/export/starexec/sandbox/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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MAYBE

Problem:
 U101(tt(),V2) -> U102(isLNat(activate(V2)))
 U102(tt()) -> tt()
 U11(tt(),N,XS) -> U12(isLNat(activate(XS)),activate(N),activate(XS))
 U111(tt()) -> tt()
 U12(tt(),N,XS) -> snd(splitAt(activate(N),activate(XS)))
 U121(tt()) -> tt()
 U131(tt(),V2) -> U132(isLNat(activate(V2)))
 U132(tt()) -> tt()
 U141(tt(),V2) -> U142(isLNat(activate(V2)))
 U142(tt()) -> tt()
 U151(tt(),V2) -> U152(isLNat(activate(V2)))
 U152(tt()) -> tt()
 U161(tt(),N) -> cons(activate(N),n__natsFrom(n__s(activate(N))))
 U171(tt(),N,XS) -> U172(isLNat(activate(XS)),activate(N),activate(XS))
 U172(tt(),N,XS) -> head(afterNth(activate(N),activate(XS)))
 U181(tt(),Y) -> U182(isLNat(activate(Y)),activate(Y))
 U182(tt(),Y) -> activate(Y)
 U191(tt(),XS) -> pair(nil(),activate(XS))
 U201(tt(),N,X,XS) -> U202(isNatural(activate(X)),activate(N),activate(X),activate(XS))
 U202(tt(),N,X,XS) -> U203(isLNat(activate(XS)),activate(N),activate(X),activate(XS))
 U203(tt(),N,X,XS) -> U204(splitAt(activate(N),activate(XS)),activate(X))
 U204(pair(YS,ZS),X) -> pair(cons(activate(X),YS),ZS)
 U21(tt(),X,Y) -> U22(isLNat(activate(Y)),activate(X))
 U211(tt(),XS) -> U212(isLNat(activate(XS)),activate(XS))
 U212(tt(),XS) -> activate(XS)
 U22(tt(),X) -> activate(X)
 U221(tt(),N,XS) -> U222(isLNat(activate(XS)),activate(N),activate(XS))
 U222(tt(),N,XS) -> fst(splitAt(activate(N),activate(XS)))
 U31(tt(),N,XS) -> U32(isLNat(activate(XS)),activate(N))
 U32(tt(),N) -> activate(N)
 U41(tt(),V2) -> U42(isLNat(activate(V2)))
 U42(tt()) -> tt()
 U51(tt(),V2) -> U52(isLNat(activate(V2)))
 U52(tt()) -> tt()
 U61(tt()) -> tt()
 U71(tt()) -> tt()
 U81(tt()) -> tt()
 U91(tt()) -> tt()
 afterNth(N,XS) -> U11(isNatural(N),N,XS)
 fst(pair(X,Y)) -> U21(isLNat(X),X,Y)
 head(cons(N,XS)) -> U31(isNatural(N),N,activate(XS))
 isLNat(n__nil()) -> tt()
 isLNat(n__afterNth(V1,V2)) -> U41(isNatural(activate(V1)),activate(V2))
 isLNat(n__cons(V1,V2)) -> U51(isNatural(activate(V1)),activate(V2))
 isLNat(n__fst(V1)) -> U61(isPLNat(activate(V1)))
 isLNat(n__natsFrom(V1)) -> U71(isNatural(activate(V1)))
 isLNat(n__snd(V1)) -> U81(isPLNat(activate(V1)))
 isLNat(n__tail(V1)) -> U91(isLNat(activate(V1)))
 isLNat(n__take(V1,V2)) -> U101(isNatural(activate(V1)),activate(V2))
 isNatural(n__0()) -> tt()
 isNatural(n__head(V1)) -> U111(isLNat(activate(V1)))
 isNatural(n__s(V1)) -> U121(isNatural(activate(V1)))
 isNatural(n__sel(V1,V2)) -> U131(isNatural(activate(V1)),activate(V2))
 isPLNat(n__pair(V1,V2)) -> U141(isLNat(activate(V1)),activate(V2))
 isPLNat(n__splitAt(V1,V2)) -> U151(isNatural(activate(V1)),activate(V2))
 natsFrom(N) -> U161(isNatural(N),N)
 sel(N,XS) -> U171(isNatural(N),N,XS)
 snd(pair(X,Y)) -> U181(isLNat(X),Y)
 splitAt(0(),XS) -> U191(isLNat(XS),XS)
 splitAt(s(N),cons(X,XS)) -> U201(isNatural(N),N,X,activate(XS))
 tail(cons(N,XS)) -> U211(isNatural(N),activate(XS))
 take(N,XS) -> U221(isNatural(N),N,XS)
 natsFrom(X) -> n__natsFrom(X)
 s(X) -> n__s(X)
 nil() -> n__nil()
 afterNth(X1,X2) -> n__afterNth(X1,X2)
 cons(X1,X2) -> n__cons(X1,X2)
 fst(X) -> n__fst(X)
 snd(X) -> n__snd(X)
 tail(X) -> n__tail(X)
 take(X1,X2) -> n__take(X1,X2)
 0() -> n__0()
 head(X) -> n__head(X)
 sel(X1,X2) -> n__sel(X1,X2)
 pair(X1,X2) -> n__pair(X1,X2)
 splitAt(X1,X2) -> n__splitAt(X1,X2)
 activate(n__natsFrom(X)) -> natsFrom(activate(X))
 activate(n__s(X)) -> s(activate(X))
 activate(n__nil()) -> nil()
 activate(n__afterNth(X1,X2)) -> afterNth(activate(X1),activate(X2))
 activate(n__cons(X1,X2)) -> cons(activate(X1),X2)
 activate(n__fst(X)) -> fst(activate(X))
 activate(n__snd(X)) -> snd(activate(X))
 activate(n__tail(X)) -> tail(activate(X))
 activate(n__take(X1,X2)) -> take(activate(X1),activate(X2))
 activate(n__0()) -> 0()
 activate(n__head(X)) -> head(activate(X))
 activate(n__sel(X1,X2)) -> sel(activate(X1),activate(X2))
 activate(n__pair(X1,X2)) -> pair(activate(X1),activate(X2))
 activate(n__splitAt(X1,X2)) -> splitAt(activate(X1),activate(X2))
 activate(X) -> X

Proof:
 Open