Certification Problem
Input (TPDB TRS_Outermost/Strategy_outermost_added_08/Ex7_BLR02)
The rewrite relation of the following TRS is considered.
|
from(X) |
→ |
cons(X,from(s(X))) |
(1) |
|
head(cons(X,XS)) |
→ |
X |
(2) |
|
2nd(cons(X,XS)) |
→ |
head(XS) |
(3) |
|
take(0,XS) |
→ |
nil |
(4) |
|
take(s(N),cons(X,XS)) |
→ |
cons(X,take(N,XS)) |
(5) |
|
sel(0,cons(X,XS)) |
→ |
X |
(6) |
|
sel(s(N),cons(X,XS)) |
→ |
sel(N,XS) |
(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
|
= |
from(X) |
|
→
|
cons(X,from(s(X))) |
|
= |
t1
|
where t1 =
C[t0σ]
and
σ =
{X/s(X)}
and
C = cons(X,☐)