→ |
y |
| s(x) ≈ t(y) |
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.