Certification Problem
Input (TPDB TRS_Outermost/Strategy_outermost_added_08/OvConsOS_nokinds-noand_L)
The rewrite relation of the following TRS is considered.
U72(tt) |
→ |
s(length(L)) |
(1) |
U93(tt) |
→ |
cons(N) |
(2) |
zeros |
→ |
cons(0) |
(3) |
U11(tt) |
→ |
tt |
(4) |
U21(tt) |
→ |
tt |
(5) |
U31(tt) |
→ |
tt |
(6) |
U41(tt) |
→ |
U42(isNatIList) |
(7) |
U42(tt) |
→ |
tt |
(8) |
U51(tt) |
→ |
U52(isNatList) |
(9) |
U52(tt) |
→ |
tt |
(10) |
U61(tt) |
→ |
U62(isNatIList) |
(11) |
U62(tt) |
→ |
tt |
(12) |
U71(tt) |
→ |
U72(isNat) |
(13) |
U81(tt) |
→ |
nil |
(14) |
U91(tt) |
→ |
U92(isNat) |
(15) |
U92(tt) |
→ |
U93(isNat) |
(16) |
isNat |
→ |
tt |
(17) |
isNat |
→ |
U11(isNatList) |
(18) |
isNat |
→ |
U21(isNat) |
(19) |
isNatIList |
→ |
U31(isNatList) |
(20) |
isNatIList |
→ |
tt |
(21) |
isNatIList |
→ |
U41(isNat) |
(22) |
isNatList |
→ |
tt |
(23) |
isNatList |
→ |
U51(isNat) |
(24) |
isNatList |
→ |
U61(isNat) |
(25) |
length(nil) |
→ |
0 |
(26) |
length(cons(N)) |
→ |
U71(isNatList) |
(27) |
take(0,IL) |
→ |
U81(isNatIList) |
(28) |
take(s(M),cons(N)) |
→ |
U91(isNatIList) |
(29) |
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
|
= |
U72(tt) |
|
→
|
s(length(U72(tt))) |
|
= |
t1
|
where t1 =
C[t0]
and
C = s(length(☐))