Certification Problem
Input (TPDB TRS_Standard/Transformed_CSR_04/OvConsOS_nosorts-noand_L)
The rewrite relation of the following TRS is considered.
|
U12(tt) |
→ |
s(length(L)) |
(1) |
|
U23(tt) |
→ |
cons(N) |
(2) |
| zeros |
→ |
cons(0) |
(3) |
|
U11(tt) |
→ |
U12(tt) |
(4) |
|
U21(tt) |
→ |
U22(tt) |
(5) |
|
U22(tt) |
→ |
U23(tt) |
(6) |
|
length(nil) |
→ |
0 |
(7) |
|
length(cons(N)) |
→ |
U11(tt) |
(8) |
|
take(0,IL) |
→ |
nil |
(9) |
|
take(s(M),cons(N)) |
→ |
U21(tt) |
(10) |
Property / Task
Prove or disprove termination.Answer / Result
No.Proof (by ttt2 @ termCOMP 2023)
1 Loop
The following loop proves nontermination.
| t0
|
= |
U12(tt) |
|
→
|
s(length(U12(tt))) |
|
= |
t1
|
where t1 =
C[t0σ]
and
σ =
{L/U12(tt)}
and
C = s(length(☐))