WORST_CASE(?,O(n^1))
* Step 1: NaturalPI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            0() -> n__0()
            activate(X) -> X
            activate(n__0()) -> 0()
            activate(n__f(X)) -> f(activate(X))
            activate(n__s(X)) -> s(activate(X))
            f(X) -> n__f(X)
            f(0()) -> cons(0(),n__f(n__s(n__0())))
            f(s(0())) -> f(p(s(0())))
            p(s(0())) -> 0()
            s(X) -> n__s(X)
        - Signature:
            {0/0,activate/1,f/1,p/1,s/1} / {cons/2,n__0/0,n__f/1,n__s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {0,activate,f,p,s} and constructors {cons,n__0,n__f,n__s}
    + 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},
          uargs(s) = {1}
        
        Following symbols are considered usable:
          {0,activate,f,p,s}
        TcT has computed the following interpretation:
                 p(0) = 2       
          p(activate) = 2 + 8*x1
              p(cons) = 4 + x1  
                 p(f) = 8 + x1  
              p(n__0) = 1       
              p(n__f) = 2 + x1  
              p(n__s) = 1 + x1  
                 p(p) = 4       
                 p(s) = 4 + x1  
        
        Following rules are strictly oriented:
                      0() = 2                           
                          > 1                           
                          = n__0()                      
        
              activate(X) = 2 + 8*X                     
                          > X                           
                          = X                           
        
         activate(n__0()) = 10                          
                          > 2                           
                          = 0()                         
        
        activate(n__f(X)) = 18 + 8*X                    
                          > 10 + 8*X                    
                          = f(activate(X))              
        
        activate(n__s(X)) = 10 + 8*X                    
                          > 6 + 8*X                     
                          = s(activate(X))              
        
                     f(X) = 8 + X                       
                          > 2 + X                       
                          = n__f(X)                     
        
                   f(0()) = 10                          
                          > 6                           
                          = cons(0(),n__f(n__s(n__0())))
        
                f(s(0())) = 14                          
                          > 12                          
                          = f(p(s(0())))                
        
                p(s(0())) = 4                           
                          > 2                           
                          = 0()                         
        
                     s(X) = 4 + X                       
                          > 1 + X                       
                          = n__s(X)                     
        
        
        Following rules are (at-least) weakly oriented:
        

WORST_CASE(?,O(n^1))