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)
            after(0(),XS) -> XS
            after(s(N),cons(X,XS)) -> after(N,activate(XS))
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
        - Signature:
            {activate/1,after/2,from/1} / {0/0,cons/2,n__from/1,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate,after,from} 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)
            after(0(),XS) -> XS
            after(s(N),cons(X,XS)) -> after(N,activate(XS))
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
        - Signature:
            {activate/1,after/2,from/1} / {0/0,cons/2,n__from/1,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate,after,from} 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(after) = {2}
        
        Following symbols are considered usable:
          {activate,after,from}
        TcT has computed the following interpretation:
                 p(0) = 1              
          p(activate) = 1 + x1         
             p(after) = 4 + 9*x1 + 2*x2
              p(cons) = x2             
              p(from) = 0              
           p(n__from) = 0              
                 p(s) = 2 + x1         
        
        Following rules are strictly oriented:
                   activate(X) = 1 + X                
                               > X                    
                               = X                    
        
          activate(n__from(X)) = 1                    
                               > 0                    
                               = from(X)              
        
                 after(0(),XS) = 13 + 2*XS            
                               > XS                   
                               = XS                   
        
        after(s(N),cons(X,XS)) = 22 + 9*N + 2*XS      
                               > 6 + 9*N + 2*XS       
                               = after(N,activate(XS))
        
        
        Following rules are (at-least) weakly oriented:
        from(X) =  0                    
                >= 0                    
                =  cons(X,n__from(s(X)))
        
        from(X) =  0                    
                >= 0                    
                =  n__from(X)           
        
* Step 3: NaturalPI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
        - Weak TRS:
            activate(X) -> X
            activate(n__from(X)) -> from(X)
            after(0(),XS) -> XS
            after(s(N),cons(X,XS)) -> after(N,activate(XS))
        - Signature:
            {activate/1,after/2,from/1} / {0/0,cons/2,n__from/1,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate,after,from} 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(after) = {2}
        
        Following symbols are considered usable:
          {activate,after,from}
        TcT has computed the following interpretation:
                 p(0) = 2          
          p(activate) = 7 + x1     
             p(after) = 3*x1 + 4*x2
              p(cons) = 1 + x2     
              p(from) = 9          
           p(n__from) = 2          
                 p(s) = 8 + x1     
        
        Following rules are strictly oriented:
        from(X) = 9                    
                > 3                    
                = cons(X,n__from(s(X)))
        
        from(X) = 9                    
                > 2                    
                = n__from(X)           
        
        
        Following rules are (at-least) weakly oriented:
                   activate(X) =  7 + X                
                               >= X                    
                               =  X                    
        
          activate(n__from(X)) =  9                    
                               >= 9                    
                               =  from(X)              
        
                 after(0(),XS) =  6 + 4*XS             
                               >= XS                   
                               =  XS                   
        
        after(s(N),cons(X,XS)) =  28 + 3*N + 4*XS      
                               >= 28 + 3*N + 4*XS      
                               =  after(N,activate(XS))
        
* Step 4: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            activate(X) -> X
            activate(n__from(X)) -> from(X)
            after(0(),XS) -> XS
            after(s(N),cons(X,XS)) -> after(N,activate(XS))
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
        - Signature:
            {activate/1,after/2,from/1} / {0/0,cons/2,n__from/1,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate,after,from} and constructors {0,cons,n__from,s}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))