Certification Problem
Input (TPDB TRS_Standard/Transformed_CSR_04/LISTUTILITIES_nosorts_L)
The rewrite relation of the following TRS is considered.
|
U11(tt) |
→ |
U12(splitAt(N,XS)) |
(1) |
|
U12(pair(YS,ZS)) |
→ |
pair(cons(X),ZS) |
(2) |
|
and(tt) |
→ |
X |
(3) |
|
tail(cons(N)) |
→ |
XS |
(4) |
|
afterNth(N,XS) |
→ |
snd(splitAt(N,XS)) |
(5) |
|
fst(pair(X,Y)) |
→ |
X |
(6) |
|
head(cons(N)) |
→ |
N |
(7) |
|
natsFrom(N) |
→ |
cons(N) |
(8) |
|
sel(N,XS) |
→ |
head(afterNth(N,XS)) |
(9) |
|
snd(pair(X,Y)) |
→ |
Y |
(10) |
|
splitAt(0,XS) |
→ |
pair(nil,XS) |
(11) |
|
splitAt(s(N),cons(X)) |
→ |
U11(tt) |
(12) |
|
take(N,XS) |
→ |
fst(splitAt(N,XS)) |
(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) |
|
→
|
U12(splitAt(U11(tt),XS)) |
|
= |
t1
|
where t1 =
C[t0σ]
and
σ =
{N/U11(tt)}
and
C = U12(splitAt(☐,XS))