MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            activate(n__cons(X1,X2)) -> cons(activate(X1),X2)
            activate(n__from(X)) -> from(activate(X))
            activate(n__nil()) -> nil()
            activate(n__s(X)) -> s(activate(X))
            cons(X1,X2) -> n__cons(X1,X2)
            from(X) -> cons(X,n__from(n__s(X)))
            from(X) -> n__from(X)
            length(n__cons(X,Y)) -> s(length1(activate(Y)))
            length(n__nil()) -> 0()
            length1(X) -> length(activate(X))
            nil() -> n__nil()
            s(X) -> n__s(X)
        - Signature:
            {activate/1,cons/2,from/1,length/1,length1/1,nil/0,s/1} / {0/0,n__cons/2,n__from/1,n__nil/0,n__s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate,cons,from,length,length1,nil
            ,s} and constructors {0,n__cons,n__from,n__nil,n__s}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          activate#(X) -> c_1()
          activate#(n__cons(X1,X2)) -> c_2(cons#(activate(X1),X2),activate#(X1))
          activate#(n__from(X)) -> c_3(from#(activate(X)),activate#(X))
          activate#(n__nil()) -> c_4(nil#())
          activate#(n__s(X)) -> c_5(s#(activate(X)),activate#(X))
          cons#(X1,X2) -> c_6()
          from#(X) -> c_7(cons#(X,n__from(n__s(X))))
          from#(X) -> c_8()
          length#(n__cons(X,Y)) -> c_9(s#(length1(activate(Y))),length1#(activate(Y)),activate#(Y))
          length#(n__nil()) -> c_10()
          length1#(X) -> c_11(length#(activate(X)),activate#(X))
          nil#() -> c_12()
          s#(X) -> c_13()
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            activate#(X) -> c_1()
            activate#(n__cons(X1,X2)) -> c_2(cons#(activate(X1),X2),activate#(X1))
            activate#(n__from(X)) -> c_3(from#(activate(X)),activate#(X))
            activate#(n__nil()) -> c_4(nil#())
            activate#(n__s(X)) -> c_5(s#(activate(X)),activate#(X))
            cons#(X1,X2) -> c_6()
            from#(X) -> c_7(cons#(X,n__from(n__s(X))))
            from#(X) -> c_8()
            length#(n__cons(X,Y)) -> c_9(s#(length1(activate(Y))),length1#(activate(Y)),activate#(Y))
            length#(n__nil()) -> c_10()
            length1#(X) -> c_11(length#(activate(X)),activate#(X))
            nil#() -> c_12()
            s#(X) -> c_13()
        - Weak TRS:
            activate(X) -> X
            activate(n__cons(X1,X2)) -> cons(activate(X1),X2)
            activate(n__from(X)) -> from(activate(X))
            activate(n__nil()) -> nil()
            activate(n__s(X)) -> s(activate(X))
            cons(X1,X2) -> n__cons(X1,X2)
            from(X) -> cons(X,n__from(n__s(X)))
            from(X) -> n__from(X)
            length(n__cons(X,Y)) -> s(length1(activate(Y)))
            length(n__nil()) -> 0()
            length1(X) -> length(activate(X))
            nil() -> n__nil()
            s(X) -> n__s(X)
        - Signature:
            {activate/1,cons/2,from/1,length/1,length1/1,nil/0,s/1,activate#/1,cons#/2,from#/1,length#/1,length1#/1
            ,nil#/0,s#/1} / {0/0,n__cons/2,n__from/1,n__nil/0,n__s/1,c_1/0,c_2/2,c_3/2,c_4/1,c_5/2,c_6/0,c_7/1,c_8/0
            ,c_9/3,c_10/0,c_11/2,c_12/0,c_13/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,cons#,from#,length#,length1#,nil#
            ,s#} and constructors {0,n__cons,n__from,n__nil,n__s}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,6,8,10,12,13}
        by application of
          Pre({1,6,8,10,12,13}) = {2,3,4,5,7,9,11}.
        Here rules are labelled as follows:
          1: activate#(X) -> c_1()
          2: activate#(n__cons(X1,X2)) -> c_2(cons#(activate(X1),X2),activate#(X1))
          3: activate#(n__from(X)) -> c_3(from#(activate(X)),activate#(X))
          4: activate#(n__nil()) -> c_4(nil#())
          5: activate#(n__s(X)) -> c_5(s#(activate(X)),activate#(X))
          6: cons#(X1,X2) -> c_6()
          7: from#(X) -> c_7(cons#(X,n__from(n__s(X))))
          8: from#(X) -> c_8()
          9: length#(n__cons(X,Y)) -> c_9(s#(length1(activate(Y))),length1#(activate(Y)),activate#(Y))
          10: length#(n__nil()) -> c_10()
          11: length1#(X) -> c_11(length#(activate(X)),activate#(X))
          12: nil#() -> c_12()
          13: s#(X) -> c_13()
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            activate#(n__cons(X1,X2)) -> c_2(cons#(activate(X1),X2),activate#(X1))
            activate#(n__from(X)) -> c_3(from#(activate(X)),activate#(X))
            activate#(n__nil()) -> c_4(nil#())
            activate#(n__s(X)) -> c_5(s#(activate(X)),activate#(X))
            from#(X) -> c_7(cons#(X,n__from(n__s(X))))
            length#(n__cons(X,Y)) -> c_9(s#(length1(activate(Y))),length1#(activate(Y)),activate#(Y))
            length1#(X) -> c_11(length#(activate(X)),activate#(X))
        - Weak DPs:
            activate#(X) -> c_1()
            cons#(X1,X2) -> c_6()
            from#(X) -> c_8()
            length#(n__nil()) -> c_10()
            nil#() -> c_12()
            s#(X) -> c_13()
        - Weak TRS:
            activate(X) -> X
            activate(n__cons(X1,X2)) -> cons(activate(X1),X2)
            activate(n__from(X)) -> from(activate(X))
            activate(n__nil()) -> nil()
            activate(n__s(X)) -> s(activate(X))
            cons(X1,X2) -> n__cons(X1,X2)
            from(X) -> cons(X,n__from(n__s(X)))
            from(X) -> n__from(X)
            length(n__cons(X,Y)) -> s(length1(activate(Y)))
            length(n__nil()) -> 0()
            length1(X) -> length(activate(X))
            nil() -> n__nil()
            s(X) -> n__s(X)
        - Signature:
            {activate/1,cons/2,from/1,length/1,length1/1,nil/0,s/1,activate#/1,cons#/2,from#/1,length#/1,length1#/1
            ,nil#/0,s#/1} / {0/0,n__cons/2,n__from/1,n__nil/0,n__s/1,c_1/0,c_2/2,c_3/2,c_4/1,c_5/2,c_6/0,c_7/1,c_8/0
            ,c_9/3,c_10/0,c_11/2,c_12/0,c_13/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,cons#,from#,length#,length1#,nil#
            ,s#} and constructors {0,n__cons,n__from,n__nil,n__s}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {3,5}
        by application of
          Pre({3,5}) = {1,2,4,6,7}.
        Here rules are labelled as follows:
          1: activate#(n__cons(X1,X2)) -> c_2(cons#(activate(X1),X2),activate#(X1))
          2: activate#(n__from(X)) -> c_3(from#(activate(X)),activate#(X))
          3: activate#(n__nil()) -> c_4(nil#())
          4: activate#(n__s(X)) -> c_5(s#(activate(X)),activate#(X))
          5: from#(X) -> c_7(cons#(X,n__from(n__s(X))))
          6: length#(n__cons(X,Y)) -> c_9(s#(length1(activate(Y))),length1#(activate(Y)),activate#(Y))
          7: length1#(X) -> c_11(length#(activate(X)),activate#(X))
          8: activate#(X) -> c_1()
          9: cons#(X1,X2) -> c_6()
          10: from#(X) -> c_8()
          11: length#(n__nil()) -> c_10()
          12: nil#() -> c_12()
          13: s#(X) -> c_13()
* Step 4: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            activate#(n__cons(X1,X2)) -> c_2(cons#(activate(X1),X2),activate#(X1))
            activate#(n__from(X)) -> c_3(from#(activate(X)),activate#(X))
            activate#(n__s(X)) -> c_5(s#(activate(X)),activate#(X))
            length#(n__cons(X,Y)) -> c_9(s#(length1(activate(Y))),length1#(activate(Y)),activate#(Y))
            length1#(X) -> c_11(length#(activate(X)),activate#(X))
        - Weak DPs:
            activate#(X) -> c_1()
            activate#(n__nil()) -> c_4(nil#())
            cons#(X1,X2) -> c_6()
            from#(X) -> c_7(cons#(X,n__from(n__s(X))))
            from#(X) -> c_8()
            length#(n__nil()) -> c_10()
            nil#() -> c_12()
            s#(X) -> c_13()
        - Weak TRS:
            activate(X) -> X
            activate(n__cons(X1,X2)) -> cons(activate(X1),X2)
            activate(n__from(X)) -> from(activate(X))
            activate(n__nil()) -> nil()
            activate(n__s(X)) -> s(activate(X))
            cons(X1,X2) -> n__cons(X1,X2)
            from(X) -> cons(X,n__from(n__s(X)))
            from(X) -> n__from(X)
            length(n__cons(X,Y)) -> s(length1(activate(Y)))
            length(n__nil()) -> 0()
            length1(X) -> length(activate(X))
            nil() -> n__nil()
            s(X) -> n__s(X)
        - Signature:
            {activate/1,cons/2,from/1,length/1,length1/1,nil/0,s/1,activate#/1,cons#/2,from#/1,length#/1,length1#/1
            ,nil#/0,s#/1} / {0/0,n__cons/2,n__from/1,n__nil/0,n__s/1,c_1/0,c_2/2,c_3/2,c_4/1,c_5/2,c_6/0,c_7/1,c_8/0
            ,c_9/3,c_10/0,c_11/2,c_12/0,c_13/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,cons#,from#,length#,length1#,nil#
            ,s#} and constructors {0,n__cons,n__from,n__nil,n__s}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:activate#(n__cons(X1,X2)) -> c_2(cons#(activate(X1),X2),activate#(X1))
             -->_2 activate#(n__nil()) -> c_4(nil#()):7
             -->_2 activate#(n__s(X)) -> c_5(s#(activate(X)),activate#(X)):3
             -->_2 activate#(n__from(X)) -> c_3(from#(activate(X)),activate#(X)):2
             -->_1 cons#(X1,X2) -> c_6():8
             -->_2 activate#(X) -> c_1():6
             -->_2 activate#(n__cons(X1,X2)) -> c_2(cons#(activate(X1),X2),activate#(X1)):1
          
          2:S:activate#(n__from(X)) -> c_3(from#(activate(X)),activate#(X))
             -->_1 from#(X) -> c_7(cons#(X,n__from(n__s(X)))):9
             -->_2 activate#(n__nil()) -> c_4(nil#()):7
             -->_2 activate#(n__s(X)) -> c_5(s#(activate(X)),activate#(X)):3
             -->_1 from#(X) -> c_8():10
             -->_2 activate#(X) -> c_1():6
             -->_2 activate#(n__from(X)) -> c_3(from#(activate(X)),activate#(X)):2
             -->_2 activate#(n__cons(X1,X2)) -> c_2(cons#(activate(X1),X2),activate#(X1)):1
          
          3:S:activate#(n__s(X)) -> c_5(s#(activate(X)),activate#(X))
             -->_2 activate#(n__nil()) -> c_4(nil#()):7
             -->_1 s#(X) -> c_13():13
             -->_2 activate#(X) -> c_1():6
             -->_2 activate#(n__s(X)) -> c_5(s#(activate(X)),activate#(X)):3
             -->_2 activate#(n__from(X)) -> c_3(from#(activate(X)),activate#(X)):2
             -->_2 activate#(n__cons(X1,X2)) -> c_2(cons#(activate(X1),X2),activate#(X1)):1
          
          4:S:length#(n__cons(X,Y)) -> c_9(s#(length1(activate(Y))),length1#(activate(Y)),activate#(Y))
             -->_3 activate#(n__nil()) -> c_4(nil#()):7
             -->_2 length1#(X) -> c_11(length#(activate(X)),activate#(X)):5
             -->_1 s#(X) -> c_13():13
             -->_3 activate#(X) -> c_1():6
             -->_3 activate#(n__s(X)) -> c_5(s#(activate(X)),activate#(X)):3
             -->_3 activate#(n__from(X)) -> c_3(from#(activate(X)),activate#(X)):2
             -->_3 activate#(n__cons(X1,X2)) -> c_2(cons#(activate(X1),X2),activate#(X1)):1
          
          5:S:length1#(X) -> c_11(length#(activate(X)),activate#(X))
             -->_2 activate#(n__nil()) -> c_4(nil#()):7
             -->_1 length#(n__nil()) -> c_10():11
             -->_2 activate#(X) -> c_1():6
             -->_1 length#(n__cons(X,Y)) -> c_9(s#(length1(activate(Y))),length1#(activate(Y)),activate#(Y)):4
             -->_2 activate#(n__s(X)) -> c_5(s#(activate(X)),activate#(X)):3
             -->_2 activate#(n__from(X)) -> c_3(from#(activate(X)),activate#(X)):2
             -->_2 activate#(n__cons(X1,X2)) -> c_2(cons#(activate(X1),X2),activate#(X1)):1
          
          6:W:activate#(X) -> c_1()
             
          
          7:W:activate#(n__nil()) -> c_4(nil#())
             -->_1 nil#() -> c_12():12
          
          8:W:cons#(X1,X2) -> c_6()
             
          
          9:W:from#(X) -> c_7(cons#(X,n__from(n__s(X))))
             -->_1 cons#(X1,X2) -> c_6():8
          
          10:W:from#(X) -> c_8()
             
          
          11:W:length#(n__nil()) -> c_10()
             
          
          12:W:nil#() -> c_12()
             
          
          13:W:s#(X) -> c_13()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          11: length#(n__nil()) -> c_10()
          10: from#(X) -> c_8()
          9: from#(X) -> c_7(cons#(X,n__from(n__s(X))))
          8: cons#(X1,X2) -> c_6()
          6: activate#(X) -> c_1()
          13: s#(X) -> c_13()
          7: activate#(n__nil()) -> c_4(nil#())
          12: nil#() -> c_12()
* Step 5: SimplifyRHS MAYBE
    + Considered Problem:
        - Strict DPs:
            activate#(n__cons(X1,X2)) -> c_2(cons#(activate(X1),X2),activate#(X1))
            activate#(n__from(X)) -> c_3(from#(activate(X)),activate#(X))
            activate#(n__s(X)) -> c_5(s#(activate(X)),activate#(X))
            length#(n__cons(X,Y)) -> c_9(s#(length1(activate(Y))),length1#(activate(Y)),activate#(Y))
            length1#(X) -> c_11(length#(activate(X)),activate#(X))
        - Weak TRS:
            activate(X) -> X
            activate(n__cons(X1,X2)) -> cons(activate(X1),X2)
            activate(n__from(X)) -> from(activate(X))
            activate(n__nil()) -> nil()
            activate(n__s(X)) -> s(activate(X))
            cons(X1,X2) -> n__cons(X1,X2)
            from(X) -> cons(X,n__from(n__s(X)))
            from(X) -> n__from(X)
            length(n__cons(X,Y)) -> s(length1(activate(Y)))
            length(n__nil()) -> 0()
            length1(X) -> length(activate(X))
            nil() -> n__nil()
            s(X) -> n__s(X)
        - Signature:
            {activate/1,cons/2,from/1,length/1,length1/1,nil/0,s/1,activate#/1,cons#/2,from#/1,length#/1,length1#/1
            ,nil#/0,s#/1} / {0/0,n__cons/2,n__from/1,n__nil/0,n__s/1,c_1/0,c_2/2,c_3/2,c_4/1,c_5/2,c_6/0,c_7/1,c_8/0
            ,c_9/3,c_10/0,c_11/2,c_12/0,c_13/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,cons#,from#,length#,length1#,nil#
            ,s#} and constructors {0,n__cons,n__from,n__nil,n__s}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:activate#(n__cons(X1,X2)) -> c_2(cons#(activate(X1),X2),activate#(X1))
             -->_2 activate#(n__s(X)) -> c_5(s#(activate(X)),activate#(X)):3
             -->_2 activate#(n__from(X)) -> c_3(from#(activate(X)),activate#(X)):2
             -->_2 activate#(n__cons(X1,X2)) -> c_2(cons#(activate(X1),X2),activate#(X1)):1
          
          2:S:activate#(n__from(X)) -> c_3(from#(activate(X)),activate#(X))
             -->_2 activate#(n__s(X)) -> c_5(s#(activate(X)),activate#(X)):3
             -->_2 activate#(n__from(X)) -> c_3(from#(activate(X)),activate#(X)):2
             -->_2 activate#(n__cons(X1,X2)) -> c_2(cons#(activate(X1),X2),activate#(X1)):1
          
          3:S:activate#(n__s(X)) -> c_5(s#(activate(X)),activate#(X))
             -->_2 activate#(n__s(X)) -> c_5(s#(activate(X)),activate#(X)):3
             -->_2 activate#(n__from(X)) -> c_3(from#(activate(X)),activate#(X)):2
             -->_2 activate#(n__cons(X1,X2)) -> c_2(cons#(activate(X1),X2),activate#(X1)):1
          
          4:S:length#(n__cons(X,Y)) -> c_9(s#(length1(activate(Y))),length1#(activate(Y)),activate#(Y))
             -->_2 length1#(X) -> c_11(length#(activate(X)),activate#(X)):5
             -->_3 activate#(n__s(X)) -> c_5(s#(activate(X)),activate#(X)):3
             -->_3 activate#(n__from(X)) -> c_3(from#(activate(X)),activate#(X)):2
             -->_3 activate#(n__cons(X1,X2)) -> c_2(cons#(activate(X1),X2),activate#(X1)):1
          
          5:S:length1#(X) -> c_11(length#(activate(X)),activate#(X))
             -->_1 length#(n__cons(X,Y)) -> c_9(s#(length1(activate(Y))),length1#(activate(Y)),activate#(Y)):4
             -->_2 activate#(n__s(X)) -> c_5(s#(activate(X)),activate#(X)):3
             -->_2 activate#(n__from(X)) -> c_3(from#(activate(X)),activate#(X)):2
             -->_2 activate#(n__cons(X1,X2)) -> c_2(cons#(activate(X1),X2),activate#(X1)):1
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          activate#(n__cons(X1,X2)) -> c_2(activate#(X1))
          activate#(n__from(X)) -> c_3(activate#(X))
          activate#(n__s(X)) -> c_5(activate#(X))
          length#(n__cons(X,Y)) -> c_9(length1#(activate(Y)),activate#(Y))
* Step 6: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            activate#(n__cons(X1,X2)) -> c_2(activate#(X1))
            activate#(n__from(X)) -> c_3(activate#(X))
            activate#(n__s(X)) -> c_5(activate#(X))
            length#(n__cons(X,Y)) -> c_9(length1#(activate(Y)),activate#(Y))
            length1#(X) -> c_11(length#(activate(X)),activate#(X))
        - Weak TRS:
            activate(X) -> X
            activate(n__cons(X1,X2)) -> cons(activate(X1),X2)
            activate(n__from(X)) -> from(activate(X))
            activate(n__nil()) -> nil()
            activate(n__s(X)) -> s(activate(X))
            cons(X1,X2) -> n__cons(X1,X2)
            from(X) -> cons(X,n__from(n__s(X)))
            from(X) -> n__from(X)
            length(n__cons(X,Y)) -> s(length1(activate(Y)))
            length(n__nil()) -> 0()
            length1(X) -> length(activate(X))
            nil() -> n__nil()
            s(X) -> n__s(X)
        - Signature:
            {activate/1,cons/2,from/1,length/1,length1/1,nil/0,s/1,activate#/1,cons#/2,from#/1,length#/1,length1#/1
            ,nil#/0,s#/1} / {0/0,n__cons/2,n__from/1,n__nil/0,n__s/1,c_1/0,c_2/1,c_3/1,c_4/1,c_5/1,c_6/0,c_7/1,c_8/0
            ,c_9/2,c_10/0,c_11/2,c_12/0,c_13/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,cons#,from#,length#,length1#,nil#
            ,s#} and constructors {0,n__cons,n__from,n__nil,n__s}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          activate(X) -> X
          activate(n__cons(X1,X2)) -> cons(activate(X1),X2)
          activate(n__from(X)) -> from(activate(X))
          activate(n__nil()) -> nil()
          activate(n__s(X)) -> s(activate(X))
          cons(X1,X2) -> n__cons(X1,X2)
          from(X) -> cons(X,n__from(n__s(X)))
          from(X) -> n__from(X)
          nil() -> n__nil()
          s(X) -> n__s(X)
          activate#(n__cons(X1,X2)) -> c_2(activate#(X1))
          activate#(n__from(X)) -> c_3(activate#(X))
          activate#(n__s(X)) -> c_5(activate#(X))
          length#(n__cons(X,Y)) -> c_9(length1#(activate(Y)),activate#(Y))
          length1#(X) -> c_11(length#(activate(X)),activate#(X))
* Step 7: Decompose MAYBE
    + Considered Problem:
        - Strict DPs:
            activate#(n__cons(X1,X2)) -> c_2(activate#(X1))
            activate#(n__from(X)) -> c_3(activate#(X))
            activate#(n__s(X)) -> c_5(activate#(X))
            length#(n__cons(X,Y)) -> c_9(length1#(activate(Y)),activate#(Y))
            length1#(X) -> c_11(length#(activate(X)),activate#(X))
        - Weak TRS:
            activate(X) -> X
            activate(n__cons(X1,X2)) -> cons(activate(X1),X2)
            activate(n__from(X)) -> from(activate(X))
            activate(n__nil()) -> nil()
            activate(n__s(X)) -> s(activate(X))
            cons(X1,X2) -> n__cons(X1,X2)
            from(X) -> cons(X,n__from(n__s(X)))
            from(X) -> n__from(X)
            nil() -> n__nil()
            s(X) -> n__s(X)
        - Signature:
            {activate/1,cons/2,from/1,length/1,length1/1,nil/0,s/1,activate#/1,cons#/2,from#/1,length#/1,length1#/1
            ,nil#/0,s#/1} / {0/0,n__cons/2,n__from/1,n__nil/0,n__s/1,c_1/0,c_2/1,c_3/1,c_4/1,c_5/1,c_6/0,c_7/1,c_8/0
            ,c_9/2,c_10/0,c_11/2,c_12/0,c_13/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,cons#,from#,length#,length1#,nil#
            ,s#} and constructors {0,n__cons,n__from,n__nil,n__s}
    + 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__cons(X1,X2)) -> c_2(activate#(X1))
              activate#(n__from(X)) -> c_3(activate#(X))
              activate#(n__s(X)) -> c_5(activate#(X))
          - Weak DPs:
              length#(n__cons(X,Y)) -> c_9(length1#(activate(Y)),activate#(Y))
              length1#(X) -> c_11(length#(activate(X)),activate#(X))
          - Weak TRS:
              activate(X) -> X
              activate(n__cons(X1,X2)) -> cons(activate(X1),X2)
              activate(n__from(X)) -> from(activate(X))
              activate(n__nil()) -> nil()
              activate(n__s(X)) -> s(activate(X))
              cons(X1,X2) -> n__cons(X1,X2)
              from(X) -> cons(X,n__from(n__s(X)))
              from(X) -> n__from(X)
              nil() -> n__nil()
              s(X) -> n__s(X)
          - Signature:
              {activate/1,cons/2,from/1,length/1,length1/1,nil/0,s/1,activate#/1,cons#/2,from#/1,length#/1,length1#/1
              ,nil#/0,s#/1} / {0/0,n__cons/2,n__from/1,n__nil/0,n__s/1,c_1/0,c_2/1,c_3/1,c_4/1,c_5/1,c_6/0,c_7/1,c_8/0
              ,c_9/2,c_10/0,c_11/2,c_12/0,c_13/0}
          - Obligation:
              innermost runtime complexity wrt. defined symbols {activate#,cons#,from#,length#,length1#,nil#
              ,s#} and constructors {0,n__cons,n__from,n__nil,n__s}
        
        Problem (S)
          - Strict DPs:
              length#(n__cons(X,Y)) -> c_9(length1#(activate(Y)),activate#(Y))
              length1#(X) -> c_11(length#(activate(X)),activate#(X))
          - Weak DPs:
              activate#(n__cons(X1,X2)) -> c_2(activate#(X1))
              activate#(n__from(X)) -> c_3(activate#(X))
              activate#(n__s(X)) -> c_5(activate#(X))
          - Weak TRS:
              activate(X) -> X
              activate(n__cons(X1,X2)) -> cons(activate(X1),X2)
              activate(n__from(X)) -> from(activate(X))
              activate(n__nil()) -> nil()
              activate(n__s(X)) -> s(activate(X))
              cons(X1,X2) -> n__cons(X1,X2)
              from(X) -> cons(X,n__from(n__s(X)))
              from(X) -> n__from(X)
              nil() -> n__nil()
              s(X) -> n__s(X)
          - Signature:
              {activate/1,cons/2,from/1,length/1,length1/1,nil/0,s/1,activate#/1,cons#/2,from#/1,length#/1,length1#/1
              ,nil#/0,s#/1} / {0/0,n__cons/2,n__from/1,n__nil/0,n__s/1,c_1/0,c_2/1,c_3/1,c_4/1,c_5/1,c_6/0,c_7/1,c_8/0
              ,c_9/2,c_10/0,c_11/2,c_12/0,c_13/0}
          - Obligation:
              innermost runtime complexity wrt. defined symbols {activate#,cons#,from#,length#,length1#,nil#
              ,s#} and constructors {0,n__cons,n__from,n__nil,n__s}
** Step 7.a:1: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          activate#(n__cons(X1,X2)) -> c_2(activate#(X1))
          activate#(n__from(X)) -> c_3(activate#(X))
          activate#(n__s(X)) -> c_5(activate#(X))
      - Weak DPs:
          length#(n__cons(X,Y)) -> c_9(length1#(activate(Y)),activate#(Y))
          length1#(X) -> c_11(length#(activate(X)),activate#(X))
      - Weak TRS:
          activate(X) -> X
          activate(n__cons(X1,X2)) -> cons(activate(X1),X2)
          activate(n__from(X)) -> from(activate(X))
          activate(n__nil()) -> nil()
          activate(n__s(X)) -> s(activate(X))
          cons(X1,X2) -> n__cons(X1,X2)
          from(X) -> cons(X,n__from(n__s(X)))
          from(X) -> n__from(X)
          nil() -> n__nil()
          s(X) -> n__s(X)
      - Signature:
          {activate/1,cons/2,from/1,length/1,length1/1,nil/0,s/1,activate#/1,cons#/2,from#/1,length#/1,length1#/1
          ,nil#/0,s#/1} / {0/0,n__cons/2,n__from/1,n__nil/0,n__s/1,c_1/0,c_2/1,c_3/1,c_4/1,c_5/1,c_6/0,c_7/1,c_8/0
          ,c_9/2,c_10/0,c_11/2,c_12/0,c_13/0}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {activate#,cons#,from#,length#,length1#,nil#
          ,s#} and constructors {0,n__cons,n__from,n__nil,n__s}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
** Step 7.b:1: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            length#(n__cons(X,Y)) -> c_9(length1#(activate(Y)),activate#(Y))
            length1#(X) -> c_11(length#(activate(X)),activate#(X))
        - Weak DPs:
            activate#(n__cons(X1,X2)) -> c_2(activate#(X1))
            activate#(n__from(X)) -> c_3(activate#(X))
            activate#(n__s(X)) -> c_5(activate#(X))
        - Weak TRS:
            activate(X) -> X
            activate(n__cons(X1,X2)) -> cons(activate(X1),X2)
            activate(n__from(X)) -> from(activate(X))
            activate(n__nil()) -> nil()
            activate(n__s(X)) -> s(activate(X))
            cons(X1,X2) -> n__cons(X1,X2)
            from(X) -> cons(X,n__from(n__s(X)))
            from(X) -> n__from(X)
            nil() -> n__nil()
            s(X) -> n__s(X)
        - Signature:
            {activate/1,cons/2,from/1,length/1,length1/1,nil/0,s/1,activate#/1,cons#/2,from#/1,length#/1,length1#/1
            ,nil#/0,s#/1} / {0/0,n__cons/2,n__from/1,n__nil/0,n__s/1,c_1/0,c_2/1,c_3/1,c_4/1,c_5/1,c_6/0,c_7/1,c_8/0
            ,c_9/2,c_10/0,c_11/2,c_12/0,c_13/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,cons#,from#,length#,length1#,nil#
            ,s#} and constructors {0,n__cons,n__from,n__nil,n__s}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:length#(n__cons(X,Y)) -> c_9(length1#(activate(Y)),activate#(Y))
             -->_2 activate#(n__s(X)) -> c_5(activate#(X)):5
             -->_2 activate#(n__from(X)) -> c_3(activate#(X)):4
             -->_2 activate#(n__cons(X1,X2)) -> c_2(activate#(X1)):3
             -->_1 length1#(X) -> c_11(length#(activate(X)),activate#(X)):2
          
          2:S:length1#(X) -> c_11(length#(activate(X)),activate#(X))
             -->_2 activate#(n__s(X)) -> c_5(activate#(X)):5
             -->_2 activate#(n__from(X)) -> c_3(activate#(X)):4
             -->_2 activate#(n__cons(X1,X2)) -> c_2(activate#(X1)):3
             -->_1 length#(n__cons(X,Y)) -> c_9(length1#(activate(Y)),activate#(Y)):1
          
          3:W:activate#(n__cons(X1,X2)) -> c_2(activate#(X1))
             -->_1 activate#(n__s(X)) -> c_5(activate#(X)):5
             -->_1 activate#(n__from(X)) -> c_3(activate#(X)):4
             -->_1 activate#(n__cons(X1,X2)) -> c_2(activate#(X1)):3
          
          4:W:activate#(n__from(X)) -> c_3(activate#(X))
             -->_1 activate#(n__s(X)) -> c_5(activate#(X)):5
             -->_1 activate#(n__from(X)) -> c_3(activate#(X)):4
             -->_1 activate#(n__cons(X1,X2)) -> c_2(activate#(X1)):3
          
          5:W:activate#(n__s(X)) -> c_5(activate#(X))
             -->_1 activate#(n__s(X)) -> c_5(activate#(X)):5
             -->_1 activate#(n__from(X)) -> c_3(activate#(X)):4
             -->_1 activate#(n__cons(X1,X2)) -> c_2(activate#(X1)):3
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          5: activate#(n__s(X)) -> c_5(activate#(X))
          4: activate#(n__from(X)) -> c_3(activate#(X))
          3: activate#(n__cons(X1,X2)) -> c_2(activate#(X1))
** Step 7.b:2: SimplifyRHS MAYBE
    + Considered Problem:
        - Strict DPs:
            length#(n__cons(X,Y)) -> c_9(length1#(activate(Y)),activate#(Y))
            length1#(X) -> c_11(length#(activate(X)),activate#(X))
        - Weak TRS:
            activate(X) -> X
            activate(n__cons(X1,X2)) -> cons(activate(X1),X2)
            activate(n__from(X)) -> from(activate(X))
            activate(n__nil()) -> nil()
            activate(n__s(X)) -> s(activate(X))
            cons(X1,X2) -> n__cons(X1,X2)
            from(X) -> cons(X,n__from(n__s(X)))
            from(X) -> n__from(X)
            nil() -> n__nil()
            s(X) -> n__s(X)
        - Signature:
            {activate/1,cons/2,from/1,length/1,length1/1,nil/0,s/1,activate#/1,cons#/2,from#/1,length#/1,length1#/1
            ,nil#/0,s#/1} / {0/0,n__cons/2,n__from/1,n__nil/0,n__s/1,c_1/0,c_2/1,c_3/1,c_4/1,c_5/1,c_6/0,c_7/1,c_8/0
            ,c_9/2,c_10/0,c_11/2,c_12/0,c_13/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,cons#,from#,length#,length1#,nil#
            ,s#} and constructors {0,n__cons,n__from,n__nil,n__s}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:length#(n__cons(X,Y)) -> c_9(length1#(activate(Y)),activate#(Y))
             -->_1 length1#(X) -> c_11(length#(activate(X)),activate#(X)):2
          
          2:S:length1#(X) -> c_11(length#(activate(X)),activate#(X))
             -->_1 length#(n__cons(X,Y)) -> c_9(length1#(activate(Y)),activate#(Y)):1
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          length#(n__cons(X,Y)) -> c_9(length1#(activate(Y)))
          length1#(X) -> c_11(length#(activate(X)))
** Step 7.b:3: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          length#(n__cons(X,Y)) -> c_9(length1#(activate(Y)))
          length1#(X) -> c_11(length#(activate(X)))
      - Weak TRS:
          activate(X) -> X
          activate(n__cons(X1,X2)) -> cons(activate(X1),X2)
          activate(n__from(X)) -> from(activate(X))
          activate(n__nil()) -> nil()
          activate(n__s(X)) -> s(activate(X))
          cons(X1,X2) -> n__cons(X1,X2)
          from(X) -> cons(X,n__from(n__s(X)))
          from(X) -> n__from(X)
          nil() -> n__nil()
          s(X) -> n__s(X)
      - Signature:
          {activate/1,cons/2,from/1,length/1,length1/1,nil/0,s/1,activate#/1,cons#/2,from#/1,length#/1,length1#/1
          ,nil#/0,s#/1} / {0/0,n__cons/2,n__from/1,n__nil/0,n__s/1,c_1/0,c_2/1,c_3/1,c_4/1,c_5/1,c_6/0,c_7/1,c_8/0
          ,c_9/1,c_10/0,c_11/1,c_12/0,c_13/0}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {activate#,cons#,from#,length#,length1#,nil#
          ,s#} and constructors {0,n__cons,n__from,n__nil,n__s}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE