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