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(☐))