(VAR V1 V V2 L IL M N X X1 X2 X3 X4) (RULES 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) )