Certification Problem
Input (TPDB TRS_Outermost/Strategy_outermost_added_08/Ex6_Luc98)
The rewrite relation of the following TRS is considered.
|
first(0,X) |
→ |
nil |
(1) |
|
first(s(X),cons(Y,Z)) |
→ |
cons(Y,first(X,Z)) |
(2) |
|
from(X) |
→ |
cons(X,from(s(X))) |
(3) |
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
|
= |
from(X) |
|
→
|
cons(X,from(s(X))) |
|
= |
t1
|
where t1 =
C[t0σ]
and
σ =
{X/s(X)}
and
C = cons(X,☐)