WORST_CASE(?,O(n^1))
* Step 1: NaturalMI 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:
        NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation:
        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) = [5]          
          p(activate) = [5] x1 + [1] 
              p(cons) = [8]          
                 p(f) = [1] x1 + [4] 
              p(n__0) = [1]          
              p(n__f) = [1] x1 + [1] 
              p(n__s) = [1] x1 + [4] 
                 p(p) = [7]          
                 p(s) = [1] x1 + [11]
        
        Following rules are strictly oriented:
                      0() = [5]                         
                          > [1]                         
                          = n__0()                      
        
              activate(X) = [5] X + [1]                 
                          > [1] X + [0]                 
                          = X                           
        
         activate(n__0()) = [6]                         
                          > [5]                         
                          = 0()                         
        
        activate(n__f(X)) = [5] X + [6]                 
                          > [5] X + [5]                 
                          = f(activate(X))              
        
        activate(n__s(X)) = [5] X + [21]                
                          > [5] X + [12]                
                          = s(activate(X))              
        
                     f(X) = [1] X + [4]                 
                          > [1] X + [1]                 
                          = n__f(X)                     
        
                   f(0()) = [9]                         
                          > [8]                         
                          = cons(0(),n__f(n__s(n__0())))
        
                f(s(0())) = [20]                        
                          > [11]                        
                          = f(p(s(0())))                
        
                p(s(0())) = [7]                         
                          > [5]                         
                          = 0()                         
        
                     s(X) = [1] X + [11]                
                          > [1] X + [4]                 
                          = n__s(X)                     
        
        
        Following rules are (at-least) weakly oriented:
        

WORST_CASE(?,O(n^1))