(VAR L IL M N X1 X2 X3 X4 X)
(RULES 
active(zeros) -> mark(cons(0,zeros))
active(U11(tt,L)) -> mark(U12(tt,L))
active(U12(tt,L)) -> mark(s(length(L)))
active(U21(tt,IL,M,N)) -> mark(U22(tt,IL,M,N))
active(U22(tt,IL,M,N)) -> mark(U23(tt,IL,M,N))
active(U23(tt,IL,M,N)) -> mark(cons(N,take(M,IL)))
active(length(nil)) -> mark(0)
active(length(cons(N,L))) -> mark(U11(tt,L))
active(take(0,IL)) -> mark(nil)
active(take(s(M),cons(N,IL))) -> mark(U21(tt,IL,M,N))
active(cons(X1,X2)) -> cons(active(X1),X2)
active(U11(X1,X2)) -> U11(active(X1),X2)
active(U12(X1,X2)) -> U12(active(X1),X2)
active(s(X)) -> s(active(X))
active(length(X)) -> length(active(X))
active(U21(X1,X2,X3,X4)) -> U21(active(X1),X2,X3,X4)
active(U22(X1,X2,X3,X4)) -> U22(active(X1),X2,X3,X4)
active(U23(X1,X2,X3,X4)) -> U23(active(X1),X2,X3,X4)
active(take(X1,X2)) -> take(active(X1),X2)
active(take(X1,X2)) -> take(X1,active(X2))
cons(mark(X1),X2) -> mark(cons(X1,X2))
U11(mark(X1),X2) -> mark(U11(X1,X2))
U12(mark(X1),X2) -> mark(U12(X1,X2))
s(mark(X)) -> mark(s(X))
length(mark(X)) -> mark(length(X))
U21(mark(X1),X2,X3,X4) -> mark(U21(X1,X2,X3,X4))
U22(mark(X1),X2,X3,X4) -> mark(U22(X1,X2,X3,X4))
U23(mark(X1),X2,X3,X4) -> mark(U23(X1,X2,X3,X4))
take(mark(X1),X2) -> mark(take(X1,X2))
take(X1,mark(X2)) -> mark(take(X1,X2))
proper(zeros) -> ok(zeros)
proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
proper(0) -> ok(0)
proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
proper(tt) -> ok(tt)
proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
proper(s(X)) -> s(proper(X))
proper(length(X)) -> length(proper(X))
proper(U21(X1,X2,X3,X4)) -> U21(proper(X1),proper(X2),proper(X3),proper(X4))
proper(U22(X1,X2,X3,X4)) -> U22(proper(X1),proper(X2),proper(X3),proper(X4))
proper(U23(X1,X2,X3,X4)) -> U23(proper(X1),proper(X2),proper(X3),proper(X4))
proper(take(X1,X2)) -> take(proper(X1),proper(X2))
proper(nil) -> ok(nil)
cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
s(ok(X)) -> ok(s(X))
length(ok(X)) -> ok(length(X))
U21(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U21(X1,X2,X3,X4))
U22(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U22(X1,X2,X3,X4))
U23(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U23(X1,X2,X3,X4))
take(ok(X1),ok(X2)) -> ok(take(X1,X2))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
)