Certification Problem
Input (TPDB TRS_Outermost/Strategy_outermost_added_08/PALINDROME_complete_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) |
|
U11(tt) |
→ |
U12(isNeList) |
(5) |
|
U12(tt) |
→ |
tt |
(6) |
|
U21(tt) |
→ |
U22(isList) |
(7) |
|
U22(tt) |
→ |
U23(isList) |
(8) |
|
U23(tt) |
→ |
tt |
(9) |
|
U31(tt) |
→ |
U32(isQid) |
(10) |
|
U32(tt) |
→ |
tt |
(11) |
|
U41(tt) |
→ |
U42(isList) |
(12) |
|
U42(tt) |
→ |
U43(isNeList) |
(13) |
|
U43(tt) |
→ |
tt |
(14) |
|
U51(tt) |
→ |
U52(isNeList) |
(15) |
|
U52(tt) |
→ |
U53(isList) |
(16) |
|
U53(tt) |
→ |
tt |
(17) |
|
U61(tt) |
→ |
U62(isQid) |
(18) |
|
U62(tt) |
→ |
tt |
(19) |
|
U71(tt) |
→ |
U72(isNePal) |
(20) |
|
U72(tt) |
→ |
tt |
(21) |
| isList |
→ |
U11(isPalListKind) |
(22) |
| isList |
→ |
tt |
(23) |
| isList |
→ |
U21(and(isPalListKind)) |
(24) |
| isNeList |
→ |
U31(isPalListKind) |
(25) |
| isNeList |
→ |
U41(and(isPalListKind)) |
(26) |
| isNeList |
→ |
U51(and(isPalListKind)) |
(27) |
| isNePal |
→ |
U61(isPalListKind) |
(28) |
| isNePal |
→ |
and(and(isQid)) |
(29) |
| isPal |
→ |
U71(isPalListKind) |
(30) |
| isPal |
→ |
tt |
(31) |
| isPalListKind |
→ |
tt |
(32) |
| isPalListKind |
→ |
and(isPalListKind) |
(33) |
| isQid |
→ |
tt |
(34) |
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