Certification Problem
Input (TPDB TRS_Outermost/Strategy_outermost_added_08/Ex9_Luc06_Z)
The rewrite relation of the following TRS is considered.
|
f(n__a,X,X) |
→ |
f(activate(X),b,n__b) |
(1) |
| b |
→ |
a |
(2) |
| a |
→ |
n__a |
(3) |
| b |
→ |
n__b |
(4) |
|
activate(n__a) |
→ |
a |
(5) |
|
activate(n__b) |
→ |
b |
(6) |
|
activate(X) |
→ |
X |
(7) |
The evaluation strategy is outermostProperty / Task
Prove or disprove termination.Answer / Result
No.Proof (by AProVE @ termCOMP 2023)
1 Loop
The following loop proves nontermination.
| t0
|
= |
f(n__a,n__b,n__b) |
|
→
|
f(activate(n__b),b,n__b) |
|
→
|
f(b,b,n__b) |
|
→
|
f(a,b,n__b) |
|
→
|
f(n__a,b,n__b) |
|
→
|
f(n__a,n__b,n__b) |
|
= |
t5
|
where t5 =
t0