Certification Problem
Input (TPDB TRS_Standard/Transformed_CSR_04/LISTUTILITIES_nosorts-noand_L)
The rewrite relation of the following TRS is considered.
|
U12(tt) |
→ |
snd(splitAt(N,XS)) |
(1) |
|
U22(tt) |
→ |
X |
(2) |
|
U32(tt) |
→ |
N |
(3) |
|
U42(tt) |
→ |
head(afterNth(N,XS)) |
(4) |
|
U52(tt) |
→ |
Y |
(5) |
|
U63(tt) |
→ |
U64(splitAt(N,XS)) |
(6) |
|
U64(pair(YS,ZS)) |
→ |
pair(cons(X),ZS) |
(7) |
|
U72(tt) |
→ |
XS |
(8) |
|
U82(tt) |
→ |
fst(splitAt(N,XS)) |
(9) |
|
U11(tt) |
→ |
U12(tt) |
(10) |
|
U21(tt) |
→ |
U22(tt) |
(11) |
|
U31(tt) |
→ |
U32(tt) |
(12) |
|
U41(tt) |
→ |
U42(tt) |
(13) |
|
U51(tt) |
→ |
U52(tt) |
(14) |
|
U61(tt) |
→ |
U62(tt) |
(15) |
|
U62(tt) |
→ |
U63(tt) |
(16) |
|
U71(tt) |
→ |
U72(tt) |
(17) |
|
U81(tt) |
→ |
U82(tt) |
(18) |
|
afterNth(N,XS) |
→ |
U11(tt) |
(19) |
|
fst(pair(X,Y)) |
→ |
U21(tt) |
(20) |
|
head(cons(N)) |
→ |
U31(tt) |
(21) |
|
natsFrom(N) |
→ |
cons(N) |
(22) |
|
sel(N,XS) |
→ |
U41(tt) |
(23) |
|
snd(pair(X,Y)) |
→ |
U51(tt) |
(24) |
|
splitAt(0,XS) |
→ |
pair(nil,XS) |
(25) |
|
splitAt(s(N),cons(X)) |
→ |
U61(tt) |
(26) |
|
tail(cons(N)) |
→ |
U71(tt) |
(27) |
|
take(N,XS) |
→ |
U81(tt) |
(28) |
Property / Task
Prove or disprove termination.Answer / Result
No.Proof (by ttt2 @ termCOMP 2023)
1 Loop
The following loop proves nontermination.
| t0
|
= |
U12(tt) |
|
→
|
snd(splitAt(U12(tt),XS)) |
|
= |
t1
|
where t1 =
C[t0σ]
and
σ =
{N/U12(tt)}
and
C = snd(splitAt(☐,XS))