/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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NO

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

Proof:
 Fresh Variable Processor:
  loop length: 1
  terms:
   U12(tt())
  context: snd(splitAt([],XS))
  substitution:
   N -> U12(tt())
  Qed