Certification Problem
Input (COPS 262)
The rewrite relation of the following conditional TRS is considered.
|
plus(0,y) |
→ |
y |
|
plus(s(x),y) |
→ |
plus(x,s(y)) |
|
f(x,y) |
→ |
z |
| plus(x,y) ≈ plus(z,z') |
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.
|
f(s(__NN15),__NN16) |
→*
|
s(__NN15) |
|
f(s(__NN15),__NN16) |
→*
|
__NN15 |
The two resulting terms cannot be joined for the following reason:
- The terms are distinct normal forms.