WORST_CASE(?,O(n^1))
* Step 1: NaturalPI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            activate(n__f(X)) -> f(X)
            f(X) -> if(X,c(),n__f(true()))
            f(X) -> n__f(X)
            if(false(),X,Y) -> activate(Y)
            if(true(),X,Y) -> X
        - Signature:
            {activate/1,f/1,if/3} / {c/0,false/0,n__f/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate,f,if} and constructors {c,false,n__f,true}
    + 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:
          none
        
        Following symbols are considered usable:
          {activate,f,if}
        TcT has computed the following interpretation:
          p(activate) = 12 + 8*x1             
                 p(c) = 0                     
                 p(f) = 11 + 6*x1             
             p(false) = 1                     
                p(if) = 8 + 5*x1 + 8*x2 + 8*x3
              p(n__f) = x1                    
              p(true) = 0                     
        
        Following rules are strictly oriented:
              activate(X) = 12 + 8*X              
                          > X                     
                          = X                     
        
        activate(n__f(X)) = 12 + 8*X              
                          > 11 + 6*X              
                          = f(X)                  
        
                     f(X) = 11 + 6*X              
                          > 8 + 5*X               
                          = if(X,c(),n__f(true()))
        
                     f(X) = 11 + 6*X              
                          > X                     
                          = n__f(X)               
        
          if(false(),X,Y) = 13 + 8*X + 8*Y        
                          > 12 + 8*Y              
                          = activate(Y)           
        
           if(true(),X,Y) = 8 + 8*X + 8*Y         
                          > X                     
                          = X                     
        
        
        Following rules are (at-least) weakly oriented:
        

WORST_CASE(?,O(n^1))