Certification Problem
Input (TPDB TRS_Standard/Transformed_CSR_04/PALINDROME_complete-noand_L)
The rewrite relation of the following TRS is considered.
|
__(__(X,Y),Z) |
→ |
__(X,__(Y,Z)) |
(1) |
|
__(X,nil) |
→ |
X |
(2) |
|
__(nil,X) |
→ |
X |
(3) |
|
U11(tt) |
→ |
U12(isPalListKind) |
(4) |
|
U12(tt) |
→ |
U13(isNeList) |
(5) |
|
U13(tt) |
→ |
tt |
(6) |
|
U21(tt) |
→ |
U22(isPalListKind) |
(7) |
|
U22(tt) |
→ |
U23(isPalListKind) |
(8) |
|
U23(tt) |
→ |
U24(isPalListKind) |
(9) |
|
U24(tt) |
→ |
U25(isList) |
(10) |
|
U25(tt) |
→ |
U26(isList) |
(11) |
|
U26(tt) |
→ |
tt |
(12) |
|
U31(tt) |
→ |
U32(isPalListKind) |
(13) |
|
U32(tt) |
→ |
U33(isQid) |
(14) |
|
U33(tt) |
→ |
tt |
(15) |
|
U41(tt) |
→ |
U42(isPalListKind) |
(16) |
|
U42(tt) |
→ |
U43(isPalListKind) |
(17) |
|
U43(tt) |
→ |
U44(isPalListKind) |
(18) |
|
U44(tt) |
→ |
U45(isList) |
(19) |
|
U45(tt) |
→ |
U46(isNeList) |
(20) |
|
U46(tt) |
→ |
tt |
(21) |
|
U51(tt) |
→ |
U52(isPalListKind) |
(22) |
|
U52(tt) |
→ |
U53(isPalListKind) |
(23) |
|
U53(tt) |
→ |
U54(isPalListKind) |
(24) |
|
U54(tt) |
→ |
U55(isNeList) |
(25) |
|
U55(tt) |
→ |
U56(isList) |
(26) |
|
U56(tt) |
→ |
tt |
(27) |
|
U61(tt) |
→ |
U62(isPalListKind) |
(28) |
|
U62(tt) |
→ |
U63(isQid) |
(29) |
|
U63(tt) |
→ |
tt |
(30) |
|
U71(tt) |
→ |
U72(isPalListKind) |
(31) |
|
U72(tt) |
→ |
U73(isPal) |
(32) |
|
U73(tt) |
→ |
U74(isPalListKind) |
(33) |
|
U74(tt) |
→ |
tt |
(34) |
|
U81(tt) |
→ |
U82(isPalListKind) |
(35) |
|
U82(tt) |
→ |
U83(isNePal) |
(36) |
|
U83(tt) |
→ |
tt |
(37) |
|
U91(tt) |
→ |
U92(isPalListKind) |
(38) |
|
U92(tt) |
→ |
tt |
(39) |
| isList |
→ |
U11(isPalListKind) |
(40) |
| isList |
→ |
tt |
(41) |
| isList |
→ |
U21(isPalListKind) |
(42) |
| isNeList |
→ |
U31(isPalListKind) |
(43) |
| isNeList |
→ |
U41(isPalListKind) |
(44) |
| isNeList |
→ |
U51(isPalListKind) |
(45) |
| isNePal |
→ |
U61(isPalListKind) |
(46) |
| isNePal |
→ |
U71(isQid) |
(47) |
| isPal |
→ |
U81(isPalListKind) |
(48) |
| isPal |
→ |
tt |
(49) |
| isPalListKind |
→ |
tt |
(50) |
| isPalListKind |
→ |
U91(isPalListKind) |
(51) |
| isQid |
→ |
tt |
(52) |
Property / Task
Prove or disprove termination.Answer / Result
No.Proof (by ttt2 @ termCOMP 2023)
1 Loop
The following loop proves nontermination.
| t0
|
= |
isPalListKind |
|
→
|
U91(isPalListKind) |
|
= |
t1
|
where t1 =
C[t0]
and
C = U91(☐)