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


--------------------------------------------------------------------------------


NO

Problem:
 U11(tt()) -> snd(splitAt(N,XS))
 U161(tt()) -> cons(N)
 U171(tt()) -> head(afterNth(N,XS))
 U181(tt()) -> Y
 U191(tt()) -> pair(nil(),XS)
 U201(tt()) -> U202(splitAt(N,XS))
 U202(pair(YS,ZS)) -> pair(cons(X),ZS)
 U21(tt()) -> X
 U211(tt()) -> XS
 U221(tt()) -> fst(splitAt(N,XS))
 U31(tt()) -> N
 and(tt()) -> X
 U101(tt()) -> U102(isNatural())
 U102(tt()) -> U103(isLNat())
 U103(tt()) -> tt()
 U111(tt()) -> U112(isLNat())
 U112(tt()) -> tt()
 U121(tt()) -> U122(isNatural())
 U122(tt()) -> tt()
 U131(tt()) -> U132(isNatural())
 U132(tt()) -> U133(isLNat())
 U133(tt()) -> tt()
 U141(tt()) -> U142(isLNat())
 U142(tt()) -> U143(isLNat())
 U143(tt()) -> tt()
 U151(tt()) -> U152(isNatural())
 U152(tt()) -> U153(isLNat())
 U153(tt()) -> tt()
 U41(tt()) -> U42(isNatural())
 U42(tt()) -> U43(isLNat())
 U43(tt()) -> tt()
 U51(tt()) -> U52(isNatural())
 U52(tt()) -> U53(isLNat())
 U53(tt()) -> tt()
 U61(tt()) -> U62(isPLNat())
 U62(tt()) -> tt()
 U71(tt()) -> U72(isNatural())
 U72(tt()) -> tt()
 U81(tt()) -> U82(isPLNat())
 U82(tt()) -> tt()
 U91(tt()) -> U92(isLNat())
 U92(tt()) -> tt()
 afterNth(N,XS) -> U11(and(and(isNatural())))
 fst(pair(X,Y)) -> U21(and(and(isLNat())))
 head(cons(N)) -> U31(and(and(isNatural())))
 isLNat() -> tt()
 isLNat() -> U41(and(isNaturalKind()))
 isLNat() -> U51(and(isNaturalKind()))
 isLNat() -> U61(isPLNatKind())
 isLNat() -> U71(isNaturalKind())
 isLNat() -> U81(isPLNatKind())
 isLNat() -> U91(isLNatKind())
 isLNat() -> U101(and(isNaturalKind()))
 isLNatKind() -> tt()
 isLNatKind() -> and(isNaturalKind())
 isLNatKind() -> isPLNatKind()
 isLNatKind() -> isNaturalKind()
 isLNatKind() -> isLNatKind()
 isNatural() -> tt()
 isNatural() -> U111(isLNatKind())
 isNatural() -> U121(isNaturalKind())
 isNatural() -> U131(and(isNaturalKind()))
 isNaturalKind() -> tt()
 isNaturalKind() -> isLNatKind()
 isNaturalKind() -> isNaturalKind()
 isNaturalKind() -> and(isNaturalKind())
 isPLNat() -> U141(and(isLNatKind()))
 isPLNat() -> U151(and(isNaturalKind()))
 isPLNatKind() -> and(isLNatKind())
 isPLNatKind() -> and(isNaturalKind())
 natsFrom(N) -> U161(and(isNatural()))
 sel(N,XS) -> U171(and(and(isNatural())))
 snd(pair(X,Y)) -> U181(and(and(isLNat())))
 splitAt(0(),XS) -> U191(and(isLNat()))
 splitAt(s(N),cons(X)) -> U201(and(and(isNatural())))
 tail(cons(N)) -> U211(and(and(isNatural())))
 take(N,XS) -> U221(and(and(isNatural())))

Proof:
 Fresh Variable Processor:
  loop length: 1
  terms:
   U11(tt())
  context: snd(splitAt([],XS))
  substitution:
   N -> U11(tt())
  Qed