Certification Problem
Input (TPDB TRS_Outermost/Strategy_outermost_added_08/PALINDROME_nokinds_L)
The rewrite relation of the following TRS is considered.
|
and(tt) |
→ |
X |
(1) |
|
__(__(X,Y),Z) |
→ |
__(X,__(Y,Z)) |
(2) |
|
__(X,nil) |
→ |
X |
(3) |
|
__(nil,X) |
→ |
X |
(4) |
| isList |
→ |
isNeList |
(5) |
| isList |
→ |
tt |
(6) |
| isList |
→ |
and(isList) |
(7) |
| isNeList |
→ |
isQid |
(8) |
| isNeList |
→ |
and(isList) |
(9) |
| isNeList |
→ |
and(isNeList) |
(10) |
| isNePal |
→ |
isQid |
(11) |
| isNePal |
→ |
and(isQid) |
(12) |
| isPal |
→ |
isNePal |
(13) |
| isPal |
→ |
tt |
(14) |
| isQid |
→ |
tt |
(15) |
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
|
= |
and(tt) |
|
→
|
and(tt) |
|
= |
t1
|
where t1 =
t0