*** 1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        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)
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {2nd/1,activate/1,from/1} / {cons/2,cons1/2,n__from/1,s/1}
      Obligation:
        Innermost
        basic terms: {2nd,activate,from}/{cons,cons1,n__from,s}
    Applied Processor:
      DependencyPairs {dpKind_ = DT}
    Proof:
      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.
*** 1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        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()
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        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
        basic terms: {2nd#,activate#,from#}/{cons,cons1,n__from,s}
    Applied Processor:
      UsableRules
    Proof:
      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()
*** 1.1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        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()
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        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
        basic terms: {2nd#,activate#,from#}/{cons,cons1,n__from,s}
    Applied Processor:
      Trivial
    Proof:
      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.
*** 1.1.1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        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
        basic terms: {2nd#,activate#,from#}/{cons,cons1,n__from,s}
    Applied Processor:
      EmptyProcessor
    Proof:
      The problem is already closed. The intended complexity is O(1).