WORST_CASE(?,O(1))
* Step 1: DependencyPairs WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict TRS:
            2nd(cons(X,X1)) -> 2nd(cons1(X,activate(X1)))
            2nd(cons1(X,cons(Y,Z))) -> Y
            activate(X) -> X
            activate(n__from(X)) -> from(X)
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
        - Signature:
            {2nd/1,activate/1,from/1} / {cons/2,cons1/2,n__from/1,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {2nd,activate,from} and constructors {cons,cons1,n__from
            ,s}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          2nd#(cons(X,X1)) -> c_1(2nd#(cons1(X,activate(X1))),activate#(X1))
          2nd#(cons1(X,cons(Y,Z))) -> c_2()
          activate#(X) -> c_3()
          activate#(n__from(X)) -> c_4(from#(X))
          from#(X) -> c_5()
          from#(X) -> c_6()
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            2nd#(cons(X,X1)) -> c_1(2nd#(cons1(X,activate(X1))),activate#(X1))
            2nd#(cons1(X,cons(Y,Z))) -> c_2()
            activate#(X) -> c_3()
            activate#(n__from(X)) -> c_4(from#(X))
            from#(X) -> c_5()
            from#(X) -> c_6()
        - Weak TRS:
            2nd(cons(X,X1)) -> 2nd(cons1(X,activate(X1)))
            2nd(cons1(X,cons(Y,Z))) -> Y
            activate(X) -> X
            activate(n__from(X)) -> from(X)
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
        - Signature:
            {2nd/1,activate/1,from/1,2nd#/1,activate#/1,from#/1} / {cons/2,cons1/2,n__from/1,s/1,c_1/2,c_2/0,c_3/0,c_4/1
            ,c_5/0,c_6/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {2nd#,activate#,from#} and constructors {cons,cons1
            ,n__from,s}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          activate(X) -> X
          activate(n__from(X)) -> from(X)
          from(X) -> cons(X,n__from(s(X)))
          from(X) -> n__from(X)
          2nd#(cons(X,X1)) -> c_1(2nd#(cons1(X,activate(X1))),activate#(X1))
          2nd#(cons1(X,cons(Y,Z))) -> c_2()
          activate#(X) -> c_3()
          activate#(n__from(X)) -> c_4(from#(X))
          from#(X) -> c_5()
          from#(X) -> c_6()
* Step 3: Trivial WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            2nd#(cons(X,X1)) -> c_1(2nd#(cons1(X,activate(X1))),activate#(X1))
            2nd#(cons1(X,cons(Y,Z))) -> c_2()
            activate#(X) -> c_3()
            activate#(n__from(X)) -> c_4(from#(X))
            from#(X) -> c_5()
            from#(X) -> c_6()
        - Weak TRS:
            activate(X) -> X
            activate(n__from(X)) -> from(X)
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
        - Signature:
            {2nd/1,activate/1,from/1,2nd#/1,activate#/1,from#/1} / {cons/2,cons1/2,n__from/1,s/1,c_1/2,c_2/0,c_3/0,c_4/1
            ,c_5/0,c_6/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {2nd#,activate#,from#} and constructors {cons,cons1
            ,n__from,s}
    + Applied Processor:
        Trivial
    + Details:
        Consider the dependency graph
          1:S:2nd#(cons(X,X1)) -> c_1(2nd#(cons1(X,activate(X1))),activate#(X1))
             -->_2 activate#(n__from(X)) -> c_4(from#(X)):4
             -->_2 activate#(X) -> c_3():3
             -->_1 2nd#(cons1(X,cons(Y,Z))) -> c_2():2
          
          2:S:2nd#(cons1(X,cons(Y,Z))) -> c_2()
             
          
          3:S:activate#(X) -> c_3()
             
          
          4:S:activate#(n__from(X)) -> c_4(from#(X))
             -->_1 from#(X) -> c_6():6
             -->_1 from#(X) -> c_5():5
          
          5:S:from#(X) -> c_5()
             
          
          6:S:from#(X) -> c_6()
             
          
        The dependency graph contains no loops, we remove all dependency pairs.
* Step 4: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            activate(X) -> X
            activate(n__from(X)) -> from(X)
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
        - Signature:
            {2nd/1,activate/1,from/1,2nd#/1,activate#/1,from#/1} / {cons/2,cons1/2,n__from/1,s/1,c_1/2,c_2/0,c_3/0,c_4/1
            ,c_5/0,c_6/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {2nd#,activate#,from#} and constructors {cons,cons1
            ,n__from,s}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(1))