(VAR L IL M N X V1 V V2 X1 X2) (RULES zeros -> cons(0,n__zeros) U11(tt,L) -> s(length(activate(L))) U21(tt) -> nil U31(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)) -> isNatList(activate(V1)) isNat(n__s(V1)) -> isNat(activate(V1)) isNatIList(V) -> isNatList(activate(V)) isNatIList(n__zeros) -> tt isNatIList(n__cons(V1,V2)) -> and(isNat(activate(V1)),n__isNatIList(activate(V2))) isNatList(n__nil) -> tt isNatList(n__cons(V1,V2)) -> and(isNat(activate(V1)),n__isNatList(activate(V2))) isNatList(n__take(V1,V2)) -> and(isNat(activate(V1)),n__isNatIList(activate(V2))) length(nil) -> 0 length(cons(N,L)) -> U11(and(isNatList(activate(L)),n__isNat(N)),activate(L)) take(0,IL) -> U21(isNatIList(IL)) take(s(M),cons(N,IL)) -> U31(and(isNatIList(activate(IL)),n__and(isNat(M),n__isNat(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) isNatIList(X) -> n__isNatIList(X) nil -> n__nil isNatList(X) -> n__isNatList(X) isNat(X) -> n__isNat(X) and(X1,X2) -> n__and(X1,X2) activate(n__zeros) -> zeros activate(n__take(X1,X2)) -> take(X1,X2) activate(n__0) -> 0 activate(n__length(X)) -> length(X) activate(n__s(X)) -> s(X) activate(n__cons(X1,X2)) -> cons(X1,X2) activate(n__isNatIList(X)) -> isNatIList(X) activate(n__nil) -> nil activate(n__isNatList(X)) -> isNatList(X) activate(n__isNat(X)) -> isNat(X) activate(n__and(X1,X2)) -> and(X1,X2) activate(X) -> X )