WORST_CASE(?,O(n^1))
* Step 1: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            activate(n__f(X)) -> f(X)
            f(X) -> n__f(X)
            f(0()) -> cons(0(),n__f(s(0())))
            f(s(0())) -> f(p(s(0())))
            p(s(X)) -> X
        - Signature:
            {activate/1,f/1,p/1} / {0/0,cons/2,n__f/1,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate,f,p} and constructors {0,cons,n__f,s}
    + Applied Processor:
        NaturalMI {miDimension = 2, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation (containing no more than 1 non-zero interpretation-entries in the diagonal of the component-wise maxima):
        The following argument positions are considered usable:
          uargs(f) = {1}
        
        Following symbols are considered usable:
          {activate,f,p}
        TcT has computed the following interpretation:
                 p(0) = [0]            
                        [0]            
          p(activate) = [4 0] x1 + [11]
                        [0 1]      [8] 
              p(cons) = [0 2] x2 + [1] 
                        [0 0]      [8] 
                 p(f) = [2 4] x1 + [3] 
                        [0 0]      [8] 
              p(n__f) = [1 1] x1 + [0] 
                        [0 0]      [0] 
                 p(p) = [2 0] x1 + [4] 
                        [2 0]      [0] 
                 p(s) = [1 4] x1 + [0] 
                        [0 0]      [4] 
        
        Following rules are strictly oriented:
              activate(X) = [4 0] X + [11]        
                            [0 1]     [8]         
                          > [1 0] X + [0]         
                            [0 1]     [0]         
                          = X                     
        
        activate(n__f(X)) = [4 4] X + [11]        
                            [0 0]     [8]         
                          > [2 4] X + [3]         
                            [0 0]     [8]         
                          = f(X)                  
        
                     f(X) = [2 4] X + [3]         
                            [0 0]     [8]         
                          > [1 1] X + [0]         
                            [0 0]     [0]         
                          = n__f(X)               
        
                   f(0()) = [3]                   
                            [8]                   
                          > [1]                   
                            [8]                   
                          = cons(0(),n__f(s(0())))
        
                f(s(0())) = [19]                  
                            [8]                   
                          > [11]                  
                            [8]                   
                          = f(p(s(0())))          
        
                  p(s(X)) = [2 8] X + [4]         
                            [2 8]     [0]         
                          > [1 0] X + [0]         
                            [0 1]     [0]         
                          = X                     
        
        
        Following rules are (at-least) weakly oriented:
        

WORST_CASE(?,O(n^1))