Certification Problem
Input (TPDB TRS_Standard/Transformed_CSR_04/OvConsOS_complete-noand_L)
The rewrite relation of the following TRS is considered.
|
U114(tt) |
→ |
s(length(L)) |
(1) |
|
U136(tt) |
→ |
cons(N) |
(2) |
| zeros |
→ |
cons(0) |
(3) |
|
U101(tt) |
→ |
U102(isNatKind) |
(4) |
|
U102(tt) |
→ |
U103(isNatIListKind) |
(5) |
|
U103(tt) |
→ |
U104(isNatIListKind) |
(6) |
|
U104(tt) |
→ |
U105(isNat) |
(7) |
|
U105(tt) |
→ |
U106(isNatIList) |
(8) |
|
U106(tt) |
→ |
tt |
(9) |
|
U11(tt) |
→ |
U12(isNatIListKind) |
(10) |
|
U111(tt) |
→ |
U112(isNatIListKind) |
(11) |
|
U112(tt) |
→ |
U113(isNat) |
(12) |
|
U113(tt) |
→ |
U114(isNatKind) |
(13) |
|
U12(tt) |
→ |
U13(isNatList) |
(14) |
|
U121(tt) |
→ |
U122(isNatIListKind) |
(15) |
|
U122(tt) |
→ |
nil |
(16) |
|
U13(tt) |
→ |
tt |
(17) |
|
U131(tt) |
→ |
U132(isNatIListKind) |
(18) |
|
U132(tt) |
→ |
U133(isNat) |
(19) |
|
U133(tt) |
→ |
U134(isNatKind) |
(20) |
|
U134(tt) |
→ |
U135(isNat) |
(21) |
|
U135(tt) |
→ |
U136(isNatKind) |
(22) |
|
U21(tt) |
→ |
U22(isNatKind) |
(23) |
|
U22(tt) |
→ |
U23(isNat) |
(24) |
|
U23(tt) |
→ |
tt |
(25) |
|
U31(tt) |
→ |
U32(isNatIListKind) |
(26) |
|
U32(tt) |
→ |
U33(isNatList) |
(27) |
|
U33(tt) |
→ |
tt |
(28) |
|
U41(tt) |
→ |
U42(isNatKind) |
(29) |
|
U42(tt) |
→ |
U43(isNatIListKind) |
(30) |
|
U43(tt) |
→ |
U44(isNatIListKind) |
(31) |
|
U44(tt) |
→ |
U45(isNat) |
(32) |
|
U45(tt) |
→ |
U46(isNatIList) |
(33) |
|
U46(tt) |
→ |
tt |
(34) |
|
U51(tt) |
→ |
U52(isNatIListKind) |
(35) |
|
U52(tt) |
→ |
tt |
(36) |
|
U61(tt) |
→ |
U62(isNatIListKind) |
(37) |
|
U62(tt) |
→ |
tt |
(38) |
|
U71(tt) |
→ |
tt |
(39) |
|
U81(tt) |
→ |
tt |
(40) |
|
U91(tt) |
→ |
U92(isNatKind) |
(41) |
|
U92(tt) |
→ |
U93(isNatIListKind) |
(42) |
|
U93(tt) |
→ |
U94(isNatIListKind) |
(43) |
|
U94(tt) |
→ |
U95(isNat) |
(44) |
|
U95(tt) |
→ |
U96(isNatList) |
(45) |
|
U96(tt) |
→ |
tt |
(46) |
| isNat |
→ |
tt |
(47) |
| isNat |
→ |
U11(isNatIListKind) |
(48) |
| isNat |
→ |
U21(isNatKind) |
(49) |
| isNatIList |
→ |
U31(isNatIListKind) |
(50) |
| isNatIList |
→ |
tt |
(51) |
| isNatIList |
→ |
U41(isNatKind) |
(52) |
| isNatIListKind |
→ |
tt |
(53) |
| isNatIListKind |
→ |
U51(isNatKind) |
(54) |
| isNatIListKind |
→ |
U61(isNatKind) |
(55) |
| isNatKind |
→ |
tt |
(56) |
| isNatKind |
→ |
U71(isNatIListKind) |
(57) |
| isNatKind |
→ |
U81(isNatKind) |
(58) |
| isNatList |
→ |
tt |
(59) |
| isNatList |
→ |
U91(isNatKind) |
(60) |
| isNatList |
→ |
U101(isNatKind) |
(61) |
|
length(nil) |
→ |
0 |
(62) |
|
length(cons(N)) |
→ |
U111(isNatList) |
(63) |
|
take(0,IL) |
→ |
U121(isNatIList) |
(64) |
|
take(s(M),cons(N)) |
→ |
U131(isNatIList) |
(65) |
Property / Task
Prove or disprove termination.Answer / Result
No.Proof (by ttt2 @ termCOMP 2023)
1 Loop
The following loop proves nontermination.
| t0
|
= |
U114(tt) |
|
→
|
s(length(U114(tt))) |
|
= |
t1
|
where t1 =
C[t0σ]
and
σ =
{L/U114(tt)}
and
C = s(length(☐))