WORST_CASE(?,O(n^1))
* Step 1: NaturalPI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            a() -> n__a()
            activate(X) -> X
            activate(n__a()) -> a()
            activate(n__f(X)) -> f(activate(X))
            f(X) -> n__f(X)
            f(f(a())) -> f(g(n__f(n__a())))
        - Signature:
            {a/0,activate/1,f/1} / {g/1,n__a/0,n__f/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a,activate,f} and constructors {g,n__a,n__f}
    + Applied Processor:
        NaturalPI {shape = Linear, restrict = NoRestrict, uargs = UArgs, urules = URules, selector = Nothing}
    + Details:
        We apply a polynomial interpretation of kind constructor-based(linear):
        The following argument positions are considered usable:
          uargs(f) = {1}
        
        Following symbols are considered usable:
          {a,activate,f}
        TcT has computed the following interpretation:
                 p(a) = 3       
          p(activate) = 7 + 8*x1
                 p(f) = 2 + x1  
                 p(g) = 3       
              p(n__a) = 0       
              p(n__f) = 1 + x1  
        
        Following rules are strictly oriented:
                      a() = 3                 
                          > 0                 
                          = n__a()            
        
              activate(X) = 7 + 8*X           
                          > X                 
                          = X                 
        
         activate(n__a()) = 7                 
                          > 3                 
                          = a()               
        
        activate(n__f(X)) = 15 + 8*X          
                          > 9 + 8*X           
                          = f(activate(X))    
        
                     f(X) = 2 + X             
                          > 1 + X             
                          = n__f(X)           
        
                f(f(a())) = 7                 
                          > 5                 
                          = f(g(n__f(n__a())))
        
        
        Following rules are (at-least) weakly oriented:
        

WORST_CASE(?,O(n^1))