Certification Problem
Input (TPDB TRS_Standard/Transformed_CSR_04/LISTUTILITIES_nokinds-noand_L)
The rewrite relation of the following TRS is considered.
|
U12(tt) |
→ |
snd(splitAt(N,XS)) |
(1) |
|
U161(tt) |
→ |
cons(N) |
(2) |
|
U172(tt) |
→ |
head(afterNth(N,XS)) |
(3) |
|
U182(tt) |
→ |
Y |
(4) |
|
U191(tt) |
→ |
pair(nil,XS) |
(5) |
|
U203(tt) |
→ |
U204(splitAt(N,XS)) |
(6) |
|
U204(pair(YS,ZS)) |
→ |
pair(cons(X),ZS) |
(7) |
|
U212(tt) |
→ |
XS |
(8) |
|
U22(tt) |
→ |
X |
(9) |
|
U222(tt) |
→ |
fst(splitAt(N,XS)) |
(10) |
|
U32(tt) |
→ |
N |
(11) |
|
U101(tt) |
→ |
U102(isLNat) |
(12) |
|
U102(tt) |
→ |
tt |
(13) |
|
U11(tt) |
→ |
U12(isLNat) |
(14) |
|
U111(tt) |
→ |
tt |
(15) |
|
U121(tt) |
→ |
tt |
(16) |
|
U131(tt) |
→ |
U132(isLNat) |
(17) |
|
U132(tt) |
→ |
tt |
(18) |
|
U141(tt) |
→ |
U142(isLNat) |
(19) |
|
U142(tt) |
→ |
tt |
(20) |
|
U151(tt) |
→ |
U152(isLNat) |
(21) |
|
U152(tt) |
→ |
tt |
(22) |
|
U171(tt) |
→ |
U172(isLNat) |
(23) |
|
U181(tt) |
→ |
U182(isLNat) |
(24) |
|
U201(tt) |
→ |
U202(isNatural) |
(25) |
|
U202(tt) |
→ |
U203(isLNat) |
(26) |
|
U21(tt) |
→ |
U22(isLNat) |
(27) |
|
U211(tt) |
→ |
U212(isLNat) |
(28) |
|
U221(tt) |
→ |
U222(isLNat) |
(29) |
|
U31(tt) |
→ |
U32(isLNat) |
(30) |
|
U41(tt) |
→ |
U42(isLNat) |
(31) |
|
U42(tt) |
→ |
tt |
(32) |
|
U51(tt) |
→ |
U52(isLNat) |
(33) |
|
U52(tt) |
→ |
tt |
(34) |
|
U61(tt) |
→ |
tt |
(35) |
|
U71(tt) |
→ |
tt |
(36) |
|
U81(tt) |
→ |
tt |
(37) |
|
U91(tt) |
→ |
tt |
(38) |
|
afterNth(N,XS) |
→ |
U11(isNatural) |
(39) |
|
fst(pair(X,Y)) |
→ |
U21(isLNat) |
(40) |
|
head(cons(N)) |
→ |
U31(isNatural) |
(41) |
| isLNat |
→ |
tt |
(42) |
| isLNat |
→ |
U41(isNatural) |
(43) |
| isLNat |
→ |
U51(isNatural) |
(44) |
| isLNat |
→ |
U61(isPLNat) |
(45) |
| isLNat |
→ |
U71(isNatural) |
(46) |
| isLNat |
→ |
U81(isPLNat) |
(47) |
| isLNat |
→ |
U91(isLNat) |
(48) |
| isLNat |
→ |
U101(isNatural) |
(49) |
| isNatural |
→ |
tt |
(50) |
| isNatural |
→ |
U111(isLNat) |
(51) |
| isNatural |
→ |
U121(isNatural) |
(52) |
| isNatural |
→ |
U131(isNatural) |
(53) |
| isPLNat |
→ |
U141(isLNat) |
(54) |
| isPLNat |
→ |
U151(isNatural) |
(55) |
|
natsFrom(N) |
→ |
U161(isNatural) |
(56) |
|
sel(N,XS) |
→ |
U171(isNatural) |
(57) |
|
snd(pair(X,Y)) |
→ |
U181(isLNat) |
(58) |
|
splitAt(0,XS) |
→ |
U191(isLNat) |
(59) |
|
splitAt(s(N),cons(X)) |
→ |
U201(isNatural) |
(60) |
|
tail(cons(N)) |
→ |
U211(isNatural) |
(61) |
|
take(N,XS) |
→ |
U221(isNatural) |
(62) |
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))