Certification Problem
Input (TPDB TRS_Standard/Transformed_CSR_04/OvConsOS_complete_L)
The rewrite relation of the following TRS is considered.
|
U71(tt) |
→ |
s(length(L)) |
(1) |
|
U91(tt) |
→ |
cons(N) |
(2) |
|
and(tt) |
→ |
X |
(3) |
| zeros |
→ |
cons(0) |
(4) |
|
U11(tt) |
→ |
U12(isNatList) |
(5) |
|
U12(tt) |
→ |
tt |
(6) |
|
U21(tt) |
→ |
U22(isNat) |
(7) |
|
U22(tt) |
→ |
tt |
(8) |
|
U31(tt) |
→ |
U32(isNatList) |
(9) |
|
U32(tt) |
→ |
tt |
(10) |
|
U41(tt) |
→ |
U42(isNat) |
(11) |
|
U42(tt) |
→ |
U43(isNatIList) |
(12) |
|
U43(tt) |
→ |
tt |
(13) |
|
U51(tt) |
→ |
U52(isNat) |
(14) |
|
U52(tt) |
→ |
U53(isNatList) |
(15) |
|
U53(tt) |
→ |
tt |
(16) |
|
U61(tt) |
→ |
U62(isNat) |
(17) |
|
U62(tt) |
→ |
U63(isNatIList) |
(18) |
|
U63(tt) |
→ |
tt |
(19) |
|
U81(tt) |
→ |
nil |
(20) |
| isNat |
→ |
tt |
(21) |
| isNat |
→ |
U11(isNatIListKind) |
(22) |
| isNat |
→ |
U21(isNatKind) |
(23) |
| isNatIList |
→ |
U31(isNatIListKind) |
(24) |
| isNatIList |
→ |
tt |
(25) |
| isNatIList |
→ |
U41(and(isNatKind)) |
(26) |
| isNatIListKind |
→ |
tt |
(27) |
| isNatIListKind |
→ |
and(isNatKind) |
(28) |
| isNatKind |
→ |
tt |
(29) |
| isNatKind |
→ |
isNatIListKind |
(30) |
| isNatKind |
→ |
isNatKind |
(31) |
| isNatList |
→ |
tt |
(32) |
| isNatList |
→ |
U51(and(isNatKind)) |
(33) |
| isNatList |
→ |
U61(and(isNatKind)) |
(34) |
|
length(nil) |
→ |
0 |
(35) |
|
length(cons(N)) |
→ |
U71(and(and(isNatList))) |
(36) |
|
take(0,IL) |
→ |
U81(and(isNatIList)) |
(37) |
|
take(s(M),cons(N)) |
→ |
U91(and(and(isNatIList))) |
(38) |
Property / Task
Prove or disprove termination.Answer / Result
No.Proof (by ttt2 @ termCOMP 2023)
1 Loop
The following loop proves nontermination.
| t0
|
= |
U71(tt) |
|
→
|
s(length(U71(tt))) |
|
= |
t1
|
where t1 =
C[t0σ]
and
σ =
{L/U71(tt)}
and
C = s(length(☐))