WORST_CASE(?,O(1))
* Step 1: InnermostRuleRemoval 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:
        InnermostRuleRemoval
    + Details:
        Arguments of following rules are not normal-forms.
          2nd(cons(X,n__cons(Y,Z))) -> activate(Y)
        All above mentioned rules can be savely removed.
* Step 2: DependencyPairs WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict TRS:
            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
          activate#(X) -> c_1()
          activate#(n__cons(X1,X2)) -> c_2(cons#(X1,X2))
          activate#(n__from(X)) -> c_3(from#(X))
          cons#(X1,X2) -> c_4()
          from#(X) -> c_5(cons#(X,n__from(s(X))))
          from#(X) -> c_6()
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 3: UsableRules WORST_CASE(?,O(1))
    + 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))
            cons#(X1,X2) -> c_4()
            from#(X) -> c_5(cons#(X,n__from(s(X))))
            from#(X) -> c_6()
        - Weak TRS:
            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_1/0,c_2/1
            ,c_3/1,c_4/0,c_5/1,c_6/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {2nd#,activate#,cons#,from#} and constructors {n__cons
            ,n__from,s}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          activate#(X) -> c_1()
          activate#(n__cons(X1,X2)) -> c_2(cons#(X1,X2))
          activate#(n__from(X)) -> c_3(from#(X))
          cons#(X1,X2) -> c_4()
          from#(X) -> c_5(cons#(X,n__from(s(X))))
          from#(X) -> c_6()
* Step 4: Trivial WORST_CASE(?,O(1))
    + 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))
            cons#(X1,X2) -> c_4()
            from#(X) -> c_5(cons#(X,n__from(s(X))))
            from#(X) -> c_6()
        - 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_1/0,c_2/1
            ,c_3/1,c_4/0,c_5/1,c_6/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {2nd#,activate#,cons#,from#} and constructors {n__cons
            ,n__from,s}
    + Applied Processor:
        Trivial
    + Details:
        Consider the dependency graph
          1:S:activate#(X) -> c_1()
             
          
          2:S:activate#(n__cons(X1,X2)) -> c_2(cons#(X1,X2))
             -->_1 cons#(X1,X2) -> c_4():4
          
          3:S:activate#(n__from(X)) -> c_3(from#(X))
             -->_1 from#(X) -> c_5(cons#(X,n__from(s(X)))):5
             -->_1 from#(X) -> c_6():6
          
          4:S:cons#(X1,X2) -> c_4()
             
          
          5:S:from#(X) -> c_5(cons#(X,n__from(s(X))))
             -->_1 cons#(X1,X2) -> c_4():4
          
          6:S:from#(X) -> c_6()
             
          
        The dependency graph contains no loops, we remove all dependency pairs.
* Step 5: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        
        - 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_1/0,c_2/1
            ,c_3/1,c_4/0,c_5/1,c_6/0}
        - 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))