(VAR V1 V V2 L IL M N X X1 X2) (RULES zeros -> cons(0,n__zeros) U11(tt,V1) -> U12(isNatList(activate(V1))) U12(tt) -> tt U21(tt,V1) -> U22(isNat(activate(V1))) U22(tt) -> tt U31(tt,V) -> U32(isNatList(activate(V))) U32(tt) -> tt U41(tt,V1,V2) -> U42(isNat(activate(V1)),activate(V2)) U42(tt,V2) -> U43(isNatIList(activate(V2))) U43(tt) -> tt U51(tt,V1,V2) -> U52(isNat(activate(V1)),activate(V2)) U52(tt,V2) -> U53(isNatList(activate(V2))) U53(tt) -> tt U61(tt,V1,V2) -> U62(isNat(activate(V1)),activate(V2)) U62(tt,V2) -> U63(isNatIList(activate(V2))) U63(tt) -> tt U71(tt,L) -> s(length(activate(L))) U81(tt) -> nil U91(tt,IL,M,N) -> cons(activate(N),n__take(activate(M),activate(IL))) and(tt,X) -> activate(X) isNat(n__0) -> tt isNat(n__length(V1)) -> U11(isNatIListKind(activate(V1)),activate(V1)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNatIList(V) -> U31(isNatIListKind(activate(V)),activate(V)) isNatIList(n__zeros) -> tt isNatIList(n__cons(V1,V2)) -> U41(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))),activate(V1),activate(V2)) isNatIListKind(n__nil) -> tt isNatIListKind(n__zeros) -> tt isNatIListKind(n__cons(V1,V2)) -> and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))) isNatIListKind(n__take(V1,V2)) -> and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))) isNatKind(n__0) -> tt isNatKind(n__length(V1)) -> isNatIListKind(activate(V1)) isNatKind(n__s(V1)) -> isNatKind(activate(V1)) isNatList(n__nil) -> tt isNatList(n__cons(V1,V2)) -> U51(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))),activate(V1),activate(V2)) isNatList(n__take(V1,V2)) -> U61(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))),activate(V1),activate(V2)) length(nil) -> 0 length(cons(N,L)) -> U71(and(and(isNatList(activate(L)),n__isNatIListKind(activate(L))),n__and(n__isNat(N),n__isNatKind(N))),activate(L)) take(0,IL) -> U81(and(isNatIList(IL),n__isNatIListKind(IL))) take(s(M),cons(N,IL)) -> U91(and(and(isNatIList(activate(IL)),n__isNatIListKind(activate(IL))),n__and(n__and(n__isNat(M),n__isNatKind(M)),n__and(n__isNat(N),n__isNatKind(N)))),activate(IL),M,N) zeros -> n__zeros take(X1,X2) -> n__take(X1,X2) 0 -> n__0 length(X) -> n__length(X) s(X) -> n__s(X) cons(X1,X2) -> n__cons(X1,X2) isNatIListKind(X) -> n__isNatIListKind(X) nil -> n__nil and(X1,X2) -> n__and(X1,X2) isNat(X) -> n__isNat(X) isNatKind(X) -> n__isNatKind(X) activate(n__zeros) -> zeros activate(n__take(X1,X2)) -> take(activate(X1),activate(X2)) activate(n__0) -> 0 activate(n__length(X)) -> length(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__cons(X1,X2)) -> cons(activate(X1),X2) activate(n__isNatIListKind(X)) -> isNatIListKind(X) activate(n__nil) -> nil activate(n__and(X1,X2)) -> and(activate(X1),X2) activate(n__isNat(X)) -> isNat(X) activate(n__isNatKind(X)) -> isNatKind(X) activate(X) -> X )