WORST_CASE(?,O(n^1))
* Step 1: Sum WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            activate(n__from(X)) -> from(X)
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
            sel(0(),cons(X,Y)) -> X
            sel(s(X),cons(Y,Z)) -> sel(X,activate(Z))
        - Signature:
            {activate/1,from/1,sel/2} / {0/0,cons/2,n__from/1,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate,from,sel} and constructors {0,cons,n__from,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: NaturalPI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            activate(n__from(X)) -> from(X)
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
            sel(0(),cons(X,Y)) -> X
            sel(s(X),cons(Y,Z)) -> sel(X,activate(Z))
        - Signature:
            {activate/1,from/1,sel/2} / {0/0,cons/2,n__from/1,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate,from,sel} and constructors {0,cons,n__from,s}
    + Applied Processor:
        NaturalPI {shape = Mixed 2, restrict = Restrict, uargs = UArgs, urules = URules, selector = Just any strict-rules}
    + Details:
        We apply a polynomial interpretation of kind constructor-based(mixed(2)):
        The following argument positions are considered usable:
          uargs(sel) = {2}
        
        Following symbols are considered usable:
          {activate,from,sel}
        TcT has computed the following interpretation:
                 p(0) = 0      
          p(activate) = x1     
              p(cons) = x1 + x2
              p(from) = x1     
           p(n__from) = x1     
                 p(s) = 0      
               p(sel) = 1 + x2 
        
        Following rules are strictly oriented:
        sel(0(),cons(X,Y)) = 1 + X + Y
                           > X        
                           = X        
        
        
        Following rules are (at-least) weakly oriented:
                 activate(X) =  X                    
                             >= X                    
                             =  X                    
        
        activate(n__from(X)) =  X                    
                             >= X                    
                             =  from(X)              
        
                     from(X) =  X                    
                             >= X                    
                             =  cons(X,n__from(s(X)))
        
                     from(X) =  X                    
                             >= X                    
                             =  n__from(X)           
        
         sel(s(X),cons(Y,Z)) =  1 + Y + Z            
                             >= 1 + Z                
                             =  sel(X,activate(Z))   
        
* Step 3: NaturalPI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            activate(n__from(X)) -> from(X)
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
            sel(s(X),cons(Y,Z)) -> sel(X,activate(Z))
        - Weak TRS:
            sel(0(),cons(X,Y)) -> X
        - Signature:
            {activate/1,from/1,sel/2} / {0/0,cons/2,n__from/1,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate,from,sel} and constructors {0,cons,n__from,s}
    + Applied Processor:
        NaturalPI {shape = Linear, restrict = Restrict, uargs = UArgs, urules = URules, selector = Just any strict-rules}
    + Details:
        We apply a polynomial interpretation of kind constructor-based(linear):
        The following argument positions are considered usable:
          uargs(sel) = {2}
        
        Following symbols are considered usable:
          {activate,from,sel}
        TcT has computed the following interpretation:
                 p(0) = 0          
          p(activate) = 1 + x1     
              p(cons) = 1 + x1 + x2
              p(from) = 1 + x1     
           p(n__from) = x1         
                 p(s) = 0          
               p(sel) = 2*x2       
        
        Following rules are strictly oriented:
        activate(X) = 1 + X     
                    > X         
                    = X         
        
            from(X) = 1 + X     
                    > X         
                    = n__from(X)
        
        
        Following rules are (at-least) weakly oriented:
        activate(n__from(X)) =  1 + X                
                             >= 1 + X                
                             =  from(X)              
        
                     from(X) =  1 + X                
                             >= 1 + X                
                             =  cons(X,n__from(s(X)))
        
          sel(0(),cons(X,Y)) =  2 + 2*X + 2*Y        
                             >= X                    
                             =  X                    
        
         sel(s(X),cons(Y,Z)) =  2 + 2*Y + 2*Z        
                             >= 2 + 2*Z              
                             =  sel(X,activate(Z))   
        
* Step 4: Ara WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            activate(n__from(X)) -> from(X)
            from(X) -> cons(X,n__from(s(X)))
            sel(s(X),cons(Y,Z)) -> sel(X,activate(Z))
        - Weak TRS:
            activate(X) -> X
            from(X) -> n__from(X)
            sel(0(),cons(X,Y)) -> X
        - Signature:
            {activate/1,from/1,sel/2} / {0/0,cons/2,n__from/1,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate,from,sel} and constructors {0,cons,n__from,s}
    + Applied Processor:
        Ara {araHeuristics = Heuristics, minDegree = 1, maxDegree = 1, araTimeout = 3, araRuleShifting = Nothing}
    + Details:
        Signatures used:
        ----------------
          0 :: [] -(0)-> "A"(3)
          activate :: ["A"(0)] -(2)-> "A"(0)
          cons :: ["A"(0) x "A"(0)] -(0)-> "A"(0)
          from :: ["A"(0)] -(1)-> "A"(0)
          n__from :: ["A"(0)] -(0)-> "A"(0)
          s :: ["A"(3)] -(3)-> "A"(3)
          s :: ["A"(0)] -(0)-> "A"(0)
          sel :: ["A"(3) x "A"(0)] -(0)-> "A"(0)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
        
        

WORST_CASE(?,O(n^1))