Certification Problem
Input (COPS 315)
The rewrite relation of the following conditional TRS is considered.
|
f(x) |
→ |
x |
| x ≈ e
|
|
g(d,x,x) |
→ |
A |
|
h(x,x) |
→ |
g(x,x,f(k)) |
| a |
→ |
c |
| a |
→ |
d |
| b |
→ |
c |
| b |
→ |
d |
| c |
→ |
e |
| c |
→ |
l |
| k |
→ |
l |
| k |
→ |
m |
| d |
→ |
m |
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.