Certification Problem
Input (TPDB TRS_Outermost/Strategy_outermost_added_08/Ex15_Luc98)
The rewrite relation of the following TRS is considered.
|
and(true,X) |
→ |
X |
(1) |
|
and(false,Y) |
→ |
false |
(2) |
|
if(true,X,Y) |
→ |
X |
(3) |
|
if(false,X,Y) |
→ |
Y |
(4) |
|
add(0,X) |
→ |
X |
(5) |
|
add(s(X),Y) |
→ |
s(add(X,Y)) |
(6) |
|
first(0,X) |
→ |
nil |
(7) |
|
first(s(X),cons(Y,Z)) |
→ |
cons(Y,first(X,Z)) |
(8) |
|
from(X) |
→ |
cons(X,from(s(X))) |
(9) |
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,☐)