WORST_CASE(Omega(n^1),?)
* Step 1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            ACTIVATE(z0) -> c11()
            ACTIVATE(n__take(z0,z1)) -> c10(TAKE(activate(z0),activate(z1)),ACTIVATE(z1))
            ACTIVATE(n__take(z0,z1)) -> c9(TAKE(activate(z0),activate(z1)),ACTIVATE(z0))
            ACTIVATE(n__zeros()) -> c8(ZEROS())
            AND(tt(),z0) -> c2(ACTIVATE(z0))
            LENGTH(cons(z0,z1)) -> c4(LENGTH(activate(z1)),ACTIVATE(z1))
            LENGTH(nil()) -> c3()
            TAKE(z0,z1) -> c7()
            TAKE(0(),z0) -> c5()
            TAKE(s(z0),cons(z1,z2)) -> c6(ACTIVATE(z2))
            ZEROS() -> c()
            ZEROS() -> c1()
        - Weak TRS:
            activate(z0) -> z0
            activate(n__take(z0,z1)) -> take(activate(z0),activate(z1))
            activate(n__zeros()) -> zeros()
            and(tt(),z0) -> activate(z0)
            length(cons(z0,z1)) -> s(length(activate(z1)))
            length(nil()) -> 0()
            take(z0,z1) -> n__take(z0,z1)
            take(0(),z0) -> nil()
            take(s(z0),cons(z1,z2)) -> cons(z1,n__take(z0,activate(z2)))
            zeros() -> cons(0(),n__zeros())
            zeros() -> n__zeros()
        - Signature:
            {ACTIVATE/1,AND/2,LENGTH/1,TAKE/2,ZEROS/0,activate/1,and/2,length/1,take/2,zeros/0} / {0/0,c/0,c1/0,c10/2
            ,c11/0,c2/1,c3/0,c4/2,c5/0,c6/1,c7/0,c8/1,c9/2,cons/2,n__take/2,n__zeros/0,nil/0,s/1,tt/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {ACTIVATE,AND,LENGTH,TAKE,ZEROS,activate,and,length,take
            ,zeros} and constructors {0,c,c1,c10,c11,c2,c3,c4,c5,c6,c7,c8,c9,cons,n__take,n__zeros,nil,s,tt}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            ACTIVATE(z0) -> c11()
            ACTIVATE(n__take(z0,z1)) -> c10(TAKE(activate(z0),activate(z1)),ACTIVATE(z1))
            ACTIVATE(n__take(z0,z1)) -> c9(TAKE(activate(z0),activate(z1)),ACTIVATE(z0))
            ACTIVATE(n__zeros()) -> c8(ZEROS())
            AND(tt(),z0) -> c2(ACTIVATE(z0))
            LENGTH(cons(z0,z1)) -> c4(LENGTH(activate(z1)),ACTIVATE(z1))
            LENGTH(nil()) -> c3()
            TAKE(z0,z1) -> c7()
            TAKE(0(),z0) -> c5()
            TAKE(s(z0),cons(z1,z2)) -> c6(ACTIVATE(z2))
            ZEROS() -> c()
            ZEROS() -> c1()
        - Weak TRS:
            activate(z0) -> z0
            activate(n__take(z0,z1)) -> take(activate(z0),activate(z1))
            activate(n__zeros()) -> zeros()
            and(tt(),z0) -> activate(z0)
            length(cons(z0,z1)) -> s(length(activate(z1)))
            length(nil()) -> 0()
            take(z0,z1) -> n__take(z0,z1)
            take(0(),z0) -> nil()
            take(s(z0),cons(z1,z2)) -> cons(z1,n__take(z0,activate(z2)))
            zeros() -> cons(0(),n__zeros())
            zeros() -> n__zeros()
        - Signature:
            {ACTIVATE/1,AND/2,LENGTH/1,TAKE/2,ZEROS/0,activate/1,and/2,length/1,take/2,zeros/0} / {0/0,c/0,c1/0,c10/2
            ,c11/0,c2/1,c3/0,c4/2,c5/0,c6/1,c7/0,c8/1,c9/2,cons/2,n__take/2,n__zeros/0,nil/0,s/1,tt/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {ACTIVATE,AND,LENGTH,TAKE,ZEROS,activate,and,length,take
            ,zeros} and constructors {0,c,c1,c10,c11,c2,c3,c4,c5,c6,c7,c8,c9,cons,n__take,n__zeros,nil,s,tt}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            ACTIVATE(z0) -> c11()
            ACTIVATE(n__take(z0,z1)) -> c10(TAKE(activate(z0),activate(z1)),ACTIVATE(z1))
            ACTIVATE(n__take(z0,z1)) -> c9(TAKE(activate(z0),activate(z1)),ACTIVATE(z0))
            ACTIVATE(n__zeros()) -> c8(ZEROS())
            AND(tt(),z0) -> c2(ACTIVATE(z0))
            LENGTH(cons(z0,z1)) -> c4(LENGTH(activate(z1)),ACTIVATE(z1))
            LENGTH(nil()) -> c3()
            TAKE(z0,z1) -> c7()
            TAKE(0(),z0) -> c5()
            TAKE(s(z0),cons(z1,z2)) -> c6(ACTIVATE(z2))
            ZEROS() -> c()
            ZEROS() -> c1()
        - Weak TRS:
            activate(z0) -> z0
            activate(n__take(z0,z1)) -> take(activate(z0),activate(z1))
            activate(n__zeros()) -> zeros()
            and(tt(),z0) -> activate(z0)
            length(cons(z0,z1)) -> s(length(activate(z1)))
            length(nil()) -> 0()
            take(z0,z1) -> n__take(z0,z1)
            take(0(),z0) -> nil()
            take(s(z0),cons(z1,z2)) -> cons(z1,n__take(z0,activate(z2)))
            zeros() -> cons(0(),n__zeros())
            zeros() -> n__zeros()
        - Signature:
            {ACTIVATE/1,AND/2,LENGTH/1,TAKE/2,ZEROS/0,activate/1,and/2,length/1,take/2,zeros/0} / {0/0,c/0,c1/0,c10/2
            ,c11/0,c2/1,c3/0,c4/2,c5/0,c6/1,c7/0,c8/1,c9/2,cons/2,n__take/2,n__zeros/0,nil/0,s/1,tt/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {ACTIVATE,AND,LENGTH,TAKE,ZEROS,activate,and,length,take
            ,zeros} and constructors {0,c,c1,c10,c11,c2,c3,c4,c5,c6,c7,c8,c9,cons,n__take,n__zeros,nil,s,tt}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          ACTIVATE(y){y -> n__take(x,y)} =
            ACTIVATE(n__take(x,y)) ->^+ c10(TAKE(activate(x),activate(y)),ACTIVATE(y))
              = C[ACTIVATE(y) = ACTIVATE(y){}]

WORST_CASE(Omega(n^1),?)