WORST_CASE(?,O(n^1))
* Step 1: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            a__f(X) -> f(X)
            a__f(f(a())) -> a__f(g(f(a())))
            mark(a()) -> a()
            mark(f(X)) -> a__f(X)
            mark(g(X)) -> g(mark(X))
        - Signature:
            {a__f/1,mark/1} / {a/0,f/1,g/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a__f,mark} and constructors {a,f,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(g) = {1}
        
        Following symbols are considered usable:
          {a__f,mark}
        TcT has computed the following interpretation:
             p(a) = [0]             
                    [0]             
          p(a__f) = [0 8] x1 + [2]  
                    [0 8]      [2]  
             p(f) = [0 2] x1 + [1]  
                    [0 0]      [2]  
             p(g) = [1 0] x1 + [2]  
                    [0 0]      [0]  
          p(mark) = [ 5 0] x1 + [10]
                    [12 2]      [0] 
        
        Following rules are strictly oriented:
             a__f(X) = [0 8] X + [2]  
                       [0 8]     [2]  
                     > [0 2] X + [1]  
                       [0 0]     [2]  
                     = f(X)           
        
        a__f(f(a())) = [18]           
                       [18]           
                     > [2]            
                       [2]            
                     = a__f(g(f(a())))
        
           mark(a()) = [10]           
                       [0]            
                     > [0]            
                       [0]            
                     = a()            
        
          mark(f(X)) = [0 10] X + [15]
                       [0 24]     [16]
                     > [0 8] X + [2]  
                       [0 8]     [2]  
                     = a__f(X)        
        
          mark(g(X)) = [ 5 0] X + [20]
                       [12 0]     [24]
                     > [5 0] X + [12] 
                       [0 0]     [0]  
                     = g(mark(X))     
        
        
        Following rules are (at-least) weakly oriented:
        

WORST_CASE(?,O(n^1))