WORST_CASE(?,O(n^1))
* Step 1: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            a() -> n__a()
            activate(X) -> X
            activate(n__a()) -> a()
            activate(n__f(X)) -> f(X)
            activate(n__g(X)) -> g(X)
            f(X) -> n__f(X)
            f(n__f(n__a())) -> f(n__g(f(n__a())))
            g(X) -> n__g(X)
        - Signature:
            {a/0,activate/1,f/1,g/1} / {n__a/0,n__f/1,n__g/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a,activate,f,g} and constructors {n__a,n__f,n__g}
    + 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(n__g) = {1}
        
        Following symbols are considered usable:
          {a,activate,f,g}
        TcT has computed the following interpretation:
                 p(a) = [7]           
                        [1]           
          p(activate) = [1 4] x1 + [3]
                        [1 2]      [4]
                 p(f) = [1 4] x1 + [2]
                        [1 3]      [4]
                 p(g) = [1 0] x1 + [4]
                        [0 0]      [0]
              p(n__a) = [5]           
                        [0]           
              p(n__f) = [1 4] x1 + [1]
                        [0 0]      [1]
              p(n__g) = [1 0] x1 + [2]
                        [0 0]      [0]
        
        Following rules are strictly oriented:
                      a() = [7]               
                            [1]               
                          > [5]               
                            [0]               
                          = n__a()            
        
              activate(X) = [1 4] X + [3]     
                            [1 2]     [4]     
                          > [1 0] X + [0]     
                            [0 1]     [0]     
                          = X                 
        
         activate(n__a()) = [8]               
                            [9]               
                          > [7]               
                            [1]               
                          = a()               
        
        activate(n__f(X)) = [1 4] X + [8]     
                            [1 4]     [7]     
                          > [1 4] X + [2]     
                            [1 3]     [4]     
                          = f(X)              
        
        activate(n__g(X)) = [1 0] X + [5]     
                            [1 0]     [6]     
                          > [1 0] X + [4]     
                            [0 0]     [0]     
                          = g(X)              
        
                     f(X) = [1 4] X + [2]     
                            [1 3]     [4]     
                          > [1 4] X + [1]     
                            [0 0]     [1]     
                          = n__f(X)           
        
          f(n__f(n__a())) = [12]              
                            [13]              
                          > [11]              
                            [13]              
                          = f(n__g(f(n__a())))
        
                     g(X) = [1 0] X + [4]     
                            [0 0]     [0]     
                          > [1 0] X + [2]     
                            [0 0]     [0]     
                          = n__g(X)           
        
        
        Following rules are (at-least) weakly oriented:
        

WORST_CASE(?,O(n^1))