Certification Problem
Input (COPS 382)
The rewrite relation of the following conditional TRS is considered.
|
s(a) |
→ |
c |
|
s(b) |
→ |
c |
| c |
→ |
t(k) |
| c |
→ |
t(l) |
|
f(x) |
→ |
z |
| s(x) ≈ z
|
|
g(x,x) |
→ |
h(x,x) |
Property / Task
Prove or disprove confluence.Answer / Result
No.Proof (by ConCon @ CoCo 2020)
1 Inlining of Conditions
Inlining of conditions results in the following transformed CTRS having the
same multistep rewrite relation.
|
s(a) |
→ |
c |
|
s(b) |
→ |
c |
| c |
→ |
t(k) |
| c |
→ |
t(l) |
|
f(x) |
→ |
s(x) |
|
g(x,x) |
→ |
h(x,x) |
1.1 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.