WORST_CASE(?,O(n^1))
* Step 1: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            f(f(x)) -> f(c(f(x)))
            f(f(x)) -> f(d(f(x)))
            g(c(x)) -> x
            g(c(0())) -> g(d(1()))
            g(c(1())) -> g(d(0()))
            g(d(x)) -> x
        - Signature:
            {f/1,g/1} / {0/0,1/0,c/1,d/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,g} and constructors {0,1,c,d}
    + 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:
          none
        
        Following symbols are considered usable:
          {f,g}
        TcT has computed the following interpretation:
          p(0) = [0]           
                 [0]           
          p(1) = [0]           
                 [0]           
          p(c) = [1 2] x1 + [1]
                 [0 0]      [0]
          p(d) = [1 4] x1 + [0]
                 [0 0]      [0]
          p(f) = [0 4] x1 + [0]
                 [0 0]      [1]
          p(g) = [2 0] x1 + [4]
                 [1 0]      [1]
        
        Following rules are strictly oriented:
          f(f(x)) = [4]          
                    [1]          
                  > [0]          
                    [1]          
                  = f(c(f(x)))   
        
          f(f(x)) = [4]          
                    [1]          
                  > [0]          
                    [1]          
                  = f(d(f(x)))   
        
          g(c(x)) = [2 4] x + [6]
                    [1 2]     [2]
                  > [1 0] x + [0]
                    [0 1]     [0]
                  = x            
        
        g(c(0())) = [6]          
                    [2]          
                  > [4]          
                    [1]          
                  = g(d(1()))    
        
        g(c(1())) = [6]          
                    [2]          
                  > [4]          
                    [1]          
                  = g(d(0()))    
        
          g(d(x)) = [2 8] x + [4]
                    [1 4]     [1]
                  > [1 0] x + [0]
                    [0 1]     [0]
                  = x            
        
        
        Following rules are (at-least) weakly oriented:
        

WORST_CASE(?,O(n^1))