(VAR T IL N L M X1 X2 X3 X4 X)
(RULES 
active(and(tt,T)) -> mark(T)
active(isNatIList(IL)) -> mark(isNatList(IL))
active(isNat(0)) -> mark(tt)
active(isNat(s(N))) -> mark(isNat(N))
active(isNat(length(L))) -> mark(isNatList(L))
active(isNatIList(zeros)) -> mark(tt)
active(isNatIList(cons(N,IL))) -> mark(and(isNat(N),isNatIList(IL)))
active(isNatList(nil)) -> mark(tt)
active(isNatList(cons(N,L))) -> mark(and(isNat(N),isNatList(L)))
active(isNatList(take(N,IL))) -> mark(and(isNat(N),isNatIList(IL)))
active(zeros) -> mark(cons(0,zeros))
active(take(0,IL)) -> mark(uTake1(isNatIList(IL)))
active(uTake1(tt)) -> mark(nil)
active(take(s(M),cons(N,IL))) -> mark(uTake2(and(isNat(M),and(isNat(N),isNatIList(IL))),M,N,IL))
active(uTake2(tt,M,N,IL)) -> mark(cons(N,take(M,IL)))
active(length(cons(N,L))) -> mark(uLength(and(isNat(N),isNatList(L)),L))
active(uLength(tt,L)) -> mark(s(length(L)))
mark(and(X1,X2)) -> active(and(mark(X1),mark(X2)))
mark(tt) -> active(tt)
mark(isNatIList(X)) -> active(isNatIList(X))
mark(isNatList(X)) -> active(isNatList(X))
mark(isNat(X)) -> active(isNat(X))
mark(0) -> active(0)
mark(s(X)) -> active(s(mark(X)))
mark(length(X)) -> active(length(mark(X)))
mark(zeros) -> active(zeros)
mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
mark(nil) -> active(nil)
mark(take(X1,X2)) -> active(take(mark(X1),mark(X2)))
mark(uTake1(X)) -> active(uTake1(mark(X)))
mark(uTake2(X1,X2,X3,X4)) -> active(uTake2(mark(X1),X2,X3,X4))
mark(uLength(X1,X2)) -> active(uLength(mark(X1),X2))
and(mark(X1),X2) -> and(X1,X2)
and(X1,mark(X2)) -> and(X1,X2)
and(active(X1),X2) -> and(X1,X2)
and(X1,active(X2)) -> and(X1,X2)
isNatIList(mark(X)) -> isNatIList(X)
isNatIList(active(X)) -> isNatIList(X)
isNatList(mark(X)) -> isNatList(X)
isNatList(active(X)) -> isNatList(X)
isNat(mark(X)) -> isNat(X)
isNat(active(X)) -> isNat(X)
s(mark(X)) -> s(X)
s(active(X)) -> s(X)
length(mark(X)) -> length(X)
length(active(X)) -> length(X)
cons(mark(X1),X2) -> cons(X1,X2)
cons(X1,mark(X2)) -> cons(X1,X2)
cons(active(X1),X2) -> cons(X1,X2)
cons(X1,active(X2)) -> cons(X1,X2)
take(mark(X1),X2) -> take(X1,X2)
take(X1,mark(X2)) -> take(X1,X2)
take(active(X1),X2) -> take(X1,X2)
take(X1,active(X2)) -> take(X1,X2)
uTake1(mark(X)) -> uTake1(X)
uTake1(active(X)) -> uTake1(X)
uTake2(mark(X1),X2,X3,X4) -> uTake2(X1,X2,X3,X4)
uTake2(X1,mark(X2),X3,X4) -> uTake2(X1,X2,X3,X4)
uTake2(X1,X2,mark(X3),X4) -> uTake2(X1,X2,X3,X4)
uTake2(X1,X2,X3,mark(X4)) -> uTake2(X1,X2,X3,X4)
uTake2(active(X1),X2,X3,X4) -> uTake2(X1,X2,X3,X4)
uTake2(X1,active(X2),X3,X4) -> uTake2(X1,X2,X3,X4)
uTake2(X1,X2,active(X3),X4) -> uTake2(X1,X2,X3,X4)
uTake2(X1,X2,X3,active(X4)) -> uTake2(X1,X2,X3,X4)
uLength(mark(X1),X2) -> uLength(X1,X2)
uLength(X1,mark(X2)) -> uLength(X1,X2)
uLength(active(X1),X2) -> uLength(X1,X2)
uLength(X1,active(X2)) -> uLength(X1,X2)
)