MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            activate(n__take(X1,X2)) -> take(activate(X1),activate(X2))
            activate(n__zeros()) -> zeros()
            and(tt(),X) -> activate(X)
            length(cons(N,L)) -> s(length(activate(L)))
            length(nil()) -> 0()
            take(X1,X2) -> n__take(X1,X2)
            take(0(),IL) -> nil()
            take(s(M),cons(N,IL)) -> cons(N,n__take(M,activate(IL)))
            zeros() -> cons(0(),n__zeros())
            zeros() -> n__zeros()
        - Signature:
            {activate/1,and/2,length/1,take/2,zeros/0} / {0/0,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} and constructors {0,cons
            ,n__take,n__zeros,nil,s,tt}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          activate#(X) -> c_1()
          activate#(n__take(X1,X2)) -> c_2(take#(activate(X1),activate(X2)),activate#(X1),activate#(X2))
          activate#(n__zeros()) -> c_3(zeros#())
          and#(tt(),X) -> c_4(activate#(X))
          length#(cons(N,L)) -> c_5(length#(activate(L)),activate#(L))
          length#(nil()) -> c_6()
          take#(X1,X2) -> c_7()
          take#(0(),IL) -> c_8()
          take#(s(M),cons(N,IL)) -> c_9(activate#(IL))
          zeros#() -> c_10()
          zeros#() -> c_11()
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            activate#(X) -> c_1()
            activate#(n__take(X1,X2)) -> c_2(take#(activate(X1),activate(X2)),activate#(X1),activate#(X2))
            activate#(n__zeros()) -> c_3(zeros#())
            and#(tt(),X) -> c_4(activate#(X))
            length#(cons(N,L)) -> c_5(length#(activate(L)),activate#(L))
            length#(nil()) -> c_6()
            take#(X1,X2) -> c_7()
            take#(0(),IL) -> c_8()
            take#(s(M),cons(N,IL)) -> c_9(activate#(IL))
            zeros#() -> c_10()
            zeros#() -> c_11()
        - Weak TRS:
            activate(X) -> X
            activate(n__take(X1,X2)) -> take(activate(X1),activate(X2))
            activate(n__zeros()) -> zeros()
            and(tt(),X) -> activate(X)
            length(cons(N,L)) -> s(length(activate(L)))
            length(nil()) -> 0()
            take(X1,X2) -> n__take(X1,X2)
            take(0(),IL) -> nil()
            take(s(M),cons(N,IL)) -> cons(N,n__take(M,activate(IL)))
            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,cons/2
            ,n__take/2,n__zeros/0,nil/0,s/1,tt/0,c_1/0,c_2/3,c_3/1,c_4/1,c_5/2,c_6/0,c_7/0,c_8/0,c_9/1,c_10/0,c_11/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,and#,length#,take#,zeros#} and constructors {0
            ,cons,n__take,n__zeros,nil,s,tt}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          activate(X) -> X
          activate(n__take(X1,X2)) -> take(activate(X1),activate(X2))
          activate(n__zeros()) -> zeros()
          take(X1,X2) -> n__take(X1,X2)
          take(0(),IL) -> nil()
          take(s(M),cons(N,IL)) -> cons(N,n__take(M,activate(IL)))
          zeros() -> cons(0(),n__zeros())
          zeros() -> n__zeros()
          activate#(X) -> c_1()
          activate#(n__take(X1,X2)) -> c_2(take#(activate(X1),activate(X2)),activate#(X1),activate#(X2))
          activate#(n__zeros()) -> c_3(zeros#())
          and#(tt(),X) -> c_4(activate#(X))
          length#(cons(N,L)) -> c_5(length#(activate(L)),activate#(L))
          length#(nil()) -> c_6()
          take#(X1,X2) -> c_7()
          take#(0(),IL) -> c_8()
          take#(s(M),cons(N,IL)) -> c_9(activate#(IL))
          zeros#() -> c_10()
          zeros#() -> c_11()
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            activate#(X) -> c_1()
            activate#(n__take(X1,X2)) -> c_2(take#(activate(X1),activate(X2)),activate#(X1),activate#(X2))
            activate#(n__zeros()) -> c_3(zeros#())
            and#(tt(),X) -> c_4(activate#(X))
            length#(cons(N,L)) -> c_5(length#(activate(L)),activate#(L))
            length#(nil()) -> c_6()
            take#(X1,X2) -> c_7()
            take#(0(),IL) -> c_8()
            take#(s(M),cons(N,IL)) -> c_9(activate#(IL))
            zeros#() -> c_10()
            zeros#() -> c_11()
        - Weak TRS:
            activate(X) -> X
            activate(n__take(X1,X2)) -> take(activate(X1),activate(X2))
            activate(n__zeros()) -> zeros()
            take(X1,X2) -> n__take(X1,X2)
            take(0(),IL) -> nil()
            take(s(M),cons(N,IL)) -> cons(N,n__take(M,activate(IL)))
            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,cons/2
            ,n__take/2,n__zeros/0,nil/0,s/1,tt/0,c_1/0,c_2/3,c_3/1,c_4/1,c_5/2,c_6/0,c_7/0,c_8/0,c_9/1,c_10/0,c_11/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,and#,length#,take#,zeros#} and constructors {0
            ,cons,n__take,n__zeros,nil,s,tt}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,6,7,8,10,11}
        by application of
          Pre({1,6,7,8,10,11}) = {2,3,4,5,9}.
        Here rules are labelled as follows:
          1: activate#(X) -> c_1()
          2: activate#(n__take(X1,X2)) -> c_2(take#(activate(X1),activate(X2)),activate#(X1),activate#(X2))
          3: activate#(n__zeros()) -> c_3(zeros#())
          4: and#(tt(),X) -> c_4(activate#(X))
          5: length#(cons(N,L)) -> c_5(length#(activate(L)),activate#(L))
          6: length#(nil()) -> c_6()
          7: take#(X1,X2) -> c_7()
          8: take#(0(),IL) -> c_8()
          9: take#(s(M),cons(N,IL)) -> c_9(activate#(IL))
          10: zeros#() -> c_10()
          11: zeros#() -> c_11()
* Step 4: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            activate#(n__take(X1,X2)) -> c_2(take#(activate(X1),activate(X2)),activate#(X1),activate#(X2))
            activate#(n__zeros()) -> c_3(zeros#())
            and#(tt(),X) -> c_4(activate#(X))
            length#(cons(N,L)) -> c_5(length#(activate(L)),activate#(L))
            take#(s(M),cons(N,IL)) -> c_9(activate#(IL))
        - Weak DPs:
            activate#(X) -> c_1()
            length#(nil()) -> c_6()
            take#(X1,X2) -> c_7()
            take#(0(),IL) -> c_8()
            zeros#() -> c_10()
            zeros#() -> c_11()
        - Weak TRS:
            activate(X) -> X
            activate(n__take(X1,X2)) -> take(activate(X1),activate(X2))
            activate(n__zeros()) -> zeros()
            take(X1,X2) -> n__take(X1,X2)
            take(0(),IL) -> nil()
            take(s(M),cons(N,IL)) -> cons(N,n__take(M,activate(IL)))
            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,cons/2
            ,n__take/2,n__zeros/0,nil/0,s/1,tt/0,c_1/0,c_2/3,c_3/1,c_4/1,c_5/2,c_6/0,c_7/0,c_8/0,c_9/1,c_10/0,c_11/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,and#,length#,take#,zeros#} and constructors {0
            ,cons,n__take,n__zeros,nil,s,tt}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {2}
        by application of
          Pre({2}) = {1,3,4,5}.
        Here rules are labelled as follows:
          1: activate#(n__take(X1,X2)) -> c_2(take#(activate(X1),activate(X2)),activate#(X1),activate#(X2))
          2: activate#(n__zeros()) -> c_3(zeros#())
          3: and#(tt(),X) -> c_4(activate#(X))
          4: length#(cons(N,L)) -> c_5(length#(activate(L)),activate#(L))
          5: take#(s(M),cons(N,IL)) -> c_9(activate#(IL))
          6: activate#(X) -> c_1()
          7: length#(nil()) -> c_6()
          8: take#(X1,X2) -> c_7()
          9: take#(0(),IL) -> c_8()
          10: zeros#() -> c_10()
          11: zeros#() -> c_11()
* Step 5: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            activate#(n__take(X1,X2)) -> c_2(take#(activate(X1),activate(X2)),activate#(X1),activate#(X2))
            and#(tt(),X) -> c_4(activate#(X))
            length#(cons(N,L)) -> c_5(length#(activate(L)),activate#(L))
            take#(s(M),cons(N,IL)) -> c_9(activate#(IL))
        - Weak DPs:
            activate#(X) -> c_1()
            activate#(n__zeros()) -> c_3(zeros#())
            length#(nil()) -> c_6()
            take#(X1,X2) -> c_7()
            take#(0(),IL) -> c_8()
            zeros#() -> c_10()
            zeros#() -> c_11()
        - Weak TRS:
            activate(X) -> X
            activate(n__take(X1,X2)) -> take(activate(X1),activate(X2))
            activate(n__zeros()) -> zeros()
            take(X1,X2) -> n__take(X1,X2)
            take(0(),IL) -> nil()
            take(s(M),cons(N,IL)) -> cons(N,n__take(M,activate(IL)))
            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,cons/2
            ,n__take/2,n__zeros/0,nil/0,s/1,tt/0,c_1/0,c_2/3,c_3/1,c_4/1,c_5/2,c_6/0,c_7/0,c_8/0,c_9/1,c_10/0,c_11/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,and#,length#,take#,zeros#} and constructors {0
            ,cons,n__take,n__zeros,nil,s,tt}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:activate#(n__take(X1,X2)) -> c_2(take#(activate(X1),activate(X2)),activate#(X1),activate#(X2))
             -->_3 activate#(n__zeros()) -> c_3(zeros#()):6
             -->_2 activate#(n__zeros()) -> c_3(zeros#()):6
             -->_1 take#(s(M),cons(N,IL)) -> c_9(activate#(IL)):4
             -->_1 take#(0(),IL) -> c_8():9
             -->_1 take#(X1,X2) -> c_7():8
             -->_3 activate#(X) -> c_1():5
             -->_2 activate#(X) -> c_1():5
             -->_3 activate#(n__take(X1,X2)) -> c_2(take#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):1
             -->_2 activate#(n__take(X1,X2)) -> c_2(take#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):1
          
          2:S:and#(tt(),X) -> c_4(activate#(X))
             -->_1 activate#(n__zeros()) -> c_3(zeros#()):6
             -->_1 activate#(X) -> c_1():5
             -->_1 activate#(n__take(X1,X2)) -> c_2(take#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):1
          
          3:S:length#(cons(N,L)) -> c_5(length#(activate(L)),activate#(L))
             -->_2 activate#(n__zeros()) -> c_3(zeros#()):6
             -->_1 length#(nil()) -> c_6():7
             -->_2 activate#(X) -> c_1():5
             -->_1 length#(cons(N,L)) -> c_5(length#(activate(L)),activate#(L)):3
             -->_2 activate#(n__take(X1,X2)) -> c_2(take#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):1
          
          4:S:take#(s(M),cons(N,IL)) -> c_9(activate#(IL))
             -->_1 activate#(n__zeros()) -> c_3(zeros#()):6
             -->_1 activate#(X) -> c_1():5
             -->_1 activate#(n__take(X1,X2)) -> c_2(take#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):1
          
          5:W:activate#(X) -> c_1()
             
          
          6:W:activate#(n__zeros()) -> c_3(zeros#())
             -->_1 zeros#() -> c_11():11
             -->_1 zeros#() -> c_10():10
          
          7:W:length#(nil()) -> c_6()
             
          
          8:W:take#(X1,X2) -> c_7()
             
          
          9:W:take#(0(),IL) -> c_8()
             
          
          10:W:zeros#() -> c_10()
             
          
          11:W:zeros#() -> c_11()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          7: length#(nil()) -> c_6()
          8: take#(X1,X2) -> c_7()
          9: take#(0(),IL) -> c_8()
          5: activate#(X) -> c_1()
          6: activate#(n__zeros()) -> c_3(zeros#())
          10: zeros#() -> c_10()
          11: zeros#() -> c_11()
* Step 6: RemoveHeads MAYBE
    + Considered Problem:
        - Strict DPs:
            activate#(n__take(X1,X2)) -> c_2(take#(activate(X1),activate(X2)),activate#(X1),activate#(X2))
            and#(tt(),X) -> c_4(activate#(X))
            length#(cons(N,L)) -> c_5(length#(activate(L)),activate#(L))
            take#(s(M),cons(N,IL)) -> c_9(activate#(IL))
        - Weak TRS:
            activate(X) -> X
            activate(n__take(X1,X2)) -> take(activate(X1),activate(X2))
            activate(n__zeros()) -> zeros()
            take(X1,X2) -> n__take(X1,X2)
            take(0(),IL) -> nil()
            take(s(M),cons(N,IL)) -> cons(N,n__take(M,activate(IL)))
            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,cons/2
            ,n__take/2,n__zeros/0,nil/0,s/1,tt/0,c_1/0,c_2/3,c_3/1,c_4/1,c_5/2,c_6/0,c_7/0,c_8/0,c_9/1,c_10/0,c_11/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,and#,length#,take#,zeros#} and constructors {0
            ,cons,n__take,n__zeros,nil,s,tt}
    + Applied Processor:
        RemoveHeads
    + Details:
        Consider the dependency graph
        
        1:S:activate#(n__take(X1,X2)) -> c_2(take#(activate(X1),activate(X2)),activate#(X1),activate#(X2))
           -->_1 take#(s(M),cons(N,IL)) -> c_9(activate#(IL)):4
           -->_3 activate#(n__take(X1,X2)) -> c_2(take#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):1
           -->_2 activate#(n__take(X1,X2)) -> c_2(take#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):1
        
        2:S:and#(tt(),X) -> c_4(activate#(X))
           -->_1 activate#(n__take(X1,X2)) -> c_2(take#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):1
        
        3:S:length#(cons(N,L)) -> c_5(length#(activate(L)),activate#(L))
           -->_1 length#(cons(N,L)) -> c_5(length#(activate(L)),activate#(L)):3
           -->_2 activate#(n__take(X1,X2)) -> c_2(take#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):1
        
        4:S:take#(s(M),cons(N,IL)) -> c_9(activate#(IL))
           -->_1 activate#(n__take(X1,X2)) -> c_2(take#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):1
        
        
        Following roots of the dependency graph are removed, as the considered set of starting terms is closed under reduction with respect to these rules (modulo compound contexts).
        
        [(2,and#(tt(),X) -> c_4(activate#(X)))]
* Step 7: Decompose MAYBE
    + Considered Problem:
        - Strict DPs:
            activate#(n__take(X1,X2)) -> c_2(take#(activate(X1),activate(X2)),activate#(X1),activate#(X2))
            length#(cons(N,L)) -> c_5(length#(activate(L)),activate#(L))
            take#(s(M),cons(N,IL)) -> c_9(activate#(IL))
        - Weak TRS:
            activate(X) -> X
            activate(n__take(X1,X2)) -> take(activate(X1),activate(X2))
            activate(n__zeros()) -> zeros()
            take(X1,X2) -> n__take(X1,X2)
            take(0(),IL) -> nil()
            take(s(M),cons(N,IL)) -> cons(N,n__take(M,activate(IL)))
            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,cons/2
            ,n__take/2,n__zeros/0,nil/0,s/1,tt/0,c_1/0,c_2/3,c_3/1,c_4/1,c_5/2,c_6/0,c_7/0,c_8/0,c_9/1,c_10/0,c_11/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,and#,length#,take#,zeros#} and constructors {0
            ,cons,n__take,n__zeros,nil,s,tt}
    + Applied Processor:
        Decompose {onSelection = all cycle independent sub-graph, withBound = RelativeAdd}
    + Details:
        We analyse the complexity of following sub-problems (R) and (S).
        Problem (S) is obtained from the input problem by shifting strict rules from (R) into the weak component.
        
        Problem (R)
          - Strict DPs:
              activate#(n__take(X1,X2)) -> c_2(take#(activate(X1),activate(X2)),activate#(X1),activate#(X2))
              take#(s(M),cons(N,IL)) -> c_9(activate#(IL))
          - Weak DPs:
              length#(cons(N,L)) -> c_5(length#(activate(L)),activate#(L))
          - Weak TRS:
              activate(X) -> X
              activate(n__take(X1,X2)) -> take(activate(X1),activate(X2))
              activate(n__zeros()) -> zeros()
              take(X1,X2) -> n__take(X1,X2)
              take(0(),IL) -> nil()
              take(s(M),cons(N,IL)) -> cons(N,n__take(M,activate(IL)))
              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,cons/2
              ,n__take/2,n__zeros/0,nil/0,s/1,tt/0,c_1/0,c_2/3,c_3/1,c_4/1,c_5/2,c_6/0,c_7/0,c_8/0,c_9/1,c_10/0,c_11/0}
          - Obligation:
              innermost runtime complexity wrt. defined symbols {activate#,and#,length#,take#
              ,zeros#} and constructors {0,cons,n__take,n__zeros,nil,s,tt}
        
        Problem (S)
          - Strict DPs:
              length#(cons(N,L)) -> c_5(length#(activate(L)),activate#(L))
          - Weak DPs:
              activate#(n__take(X1,X2)) -> c_2(take#(activate(X1),activate(X2)),activate#(X1),activate#(X2))
              take#(s(M),cons(N,IL)) -> c_9(activate#(IL))
          - Weak TRS:
              activate(X) -> X
              activate(n__take(X1,X2)) -> take(activate(X1),activate(X2))
              activate(n__zeros()) -> zeros()
              take(X1,X2) -> n__take(X1,X2)
              take(0(),IL) -> nil()
              take(s(M),cons(N,IL)) -> cons(N,n__take(M,activate(IL)))
              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,cons/2
              ,n__take/2,n__zeros/0,nil/0,s/1,tt/0,c_1/0,c_2/3,c_3/1,c_4/1,c_5/2,c_6/0,c_7/0,c_8/0,c_9/1,c_10/0,c_11/0}
          - Obligation:
              innermost runtime complexity wrt. defined symbols {activate#,and#,length#,take#
              ,zeros#} and constructors {0,cons,n__take,n__zeros,nil,s,tt}
** Step 7.a:1: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          activate#(n__take(X1,X2)) -> c_2(take#(activate(X1),activate(X2)),activate#(X1),activate#(X2))
          take#(s(M),cons(N,IL)) -> c_9(activate#(IL))
      - Weak DPs:
          length#(cons(N,L)) -> c_5(length#(activate(L)),activate#(L))
      - Weak TRS:
          activate(X) -> X
          activate(n__take(X1,X2)) -> take(activate(X1),activate(X2))
          activate(n__zeros()) -> zeros()
          take(X1,X2) -> n__take(X1,X2)
          take(0(),IL) -> nil()
          take(s(M),cons(N,IL)) -> cons(N,n__take(M,activate(IL)))
          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,cons/2
          ,n__take/2,n__zeros/0,nil/0,s/1,tt/0,c_1/0,c_2/3,c_3/1,c_4/1,c_5/2,c_6/0,c_7/0,c_8/0,c_9/1,c_10/0,c_11/0}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {activate#,and#,length#,take#,zeros#} and constructors {0
          ,cons,n__take,n__zeros,nil,s,tt}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
** Step 7.b:1: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            length#(cons(N,L)) -> c_5(length#(activate(L)),activate#(L))
        - Weak DPs:
            activate#(n__take(X1,X2)) -> c_2(take#(activate(X1),activate(X2)),activate#(X1),activate#(X2))
            take#(s(M),cons(N,IL)) -> c_9(activate#(IL))
        - Weak TRS:
            activate(X) -> X
            activate(n__take(X1,X2)) -> take(activate(X1),activate(X2))
            activate(n__zeros()) -> zeros()
            take(X1,X2) -> n__take(X1,X2)
            take(0(),IL) -> nil()
            take(s(M),cons(N,IL)) -> cons(N,n__take(M,activate(IL)))
            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,cons/2
            ,n__take/2,n__zeros/0,nil/0,s/1,tt/0,c_1/0,c_2/3,c_3/1,c_4/1,c_5/2,c_6/0,c_7/0,c_8/0,c_9/1,c_10/0,c_11/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,and#,length#,take#,zeros#} and constructors {0
            ,cons,n__take,n__zeros,nil,s,tt}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:length#(cons(N,L)) -> c_5(length#(activate(L)),activate#(L))
             -->_2 activate#(n__take(X1,X2)) -> c_2(take#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):2
             -->_1 length#(cons(N,L)) -> c_5(length#(activate(L)),activate#(L)):1
          
          2:W:activate#(n__take(X1,X2)) -> c_2(take#(activate(X1),activate(X2)),activate#(X1),activate#(X2))
             -->_1 take#(s(M),cons(N,IL)) -> c_9(activate#(IL)):3
             -->_3 activate#(n__take(X1,X2)) -> c_2(take#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):2
             -->_2 activate#(n__take(X1,X2)) -> c_2(take#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):2
          
          3:W:take#(s(M),cons(N,IL)) -> c_9(activate#(IL))
             -->_1 activate#(n__take(X1,X2)) -> c_2(take#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):2
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          2: activate#(n__take(X1,X2)) -> c_2(take#(activate(X1),activate(X2)),activate#(X1),activate#(X2))
          3: take#(s(M),cons(N,IL)) -> c_9(activate#(IL))
** Step 7.b:2: SimplifyRHS MAYBE
    + Considered Problem:
        - Strict DPs:
            length#(cons(N,L)) -> c_5(length#(activate(L)),activate#(L))
        - Weak TRS:
            activate(X) -> X
            activate(n__take(X1,X2)) -> take(activate(X1),activate(X2))
            activate(n__zeros()) -> zeros()
            take(X1,X2) -> n__take(X1,X2)
            take(0(),IL) -> nil()
            take(s(M),cons(N,IL)) -> cons(N,n__take(M,activate(IL)))
            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,cons/2
            ,n__take/2,n__zeros/0,nil/0,s/1,tt/0,c_1/0,c_2/3,c_3/1,c_4/1,c_5/2,c_6/0,c_7/0,c_8/0,c_9/1,c_10/0,c_11/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,and#,length#,take#,zeros#} and constructors {0
            ,cons,n__take,n__zeros,nil,s,tt}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:length#(cons(N,L)) -> c_5(length#(activate(L)),activate#(L))
             -->_1 length#(cons(N,L)) -> c_5(length#(activate(L)),activate#(L)):1
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          length#(cons(N,L)) -> c_5(length#(activate(L)))
** Step 7.b:3: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          length#(cons(N,L)) -> c_5(length#(activate(L)))
      - Weak TRS:
          activate(X) -> X
          activate(n__take(X1,X2)) -> take(activate(X1),activate(X2))
          activate(n__zeros()) -> zeros()
          take(X1,X2) -> n__take(X1,X2)
          take(0(),IL) -> nil()
          take(s(M),cons(N,IL)) -> cons(N,n__take(M,activate(IL)))
          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,cons/2
          ,n__take/2,n__zeros/0,nil/0,s/1,tt/0,c_1/0,c_2/3,c_3/1,c_4/1,c_5/1,c_6/0,c_7/0,c_8/0,c_9/1,c_10/0,c_11/0}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {activate#,and#,length#,take#,zeros#} and constructors {0
          ,cons,n__take,n__zeros,nil,s,tt}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE