MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            activate(n__cons(X1,X2)) -> cons(X1,X2)
            activate(n__from(X)) -> from(X)
            activate(n__nil()) -> nil()
            cons(X1,X2) -> n__cons(X1,X2)
            from(X) -> cons(X,n__from(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()
        - Signature:
            {activate/1,cons/2,from/1,length/1,length1/1,nil/0} / {0/0,n__cons/2,n__from/1,n__nil/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate,cons,from,length,length1
            ,nil} and constructors {0,n__cons,n__from,n__nil,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#(X1,X2))
          activate#(n__from(X)) -> c_3(from#(X))
          activate#(n__nil()) -> c_4(nil#())
          cons#(X1,X2) -> c_5()
          from#(X) -> c_6(cons#(X,n__from(s(X))))
          from#(X) -> c_7()
          length#(n__cons(X,Y)) -> c_8(length1#(activate(Y)),activate#(Y))
          length#(n__nil()) -> c_9()
          length1#(X) -> c_10(length#(activate(X)),activate#(X))
          nil#() -> 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__cons(X1,X2)) -> c_2(cons#(X1,X2))
            activate#(n__from(X)) -> c_3(from#(X))
            activate#(n__nil()) -> c_4(nil#())
            cons#(X1,X2) -> c_5()
            from#(X) -> c_6(cons#(X,n__from(s(X))))
            from#(X) -> c_7()
            length#(n__cons(X,Y)) -> c_8(length1#(activate(Y)),activate#(Y))
            length#(n__nil()) -> c_9()
            length1#(X) -> c_10(length#(activate(X)),activate#(X))
            nil#() -> c_11()
        - Weak TRS:
            activate(X) -> X
            activate(n__cons(X1,X2)) -> cons(X1,X2)
            activate(n__from(X)) -> from(X)
            activate(n__nil()) -> nil()
            cons(X1,X2) -> n__cons(X1,X2)
            from(X) -> cons(X,n__from(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()
        - Signature:
            {activate/1,cons/2,from/1,length/1,length1/1,nil/0,activate#/1,cons#/2,from#/1,length#/1,length1#/1
            ,nil#/0} / {0/0,n__cons/2,n__from/1,n__nil/0,s/1,c_1/0,c_2/1,c_3/1,c_4/1,c_5/0,c_6/1,c_7/0,c_8/2,c_9/0
            ,c_10/2,c_11/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,cons#,from#,length#,length1#
            ,nil#} and constructors {0,n__cons,n__from,n__nil,s}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          activate(X) -> X
          activate(n__cons(X1,X2)) -> cons(X1,X2)
          activate(n__from(X)) -> from(X)
          activate(n__nil()) -> nil()
          cons(X1,X2) -> n__cons(X1,X2)
          from(X) -> cons(X,n__from(s(X)))
          from(X) -> n__from(X)
          nil() -> n__nil()
          activate#(X) -> c_1()
          activate#(n__cons(X1,X2)) -> c_2(cons#(X1,X2))
          activate#(n__from(X)) -> c_3(from#(X))
          activate#(n__nil()) -> c_4(nil#())
          cons#(X1,X2) -> c_5()
          from#(X) -> c_6(cons#(X,n__from(s(X))))
          from#(X) -> c_7()
          length#(n__cons(X,Y)) -> c_8(length1#(activate(Y)),activate#(Y))
          length#(n__nil()) -> c_9()
          length1#(X) -> c_10(length#(activate(X)),activate#(X))
          nil#() -> c_11()
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            activate#(X) -> c_1()
            activate#(n__cons(X1,X2)) -> c_2(cons#(X1,X2))
            activate#(n__from(X)) -> c_3(from#(X))
            activate#(n__nil()) -> c_4(nil#())
            cons#(X1,X2) -> c_5()
            from#(X) -> c_6(cons#(X,n__from(s(X))))
            from#(X) -> c_7()
            length#(n__cons(X,Y)) -> c_8(length1#(activate(Y)),activate#(Y))
            length#(n__nil()) -> c_9()
            length1#(X) -> c_10(length#(activate(X)),activate#(X))
            nil#() -> c_11()
        - Weak TRS:
            activate(X) -> X
            activate(n__cons(X1,X2)) -> cons(X1,X2)
            activate(n__from(X)) -> from(X)
            activate(n__nil()) -> nil()
            cons(X1,X2) -> n__cons(X1,X2)
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
            nil() -> n__nil()
        - Signature:
            {activate/1,cons/2,from/1,length/1,length1/1,nil/0,activate#/1,cons#/2,from#/1,length#/1,length1#/1
            ,nil#/0} / {0/0,n__cons/2,n__from/1,n__nil/0,s/1,c_1/0,c_2/1,c_3/1,c_4/1,c_5/0,c_6/1,c_7/0,c_8/2,c_9/0
            ,c_10/2,c_11/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,cons#,from#,length#,length1#
            ,nil#} and constructors {0,n__cons,n__from,n__nil,s}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,5,7,9,11}
        by application of
          Pre({1,5,7,9,11}) = {2,3,4,6,8,10}.
        Here rules are labelled as follows:
          1: activate#(X) -> c_1()
          2: activate#(n__cons(X1,X2)) -> c_2(cons#(X1,X2))
          3: activate#(n__from(X)) -> c_3(from#(X))
          4: activate#(n__nil()) -> c_4(nil#())
          5: cons#(X1,X2) -> c_5()
          6: from#(X) -> c_6(cons#(X,n__from(s(X))))
          7: from#(X) -> c_7()
          8: length#(n__cons(X,Y)) -> c_8(length1#(activate(Y)),activate#(Y))
          9: length#(n__nil()) -> c_9()
          10: length1#(X) -> c_10(length#(activate(X)),activate#(X))
          11: nil#() -> c_11()
* Step 4: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            activate#(n__cons(X1,X2)) -> c_2(cons#(X1,X2))
            activate#(n__from(X)) -> c_3(from#(X))
            activate#(n__nil()) -> c_4(nil#())
            from#(X) -> c_6(cons#(X,n__from(s(X))))
            length#(n__cons(X,Y)) -> c_8(length1#(activate(Y)),activate#(Y))
            length1#(X) -> c_10(length#(activate(X)),activate#(X))
        - Weak DPs:
            activate#(X) -> c_1()
            cons#(X1,X2) -> c_5()
            from#(X) -> c_7()
            length#(n__nil()) -> c_9()
            nil#() -> c_11()
        - Weak TRS:
            activate(X) -> X
            activate(n__cons(X1,X2)) -> cons(X1,X2)
            activate(n__from(X)) -> from(X)
            activate(n__nil()) -> nil()
            cons(X1,X2) -> n__cons(X1,X2)
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
            nil() -> n__nil()
        - Signature:
            {activate/1,cons/2,from/1,length/1,length1/1,nil/0,activate#/1,cons#/2,from#/1,length#/1,length1#/1
            ,nil#/0} / {0/0,n__cons/2,n__from/1,n__nil/0,s/1,c_1/0,c_2/1,c_3/1,c_4/1,c_5/0,c_6/1,c_7/0,c_8/2,c_9/0
            ,c_10/2,c_11/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,cons#,from#,length#,length1#
            ,nil#} and constructors {0,n__cons,n__from,n__nil,s}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,3,4}
        by application of
          Pre({1,3,4}) = {2,5,6}.
        Here rules are labelled as follows:
          1: activate#(n__cons(X1,X2)) -> c_2(cons#(X1,X2))
          2: activate#(n__from(X)) -> c_3(from#(X))
          3: activate#(n__nil()) -> c_4(nil#())
          4: from#(X) -> c_6(cons#(X,n__from(s(X))))
          5: length#(n__cons(X,Y)) -> c_8(length1#(activate(Y)),activate#(Y))
          6: length1#(X) -> c_10(length#(activate(X)),activate#(X))
          7: activate#(X) -> c_1()
          8: cons#(X1,X2) -> c_5()
          9: from#(X) -> c_7()
          10: length#(n__nil()) -> c_9()
          11: nil#() -> c_11()
* Step 5: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            activate#(n__from(X)) -> c_3(from#(X))
            length#(n__cons(X,Y)) -> c_8(length1#(activate(Y)),activate#(Y))
            length1#(X) -> c_10(length#(activate(X)),activate#(X))
        - Weak DPs:
            activate#(X) -> c_1()
            activate#(n__cons(X1,X2)) -> c_2(cons#(X1,X2))
            activate#(n__nil()) -> c_4(nil#())
            cons#(X1,X2) -> c_5()
            from#(X) -> c_6(cons#(X,n__from(s(X))))
            from#(X) -> c_7()
            length#(n__nil()) -> c_9()
            nil#() -> c_11()
        - Weak TRS:
            activate(X) -> X
            activate(n__cons(X1,X2)) -> cons(X1,X2)
            activate(n__from(X)) -> from(X)
            activate(n__nil()) -> nil()
            cons(X1,X2) -> n__cons(X1,X2)
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
            nil() -> n__nil()
        - Signature:
            {activate/1,cons/2,from/1,length/1,length1/1,nil/0,activate#/1,cons#/2,from#/1,length#/1,length1#/1
            ,nil#/0} / {0/0,n__cons/2,n__from/1,n__nil/0,s/1,c_1/0,c_2/1,c_3/1,c_4/1,c_5/0,c_6/1,c_7/0,c_8/2,c_9/0
            ,c_10/2,c_11/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,cons#,from#,length#,length1#
            ,nil#} and constructors {0,n__cons,n__from,n__nil,s}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1}
        by application of
          Pre({1}) = {2,3}.
        Here rules are labelled as follows:
          1: activate#(n__from(X)) -> c_3(from#(X))
          2: length#(n__cons(X,Y)) -> c_8(length1#(activate(Y)),activate#(Y))
          3: length1#(X) -> c_10(length#(activate(X)),activate#(X))
          4: activate#(X) -> c_1()
          5: activate#(n__cons(X1,X2)) -> c_2(cons#(X1,X2))
          6: activate#(n__nil()) -> c_4(nil#())
          7: cons#(X1,X2) -> c_5()
          8: from#(X) -> c_6(cons#(X,n__from(s(X))))
          9: from#(X) -> c_7()
          10: length#(n__nil()) -> c_9()
          11: nil#() -> c_11()
* Step 6: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            length#(n__cons(X,Y)) -> c_8(length1#(activate(Y)),activate#(Y))
            length1#(X) -> c_10(length#(activate(X)),activate#(X))
        - Weak DPs:
            activate#(X) -> c_1()
            activate#(n__cons(X1,X2)) -> c_2(cons#(X1,X2))
            activate#(n__from(X)) -> c_3(from#(X))
            activate#(n__nil()) -> c_4(nil#())
            cons#(X1,X2) -> c_5()
            from#(X) -> c_6(cons#(X,n__from(s(X))))
            from#(X) -> c_7()
            length#(n__nil()) -> c_9()
            nil#() -> c_11()
        - Weak TRS:
            activate(X) -> X
            activate(n__cons(X1,X2)) -> cons(X1,X2)
            activate(n__from(X)) -> from(X)
            activate(n__nil()) -> nil()
            cons(X1,X2) -> n__cons(X1,X2)
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
            nil() -> n__nil()
        - Signature:
            {activate/1,cons/2,from/1,length/1,length1/1,nil/0,activate#/1,cons#/2,from#/1,length#/1,length1#/1
            ,nil#/0} / {0/0,n__cons/2,n__from/1,n__nil/0,s/1,c_1/0,c_2/1,c_3/1,c_4/1,c_5/0,c_6/1,c_7/0,c_8/2,c_9/0
            ,c_10/2,c_11/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,cons#,from#,length#,length1#
            ,nil#} and constructors {0,n__cons,n__from,n__nil,s}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:length#(n__cons(X,Y)) -> c_8(length1#(activate(Y)),activate#(Y))
             -->_2 activate#(n__nil()) -> c_4(nil#()):6
             -->_2 activate#(n__from(X)) -> c_3(from#(X)):5
             -->_2 activate#(n__cons(X1,X2)) -> c_2(cons#(X1,X2)):4
             -->_1 length1#(X) -> c_10(length#(activate(X)),activate#(X)):2
             -->_2 activate#(X) -> c_1():3
          
          2:S:length1#(X) -> c_10(length#(activate(X)),activate#(X))
             -->_2 activate#(n__nil()) -> c_4(nil#()):6
             -->_2 activate#(n__from(X)) -> c_3(from#(X)):5
             -->_2 activate#(n__cons(X1,X2)) -> c_2(cons#(X1,X2)):4
             -->_1 length#(n__nil()) -> c_9():10
             -->_2 activate#(X) -> c_1():3
             -->_1 length#(n__cons(X,Y)) -> c_8(length1#(activate(Y)),activate#(Y)):1
          
          3:W:activate#(X) -> c_1()
             
          
          4:W:activate#(n__cons(X1,X2)) -> c_2(cons#(X1,X2))
             -->_1 cons#(X1,X2) -> c_5():7
          
          5:W:activate#(n__from(X)) -> c_3(from#(X))
             -->_1 from#(X) -> c_6(cons#(X,n__from(s(X)))):8
             -->_1 from#(X) -> c_7():9
          
          6:W:activate#(n__nil()) -> c_4(nil#())
             -->_1 nil#() -> c_11():11
          
          7:W:cons#(X1,X2) -> c_5()
             
          
          8:W:from#(X) -> c_6(cons#(X,n__from(s(X))))
             -->_1 cons#(X1,X2) -> c_5():7
          
          9:W:from#(X) -> c_7()
             
          
          10:W:length#(n__nil()) -> c_9()
             
          
          11:W:nil#() -> c_11()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          3: activate#(X) -> c_1()
          10: length#(n__nil()) -> c_9()
          4: activate#(n__cons(X1,X2)) -> c_2(cons#(X1,X2))
          5: activate#(n__from(X)) -> c_3(from#(X))
          9: from#(X) -> c_7()
          8: from#(X) -> c_6(cons#(X,n__from(s(X))))
          7: cons#(X1,X2) -> c_5()
          6: activate#(n__nil()) -> c_4(nil#())
          11: nil#() -> c_11()
* Step 7: SimplifyRHS MAYBE
    + Considered Problem:
        - Strict DPs:
            length#(n__cons(X,Y)) -> c_8(length1#(activate(Y)),activate#(Y))
            length1#(X) -> c_10(length#(activate(X)),activate#(X))
        - Weak TRS:
            activate(X) -> X
            activate(n__cons(X1,X2)) -> cons(X1,X2)
            activate(n__from(X)) -> from(X)
            activate(n__nil()) -> nil()
            cons(X1,X2) -> n__cons(X1,X2)
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
            nil() -> n__nil()
        - Signature:
            {activate/1,cons/2,from/1,length/1,length1/1,nil/0,activate#/1,cons#/2,from#/1,length#/1,length1#/1
            ,nil#/0} / {0/0,n__cons/2,n__from/1,n__nil/0,s/1,c_1/0,c_2/1,c_3/1,c_4/1,c_5/0,c_6/1,c_7/0,c_8/2,c_9/0
            ,c_10/2,c_11/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,cons#,from#,length#,length1#
            ,nil#} and constructors {0,n__cons,n__from,n__nil,s}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:length#(n__cons(X,Y)) -> c_8(length1#(activate(Y)),activate#(Y))
             -->_1 length1#(X) -> c_10(length#(activate(X)),activate#(X)):2
          
          2:S:length1#(X) -> c_10(length#(activate(X)),activate#(X))
             -->_1 length#(n__cons(X,Y)) -> c_8(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_8(length1#(activate(Y)))
          length1#(X) -> c_10(length#(activate(X)))
* Step 8: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          length#(n__cons(X,Y)) -> c_8(length1#(activate(Y)))
          length1#(X) -> c_10(length#(activate(X)))
      - Weak TRS:
          activate(X) -> X
          activate(n__cons(X1,X2)) -> cons(X1,X2)
          activate(n__from(X)) -> from(X)
          activate(n__nil()) -> nil()
          cons(X1,X2) -> n__cons(X1,X2)
          from(X) -> cons(X,n__from(s(X)))
          from(X) -> n__from(X)
          nil() -> n__nil()
      - Signature:
          {activate/1,cons/2,from/1,length/1,length1/1,nil/0,activate#/1,cons#/2,from#/1,length#/1,length1#/1
          ,nil#/0} / {0/0,n__cons/2,n__from/1,n__nil/0,s/1,c_1/0,c_2/1,c_3/1,c_4/1,c_5/0,c_6/1,c_7/0,c_8/1,c_9/0
          ,c_10/1,c_11/0}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {activate#,cons#,from#,length#,length1#
          ,nil#} and constructors {0,n__cons,n__from,n__nil,s}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE