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(X)) -> X
            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 = 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},
          uargs(s) = {1}
        
        Following symbols are considered usable:
          {0,activate,f,p,s}
        TcT has computed the following interpretation:
                 p(0) = [1]           
                        [0]           
          p(activate) = [4 4] x1 + [5]
                        [0 2]      [0]
              p(cons) = [0 1] x1 + [1]
                        [0 0]      [4]
                 p(f) = [1 4] x1 + [1]
                        [0 0]      [4]
              p(n__0) = [0]           
                        [0]           
              p(n__f) = [1 3] x1 + [0]
                        [0 0]      [2]
              p(n__s) = [1 3] x1 + [0]
                        [0 0]      [2]
                 p(p) = [1 0] x1 + [0]
                        [1 0]      [0]
                 p(s) = [1 4] x1 + [1]
                        [0 0]      [3]
        
        Following rules are strictly oriented:
                      0() = [1]                         
                            [0]                         
                          > [0]                         
                            [0]                         
                          = n__0()                      
        
              activate(X) = [4 4] X + [5]               
                            [0 2]     [0]               
                          > [1 0] X + [0]               
                            [0 1]     [0]               
                          = X                           
        
         activate(n__0()) = [5]                         
                            [0]                         
                          > [1]                         
                            [0]                         
                          = 0()                         
        
        activate(n__f(X)) = [4 12] X + [13]             
                            [0  0]     [4]              
                          > [4 12] X + [6]              
                            [0  0]     [4]              
                          = f(activate(X))              
        
        activate(n__s(X)) = [4 12] X + [13]             
                            [0  0]     [4]              
                          > [4 12] X + [6]              
                            [0  0]     [3]              
                          = s(activate(X))              
        
                     f(X) = [1 4] X + [1]               
                            [0 0]     [4]               
                          > [1 3] X + [0]               
                            [0 0]     [2]               
                          = n__f(X)                     
        
                   f(0()) = [2]                         
                            [4]                         
                          > [1]                         
                            [4]                         
                          = cons(0(),n__f(n__s(n__0())))
        
                f(s(0())) = [15]                        
                            [4]                         
                          > [11]                        
                            [4]                         
                          = f(p(s(0())))                
        
                  p(s(X)) = [1 4] X + [1]               
                            [1 4]     [1]               
                          > [1 0] X + [0]               
                            [0 1]     [0]               
                          = X                           
        
                     s(X) = [1 4] X + [1]               
                            [0 0]     [3]               
                          > [1 3] X + [0]               
                            [0 0]     [2]               
                          = n__s(X)                     
        
        
        Following rules are (at-least) weakly oriented:
        

WORST_CASE(?,O(n^1))