Certification Problem
Input (TPDB TRS_Standard/Transformed_CSR_04/OvConsOS_nokinds_L)
The rewrite relation of the following TRS is considered.
U11(tt) |
→ |
s(length(L)) |
(1) |
U31(tt) |
→ |
cons(N) |
(2) |
and(tt) |
→ |
X |
(3) |
zeros |
→ |
cons(0) |
(4) |
U21(tt) |
→ |
nil |
(5) |
isNat |
→ |
tt |
(6) |
isNat |
→ |
isNatList |
(7) |
isNat |
→ |
isNat |
(8) |
isNatIList |
→ |
isNatList |
(9) |
isNatIList |
→ |
tt |
(10) |
isNatIList |
→ |
and(isNat) |
(11) |
isNatList |
→ |
tt |
(12) |
isNatList |
→ |
and(isNat) |
(13) |
length(nil) |
→ |
0 |
(14) |
length(cons(N)) |
→ |
U11(and(isNatList)) |
(15) |
take(0,IL) |
→ |
U21(isNatIList) |
(16) |
take(s(M),cons(N)) |
→ |
U31(and(isNatIList)) |
(17) |
Property / Task
Prove or disprove termination.Answer / Result
No.Proof (by ttt2 @ termCOMP 2023)
1 Loop
The following loop proves nontermination.
t0
|
= |
U11(tt) |
|
→
|
s(length(U11(tt))) |
|
= |
t1
|
where t1 =
C[t0σ]
and
σ =
{L/U11(tt)}
and
C = s(length(☐))