Certification Problem
Input (TPDB TRS_Standard/Transformed_CSR_04/LengthOfFiniteLists_nokinds_L)
The rewrite relation of the following TRS is considered.
U11(tt) |
→ |
s(length(L)) |
(1) |
and(tt) |
→ |
X |
(2) |
zeros |
→ |
cons(0) |
(3) |
isNat |
→ |
tt |
(4) |
isNat |
→ |
isNatList |
(5) |
isNat |
→ |
isNat |
(6) |
isNatIList |
→ |
isNatList |
(7) |
isNatIList |
→ |
tt |
(8) |
isNatIList |
→ |
and(isNat) |
(9) |
isNatList |
→ |
tt |
(10) |
isNatList |
→ |
and(isNat) |
(11) |
length(nil) |
→ |
0 |
(12) |
length(cons(N)) |
→ |
U11(and(isNatList)) |
(13) |
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(☐))