Certification Problem
Input (TPDB TRS_Outermost/Strategy_outermost_added_08/LengthOfFiniteLists_nosorts_Z)
The rewrite relation of the following TRS is considered.
| zeros |
→ |
cons(0,n__zeros) |
(1) |
|
and(tt,X) |
→ |
activate(X) |
(2) |
|
length(nil) |
→ |
0 |
(3) |
|
length(cons(N,L)) |
→ |
s(length(activate(L))) |
(4) |
| zeros |
→ |
n__zeros |
(5) |
|
activate(n__zeros) |
→ |
zeros |
(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
|
= |
length(activate(n__zeros)) |
|
→
|
length(zeros) |
|
→
|
length(cons(0,n__zeros)) |
|
→
|
s(length(activate(n__zeros))) |
|
= |
t3
|
where t3 =
C[t0]
and
C = s(☐)