/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__zeros() -> cons(0(),zeros())
 a__U11(tt(),V1) -> a__U12(a__isNatList(V1))
 a__U12(tt()) -> tt()
 a__U21(tt(),V1) -> a__U22(a__isNat(V1))
 a__U22(tt()) -> tt()
 a__U31(tt(),V) -> a__U32(a__isNatList(V))
 a__U32(tt()) -> tt()
 a__U41(tt(),V1,V2) -> a__U42(a__isNat(V1),V2)
 a__U42(tt(),V2) -> a__U43(a__isNatIList(V2))
 a__U43(tt()) -> tt()
 a__U51(tt(),V1,V2) -> a__U52(a__isNat(V1),V2)
 a__U52(tt(),V2) -> a__U53(a__isNatList(V2))
 a__U53(tt()) -> tt()
 a__U61(tt(),V1,V2) -> a__U62(a__isNat(V1),V2)
 a__U62(tt(),V2) -> a__U63(a__isNatIList(V2))
 a__U63(tt()) -> tt()
 a__U71(tt(),L) -> s(a__length(mark(L)))
 a__U81(tt()) -> nil()
 a__U91(tt(),IL,M,N) -> cons(mark(N),take(M,IL))
 a__and(tt(),X) -> mark(X)
 a__isNat(0()) -> tt()
 a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1)
 a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1)
 a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V)
 a__isNatIList(zeros()) -> tt()
 a__isNatIList(cons(V1,V2)) -> a__U41(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2)
 a__isNatIListKind(nil()) -> tt()
 a__isNatIListKind(zeros()) -> tt()
 a__isNatIListKind(cons(V1,V2)) -> a__and(a__isNatKind(V1),isNatIListKind(V2))
 a__isNatIListKind(take(V1,V2)) -> a__and(a__isNatKind(V1),isNatIListKind(V2))
 a__isNatKind(0()) -> tt()
 a__isNatKind(length(V1)) -> a__isNatIListKind(V1)
 a__isNatKind(s(V1)) -> a__isNatKind(V1)
 a__isNatList(nil()) -> tt()
 a__isNatList(cons(V1,V2)) -> a__U51(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2)
 a__isNatList(take(V1,V2)) -> a__U61(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2)
 a__length(nil()) -> 0()
 a__length(cons(N,L)) ->
 a__U71(a__and(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N),isNatKind(N))),L)
 a__take(0(),IL) -> a__U81(a__and(a__isNatIList(IL),isNatIListKind(IL)))
 a__take(s(M),cons(N,IL)) ->
 a__U91(a__and(a__and(a__isNatIList(IL),isNatIListKind(IL)),and(and(isNat(M),isNatKind(M)),
                                                                and(isNat(N),isNatKind(N)))),
        IL,M,N)
 mark(zeros()) -> a__zeros()
 mark(U11(X1,X2)) -> a__U11(mark(X1),X2)
 mark(U12(X)) -> a__U12(mark(X))
 mark(isNatList(X)) -> a__isNatList(X)
 mark(U21(X1,X2)) -> a__U21(mark(X1),X2)
 mark(U22(X)) -> a__U22(mark(X))
 mark(isNat(X)) -> a__isNat(X)
 mark(U31(X1,X2)) -> a__U31(mark(X1),X2)
 mark(U32(X)) -> a__U32(mark(X))
 mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3)
 mark(U42(X1,X2)) -> a__U42(mark(X1),X2)
 mark(U43(X)) -> a__U43(mark(X))
 mark(isNatIList(X)) -> a__isNatIList(X)
 mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3)
 mark(U52(X1,X2)) -> a__U52(mark(X1),X2)
 mark(U53(X)) -> a__U53(mark(X))
 mark(U61(X1,X2,X3)) -> a__U61(mark(X1),X2,X3)
 mark(U62(X1,X2)) -> a__U62(mark(X1),X2)
 mark(U63(X)) -> a__U63(mark(X))
 mark(U71(X1,X2)) -> a__U71(mark(X1),X2)
 mark(length(X)) -> a__length(mark(X))
 mark(U81(X)) -> a__U81(mark(X))
 mark(U91(X1,X2,X3,X4)) -> a__U91(mark(X1),X2,X3,X4)
 mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
 mark(and(X1,X2)) -> a__and(mark(X1),X2)
 mark(isNatIListKind(X)) -> a__isNatIListKind(X)
 mark(isNatKind(X)) -> a__isNatKind(X)
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(0()) -> 0()
 mark(tt()) -> tt()
 mark(s(X)) -> s(mark(X))
 mark(nil()) -> nil()
 a__zeros() -> zeros()
 a__U11(X1,X2) -> U11(X1,X2)
 a__U12(X) -> U12(X)
 a__isNatList(X) -> isNatList(X)
 a__U21(X1,X2) -> U21(X1,X2)
 a__U22(X) -> U22(X)
 a__isNat(X) -> isNat(X)
 a__U31(X1,X2) -> U31(X1,X2)
 a__U32(X) -> U32(X)
 a__U41(X1,X2,X3) -> U41(X1,X2,X3)
 a__U42(X1,X2) -> U42(X1,X2)
 a__U43(X) -> U43(X)
 a__isNatIList(X) -> isNatIList(X)
 a__U51(X1,X2,X3) -> U51(X1,X2,X3)
 a__U52(X1,X2) -> U52(X1,X2)
 a__U53(X) -> U53(X)
 a__U61(X1,X2,X3) -> U61(X1,X2,X3)
 a__U62(X1,X2) -> U62(X1,X2)
 a__U63(X) -> U63(X)
 a__U71(X1,X2) -> U71(X1,X2)
 a__length(X) -> length(X)
 a__U81(X) -> U81(X)
 a__U91(X1,X2,X3,X4) -> U91(X1,X2,X3,X4)
 a__take(X1,X2) -> take(X1,X2)
 a__and(X1,X2) -> and(X1,X2)
 a__isNatIListKind(X) -> isNatIListKind(X)
 a__isNatKind(X) -> isNatKind(X)

Proof:
 Open