Certification Problem
Input (TPDB TRS_Outermost/Strategy_outermost_added_08/LengthOfFiniteLists_complete-noand_L)
The rewrite relation of the following TRS is considered.
|
U94(tt) |
→ |
s(length(L)) |
(1) |
| zeros |
→ |
cons(0) |
(2) |
|
U11(tt) |
→ |
U12(isNatIListKind) |
(3) |
|
U12(tt) |
→ |
U13(isNatList) |
(4) |
|
U13(tt) |
→ |
tt |
(5) |
|
U21(tt) |
→ |
U22(isNatKind) |
(6) |
|
U22(tt) |
→ |
U23(isNat) |
(7) |
|
U23(tt) |
→ |
tt |
(8) |
|
U31(tt) |
→ |
U32(isNatIListKind) |
(9) |
|
U32(tt) |
→ |
U33(isNatList) |
(10) |
|
U33(tt) |
→ |
tt |
(11) |
|
U41(tt) |
→ |
U42(isNatKind) |
(12) |
|
U42(tt) |
→ |
U43(isNatIListKind) |
(13) |
|
U43(tt) |
→ |
U44(isNatIListKind) |
(14) |
|
U44(tt) |
→ |
U45(isNat) |
(15) |
|
U45(tt) |
→ |
U46(isNatIList) |
(16) |
|
U46(tt) |
→ |
tt |
(17) |
|
U51(tt) |
→ |
U52(isNatIListKind) |
(18) |
|
U52(tt) |
→ |
tt |
(19) |
|
U61(tt) |
→ |
tt |
(20) |
|
U71(tt) |
→ |
tt |
(21) |
|
U81(tt) |
→ |
U82(isNatKind) |
(22) |
|
U82(tt) |
→ |
U83(isNatIListKind) |
(23) |
|
U83(tt) |
→ |
U84(isNatIListKind) |
(24) |
|
U84(tt) |
→ |
U85(isNat) |
(25) |
|
U85(tt) |
→ |
U86(isNatList) |
(26) |
|
U86(tt) |
→ |
tt |
(27) |
|
U91(tt) |
→ |
U92(isNatIListKind) |
(28) |
|
U92(tt) |
→ |
U93(isNat) |
(29) |
|
U93(tt) |
→ |
U94(isNatKind) |
(30) |
| isNat |
→ |
tt |
(31) |
| isNat |
→ |
U11(isNatIListKind) |
(32) |
| isNat |
→ |
U21(isNatKind) |
(33) |
| isNatIList |
→ |
U31(isNatIListKind) |
(34) |
| isNatIList |
→ |
tt |
(35) |
| isNatIList |
→ |
U41(isNatKind) |
(36) |
| isNatIListKind |
→ |
tt |
(37) |
| isNatIListKind |
→ |
U51(isNatKind) |
(38) |
| isNatKind |
→ |
tt |
(39) |
| isNatKind |
→ |
U61(isNatIListKind) |
(40) |
| isNatKind |
→ |
U71(isNatKind) |
(41) |
| isNatList |
→ |
tt |
(42) |
| isNatList |
→ |
U81(isNatKind) |
(43) |
|
length(nil) |
→ |
0 |
(44) |
|
length(cons(N)) |
→ |
U91(isNatList) |
(45) |
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
|
= |
U94(tt) |
|
→
|
s(length(U94(tt))) |
|
= |
t1
|
where t1 =
C[t0]
and
C = s(length(☐))