/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:
 a__U11(tt(),N,XS) -> a__U12(tt(),N,XS)
 a__U12(tt(),N,XS) -> a__snd(a__splitAt(mark(N),mark(XS)))
 a__U21(tt(),X) -> a__U22(tt(),X)
 a__U22(tt(),X) -> mark(X)
 a__U31(tt(),N) -> a__U32(tt(),N)
 a__U32(tt(),N) -> mark(N)
 a__U41(tt(),N,XS) -> a__U42(tt(),N,XS)
 a__U42(tt(),N,XS) -> a__head(a__afterNth(mark(N),mark(XS)))
 a__U51(tt(),Y) -> a__U52(tt(),Y)
 a__U52(tt(),Y) -> mark(Y)
 a__U61(tt(),N,X,XS) -> a__U62(tt(),N,X,XS)
 a__U62(tt(),N,X,XS) -> a__U63(tt(),N,X,XS)
 a__U63(tt(),N,X,XS) -> a__U64(a__splitAt(mark(N),mark(XS)),X)
 a__U64(pair(YS,ZS),X) -> pair(cons(mark(X),YS),mark(ZS))
 a__U71(tt(),XS) -> a__U72(tt(),XS)
 a__U72(tt(),XS) -> mark(XS)
 a__U81(tt(),N,XS) -> a__U82(tt(),N,XS)
 a__U82(tt(),N,XS) -> a__fst(a__splitAt(mark(N),mark(XS)))
 a__afterNth(N,XS) -> a__U11(tt(),N,XS)
 a__fst(pair(X,Y)) -> a__U21(tt(),X)
 a__head(cons(N,XS)) -> a__U31(tt(),N)
 a__natsFrom(N) -> cons(mark(N),natsFrom(s(N)))
 a__sel(N,XS) -> a__U41(tt(),N,XS)
 a__snd(pair(X,Y)) -> a__U51(tt(),Y)
 a__splitAt(0(),XS) -> pair(nil(),mark(XS))
 a__splitAt(s(N),cons(X,XS)) -> a__U61(tt(),N,X,XS)
 a__tail(cons(N,XS)) -> a__U71(tt(),XS)
 a__take(N,XS) -> a__U81(tt(),N,XS)
 mark(U11(X1,X2,X3)) -> a__U11(mark(X1),X2,X3)
 mark(U12(X1,X2,X3)) -> a__U12(mark(X1),X2,X3)
 mark(snd(X)) -> a__snd(mark(X))
 mark(splitAt(X1,X2)) -> a__splitAt(mark(X1),mark(X2))
 mark(U21(X1,X2)) -> a__U21(mark(X1),X2)
 mark(U22(X1,X2)) -> a__U22(mark(X1),X2)
 mark(U31(X1,X2)) -> a__U31(mark(X1),X2)
 mark(U32(X1,X2)) -> a__U32(mark(X1),X2)
 mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3)
 mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3)
 mark(head(X)) -> a__head(mark(X))
 mark(afterNth(X1,X2)) -> a__afterNth(mark(X1),mark(X2))
 mark(U51(X1,X2)) -> a__U51(mark(X1),X2)
 mark(U52(X1,X2)) -> a__U52(mark(X1),X2)
 mark(U61(X1,X2,X3,X4)) -> a__U61(mark(X1),X2,X3,X4)
 mark(U62(X1,X2,X3,X4)) -> a__U62(mark(X1),X2,X3,X4)
 mark(U63(X1,X2,X3,X4)) -> a__U63(mark(X1),X2,X3,X4)
 mark(U64(X1,X2)) -> a__U64(mark(X1),X2)
 mark(U71(X1,X2)) -> a__U71(mark(X1),X2)
 mark(U72(X1,X2)) -> a__U72(mark(X1),X2)
 mark(U81(X1,X2,X3)) -> a__U81(mark(X1),X2,X3)
 mark(U82(X1,X2,X3)) -> a__U82(mark(X1),X2,X3)
 mark(fst(X)) -> a__fst(mark(X))
 mark(natsFrom(X)) -> a__natsFrom(mark(X))
 mark(sel(X1,X2)) -> a__sel(mark(X1),mark(X2))
 mark(tail(X)) -> a__tail(mark(X))
 mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
 mark(tt()) -> tt()
 mark(pair(X1,X2)) -> pair(mark(X1),mark(X2))
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(s(X)) -> s(mark(X))
 mark(0()) -> 0()
 mark(nil()) -> nil()
 a__U11(X1,X2,X3) -> U11(X1,X2,X3)
 a__U12(X1,X2,X3) -> U12(X1,X2,X3)
 a__snd(X) -> snd(X)
 a__splitAt(X1,X2) -> splitAt(X1,X2)
 a__U21(X1,X2) -> U21(X1,X2)
 a__U22(X1,X2) -> U22(X1,X2)
 a__U31(X1,X2) -> U31(X1,X2)
 a__U32(X1,X2) -> U32(X1,X2)
 a__U41(X1,X2,X3) -> U41(X1,X2,X3)
 a__U42(X1,X2,X3) -> U42(X1,X2,X3)
 a__head(X) -> head(X)
 a__afterNth(X1,X2) -> afterNth(X1,X2)
 a__U51(X1,X2) -> U51(X1,X2)
 a__U52(X1,X2) -> U52(X1,X2)
 a__U61(X1,X2,X3,X4) -> U61(X1,X2,X3,X4)
 a__U62(X1,X2,X3,X4) -> U62(X1,X2,X3,X4)
 a__U63(X1,X2,X3,X4) -> U63(X1,X2,X3,X4)
 a__U64(X1,X2) -> U64(X1,X2)
 a__U71(X1,X2) -> U71(X1,X2)
 a__U72(X1,X2) -> U72(X1,X2)
 a__U81(X1,X2,X3) -> U81(X1,X2,X3)
 a__U82(X1,X2,X3) -> U82(X1,X2,X3)
 a__fst(X) -> fst(X)
 a__natsFrom(X) -> natsFrom(X)
 a__sel(X1,X2) -> sel(X1,X2)
 a__tail(X) -> tail(X)
 a__take(X1,X2) -> take(X1,X2)

Proof:
 Open