(VAR T IL N L M X1 X2 X) (RULES and(tt,T) -> T isNatIList(IL) -> isNatList(activate(IL)) isNat(n__0) -> tt isNat(n__s(N)) -> isNat(activate(N)) isNat(n__length(L)) -> isNatList(activate(L)) isNatIList(n__zeros) -> tt isNatIList(n__cons(N,IL)) -> and(isNat(activate(N)),isNatIList(activate(IL))) isNatList(n__nil) -> tt isNatList(n__cons(N,L)) -> and(isNat(activate(N)),isNatList(activate(L))) isNatList(n__take(N,IL)) -> and(isNat(activate(N)),isNatIList(activate(IL))) zeros -> cons(0,n__zeros) take(0,IL) -> uTake1(isNatIList(IL)) uTake1(tt) -> nil take(s(M),cons(N,IL)) -> uTake2(and(isNat(M),and(isNat(N),isNatIList(activate(IL)))),M,N,activate(IL)) uTake2(tt,M,N,IL) -> cons(activate(N),n__take(activate(M),activate(IL))) length(cons(N,L)) -> uLength(and(isNat(N),isNatList(activate(L))),activate(L)) uLength(tt,L) -> s(length(activate(L))) 0 -> n__0 s(X) -> n__s(X) length(X) -> n__length(X) zeros -> n__zeros cons(X1,X2) -> n__cons(X1,X2) nil -> n__nil take(X1,X2) -> n__take(X1,X2) activate(n__0) -> 0 activate(n__s(X)) -> s(X) activate(n__length(X)) -> length(X) activate(n__zeros) -> zeros activate(n__cons(X1,X2)) -> cons(X1,X2) activate(n__nil) -> nil activate(n__take(X1,X2)) -> take(X1,X2) activate(X) -> X )