WORST_CASE(?,O(1))
* Step 1: Sum WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict TRS:
            2nd(cons(X,n__cons(Y,Z))) -> activate(Y)
            activate(X) -> X
            activate(n__cons(X1,X2)) -> cons(X1,X2)
            activate(n__from(X)) -> from(X)
            cons(X1,X2) -> n__cons(X1,X2)
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
        - Signature:
            {2nd/1,activate/1,cons/2,from/1} / {n__cons/2,n__from/1,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {2nd,activate,cons,from} and constructors {n__cons,n__from
            ,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: DependencyPairs WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict TRS:
            2nd(cons(X,n__cons(Y,Z))) -> activate(Y)
            activate(X) -> X
            activate(n__cons(X1,X2)) -> cons(X1,X2)
            activate(n__from(X)) -> from(X)
            cons(X1,X2) -> n__cons(X1,X2)
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
        - Signature:
            {2nd/1,activate/1,cons/2,from/1} / {n__cons/2,n__from/1,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {2nd,activate,cons,from} and constructors {n__cons,n__from
            ,s}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          2nd#(cons(X,n__cons(Y,Z))) -> c_1(activate#(Y))
          activate#(X) -> c_2()
          activate#(n__cons(X1,X2)) -> c_3(cons#(X1,X2))
          activate#(n__from(X)) -> c_4(from#(X))
          cons#(X1,X2) -> c_5()
          from#(X) -> c_6(cons#(X,n__from(s(X))))
          from#(X) -> c_7()
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 3: PredecessorEstimation WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            2nd#(cons(X,n__cons(Y,Z))) -> c_1(activate#(Y))
            activate#(X) -> c_2()
            activate#(n__cons(X1,X2)) -> c_3(cons#(X1,X2))
            activate#(n__from(X)) -> c_4(from#(X))
            cons#(X1,X2) -> c_5()
            from#(X) -> c_6(cons#(X,n__from(s(X))))
            from#(X) -> c_7()
        - Weak TRS:
            2nd(cons(X,n__cons(Y,Z))) -> activate(Y)
            activate(X) -> X
            activate(n__cons(X1,X2)) -> cons(X1,X2)
            activate(n__from(X)) -> from(X)
            cons(X1,X2) -> n__cons(X1,X2)
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
        - Signature:
            {2nd/1,activate/1,cons/2,from/1,2nd#/1,activate#/1,cons#/2,from#/1} / {n__cons/2,n__from/1,s/1,c_1/1,c_2/0
            ,c_3/1,c_4/1,c_5/0,c_6/1,c_7/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {2nd#,activate#,cons#,from#} and constructors {n__cons
            ,n__from,s}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,2,5,7}
        by application of
          Pre({1,2,5,7}) = {3,4,6}.
        Here rules are labelled as follows:
          1: 2nd#(cons(X,n__cons(Y,Z))) -> c_1(activate#(Y))
          2: activate#(X) -> c_2()
          3: activate#(n__cons(X1,X2)) -> c_3(cons#(X1,X2))
          4: activate#(n__from(X)) -> c_4(from#(X))
          5: cons#(X1,X2) -> c_5()
          6: from#(X) -> c_6(cons#(X,n__from(s(X))))
          7: from#(X) -> c_7()
* Step 4: PredecessorEstimation WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            activate#(n__cons(X1,X2)) -> c_3(cons#(X1,X2))
            activate#(n__from(X)) -> c_4(from#(X))
            from#(X) -> c_6(cons#(X,n__from(s(X))))
        - Weak DPs:
            2nd#(cons(X,n__cons(Y,Z))) -> c_1(activate#(Y))
            activate#(X) -> c_2()
            cons#(X1,X2) -> c_5()
            from#(X) -> c_7()
        - Weak TRS:
            2nd(cons(X,n__cons(Y,Z))) -> activate(Y)
            activate(X) -> X
            activate(n__cons(X1,X2)) -> cons(X1,X2)
            activate(n__from(X)) -> from(X)
            cons(X1,X2) -> n__cons(X1,X2)
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
        - Signature:
            {2nd/1,activate/1,cons/2,from/1,2nd#/1,activate#/1,cons#/2,from#/1} / {n__cons/2,n__from/1,s/1,c_1/1,c_2/0
            ,c_3/1,c_4/1,c_5/0,c_6/1,c_7/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {2nd#,activate#,cons#,from#} and constructors {n__cons
            ,n__from,s}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,3}
        by application of
          Pre({1,3}) = {2}.
        Here rules are labelled as follows:
          1: activate#(n__cons(X1,X2)) -> c_3(cons#(X1,X2))
          2: activate#(n__from(X)) -> c_4(from#(X))
          3: from#(X) -> c_6(cons#(X,n__from(s(X))))
          4: 2nd#(cons(X,n__cons(Y,Z))) -> c_1(activate#(Y))
          5: activate#(X) -> c_2()
          6: cons#(X1,X2) -> c_5()
          7: from#(X) -> c_7()
* Step 5: PredecessorEstimation WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            activate#(n__from(X)) -> c_4(from#(X))
        - Weak DPs:
            2nd#(cons(X,n__cons(Y,Z))) -> c_1(activate#(Y))
            activate#(X) -> c_2()
            activate#(n__cons(X1,X2)) -> c_3(cons#(X1,X2))
            cons#(X1,X2) -> c_5()
            from#(X) -> c_6(cons#(X,n__from(s(X))))
            from#(X) -> c_7()
        - Weak TRS:
            2nd(cons(X,n__cons(Y,Z))) -> activate(Y)
            activate(X) -> X
            activate(n__cons(X1,X2)) -> cons(X1,X2)
            activate(n__from(X)) -> from(X)
            cons(X1,X2) -> n__cons(X1,X2)
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
        - Signature:
            {2nd/1,activate/1,cons/2,from/1,2nd#/1,activate#/1,cons#/2,from#/1} / {n__cons/2,n__from/1,s/1,c_1/1,c_2/0
            ,c_3/1,c_4/1,c_5/0,c_6/1,c_7/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {2nd#,activate#,cons#,from#} and constructors {n__cons
            ,n__from,s}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1}
        by application of
          Pre({1}) = {}.
        Here rules are labelled as follows:
          1: activate#(n__from(X)) -> c_4(from#(X))
          2: 2nd#(cons(X,n__cons(Y,Z))) -> c_1(activate#(Y))
          3: activate#(X) -> c_2()
          4: activate#(n__cons(X1,X2)) -> c_3(cons#(X1,X2))
          5: cons#(X1,X2) -> c_5()
          6: from#(X) -> c_6(cons#(X,n__from(s(X))))
          7: from#(X) -> c_7()
* Step 6: RemoveWeakSuffixes WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            2nd#(cons(X,n__cons(Y,Z))) -> c_1(activate#(Y))
            activate#(X) -> c_2()
            activate#(n__cons(X1,X2)) -> c_3(cons#(X1,X2))
            activate#(n__from(X)) -> c_4(from#(X))
            cons#(X1,X2) -> c_5()
            from#(X) -> c_6(cons#(X,n__from(s(X))))
            from#(X) -> c_7()
        - Weak TRS:
            2nd(cons(X,n__cons(Y,Z))) -> activate(Y)
            activate(X) -> X
            activate(n__cons(X1,X2)) -> cons(X1,X2)
            activate(n__from(X)) -> from(X)
            cons(X1,X2) -> n__cons(X1,X2)
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
        - Signature:
            {2nd/1,activate/1,cons/2,from/1,2nd#/1,activate#/1,cons#/2,from#/1} / {n__cons/2,n__from/1,s/1,c_1/1,c_2/0
            ,c_3/1,c_4/1,c_5/0,c_6/1,c_7/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {2nd#,activate#,cons#,from#} and constructors {n__cons
            ,n__from,s}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:W:2nd#(cons(X,n__cons(Y,Z))) -> c_1(activate#(Y))
             
          
          2:W:activate#(X) -> c_2()
             
          
          3:W:activate#(n__cons(X1,X2)) -> c_3(cons#(X1,X2))
             -->_1 cons#(X1,X2) -> c_5():5
          
          4:W:activate#(n__from(X)) -> c_4(from#(X))
             -->_1 from#(X) -> c_6(cons#(X,n__from(s(X)))):6
             -->_1 from#(X) -> c_7():7
          
          5:W:cons#(X1,X2) -> c_5()
             
          
          6:W:from#(X) -> c_6(cons#(X,n__from(s(X))))
             -->_1 cons#(X1,X2) -> c_5():5
          
          7:W:from#(X) -> c_7()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          4: activate#(n__from(X)) -> c_4(from#(X))
          7: from#(X) -> c_7()
          6: from#(X) -> c_6(cons#(X,n__from(s(X))))
          3: activate#(n__cons(X1,X2)) -> c_3(cons#(X1,X2))
          5: cons#(X1,X2) -> c_5()
          2: activate#(X) -> c_2()
          1: 2nd#(cons(X,n__cons(Y,Z))) -> c_1(activate#(Y))
* Step 7: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            2nd(cons(X,n__cons(Y,Z))) -> activate(Y)
            activate(X) -> X
            activate(n__cons(X1,X2)) -> cons(X1,X2)
            activate(n__from(X)) -> from(X)
            cons(X1,X2) -> n__cons(X1,X2)
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
        - Signature:
            {2nd/1,activate/1,cons/2,from/1,2nd#/1,activate#/1,cons#/2,from#/1} / {n__cons/2,n__from/1,s/1,c_1/1,c_2/0
            ,c_3/1,c_4/1,c_5/0,c_6/1,c_7/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {2nd#,activate#,cons#,from#} and constructors {n__cons
            ,n__from,s}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(1))