/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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NO

Problem 1: 

(VAR v_NonEmpty:S N:S X:S XS:S Y:S YS:S ZS:S)
(RULES
U101(tt) -> U102(isLNat)
U102(tt) -> tt
U11(tt) -> U12(isLNat)
U111(tt) -> tt
U12(tt) -> snd(splitAt(N:S,XS:S))
U121(tt) -> tt
U131(tt) -> U132(isLNat)
U132(tt) -> tt
U141(tt) -> U142(isLNat)
U142(tt) -> tt
U151(tt) -> U152(isLNat)
U152(tt) -> tt
U161(tt) -> cons(N:S)
U171(tt) -> U172(isLNat)
U172(tt) -> head(afterNth(N:S,XS:S))
U181(tt) -> U182(isLNat)
U182(tt) -> Y:S
U191(tt) -> pair(nil,XS:S)
U201(tt) -> U202(isNatural)
U202(tt) -> U203(isLNat)
U203(tt) -> U204(splitAt(N:S,XS:S))
U204(pair(YS:S,ZS:S)) -> pair(cons(X:S),ZS:S)
U21(tt) -> U22(isLNat)
U211(tt) -> U212(isLNat)
U212(tt) -> XS:S
U22(tt) -> X:S
U221(tt) -> U222(isLNat)
U222(tt) -> fst(splitAt(N:S,XS:S))
U31(tt) -> U32(isLNat)
U32(tt) -> N:S
U41(tt) -> U42(isLNat)
U42(tt) -> tt
U51(tt) -> U52(isLNat)
U52(tt) -> tt
U61(tt) -> tt
U71(tt) -> tt
U81(tt) -> tt
U91(tt) -> tt
afterNth(N:S,XS:S) -> U11(isNatural)
fst(pair(X:S,Y:S)) -> U21(isLNat)
head(cons(N:S)) -> U31(isNatural)
isLNat -> U101(isNatural)
isLNat -> U41(isNatural)
isLNat -> U51(isNatural)
isLNat -> U61(isPLNat)
isLNat -> U71(isNatural)
isLNat -> U81(isPLNat)
isLNat -> U91(isLNat)
isLNat -> tt
isNatural -> U111(isLNat)
isNatural -> U121(isNatural)
isNatural -> U131(isNatural)
isNatural -> tt
isPLNat -> U141(isLNat)
isPLNat -> U151(isNatural)
natsFrom(N:S) -> U161(isNatural)
sel(N:S,XS:S) -> U171(isNatural)
snd(pair(X:S,Y:S)) -> U181(isLNat)
splitAt(0,XS:S) -> U191(isLNat)
splitAt(s(N:S),cons(X:S)) -> U201(isNatural)
tail(cons(N:S)) -> U211(isNatural)
take(N:S,XS:S) -> U221(isNatural)
)

Problem 1: 

Extra Variables Processor:
-> Rules:
 U101(tt) -> U102(isLNat)
 U102(tt) -> tt
 U11(tt) -> U12(isLNat)
 U111(tt) -> tt
 U12(tt) -> snd(splitAt(N:S,XS:S))
 U121(tt) -> tt
 U131(tt) -> U132(isLNat)
 U132(tt) -> tt
 U141(tt) -> U142(isLNat)
 U142(tt) -> tt
 U151(tt) -> U152(isLNat)
 U152(tt) -> tt
 U161(tt) -> cons(N:S)
 U171(tt) -> U172(isLNat)
 U172(tt) -> head(afterNth(N:S,XS:S))
 U181(tt) -> U182(isLNat)
 U182(tt) -> Y:S
 U191(tt) -> pair(nil,XS:S)
 U201(tt) -> U202(isNatural)
 U202(tt) -> U203(isLNat)
 U203(tt) -> U204(splitAt(N:S,XS:S))
 U204(pair(YS:S,ZS:S)) -> pair(cons(X:S),ZS:S)
 U21(tt) -> U22(isLNat)
 U211(tt) -> U212(isLNat)
 U212(tt) -> XS:S
 U22(tt) -> X:S
 U221(tt) -> U222(isLNat)
 U222(tt) -> fst(splitAt(N:S,XS:S))
 U31(tt) -> U32(isLNat)
 U32(tt) -> N:S
 U41(tt) -> U42(isLNat)
 U42(tt) -> tt
 U51(tt) -> U52(isLNat)
 U52(tt) -> tt
 U61(tt) -> tt
 U71(tt) -> tt
 U81(tt) -> tt
 U91(tt) -> tt
 afterNth(N:S,XS:S) -> U11(isNatural)
 fst(pair(X:S,Y:S)) -> U21(isLNat)
 head(cons(N:S)) -> U31(isNatural)
 isLNat -> U101(isNatural)
 isLNat -> U41(isNatural)
 isLNat -> U51(isNatural)
 isLNat -> U61(isPLNat)
 isLNat -> U71(isNatural)
 isLNat -> U81(isPLNat)
 isLNat -> U91(isLNat)
 isLNat -> tt
 isNatural -> U111(isLNat)
 isNatural -> U121(isNatural)
 isNatural -> U131(isNatural)
 isNatural -> tt
 isPLNat -> U141(isLNat)
 isPLNat -> U151(isNatural)
 natsFrom(N:S) -> U161(isNatural)
 sel(N:S,XS:S) -> U171(isNatural)
 snd(pair(X:S,Y:S)) -> U181(isLNat)
 splitAt(0,XS:S) -> U191(isLNat)
 splitAt(s(N:S),cons(X:S)) -> U201(isNatural)
 tail(cons(N:S)) -> U211(isNatural)
 take(N:S,XS:S) -> U221(isNatural)
-> The system has extra variables.

The problem is infinite.