WORST_CASE(?,O(n^2))
* Step 1: NaturalMI WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            f(0()) -> true()
            f(1()) -> false()
            f(s(x)) -> f(x)
            g(x,c(y)) -> g(x,g(s(c(y)),y))
            g(s(x),s(y)) -> if(f(x),s(x),s(y))
            if(false(),x,y) -> y
            if(true(),x,y) -> x
        - Signature:
            {f/1,g/2,if/3} / {0/0,1/0,c/1,false/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,g,if} and constructors {0,1,c,false,s,true}
    + Applied Processor:
        NaturalMI {miDimension = 2, miDegree = 2, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation:
        The following argument positions are considered usable:
          uargs(g) = {2},
          uargs(if) = {1}
        
        Following symbols are considered usable:
          {f,g,if}
        TcT has computed the following interpretation:
              p(0) = [0]                                 
                     [7]                                 
              p(1) = [2]                                 
                     [6]                                 
              p(c) = [1 0] x1 + [7]                      
                     [0 0]      [1]                      
              p(f) = [0 1] x1 + [0]                      
                     [0 0]      [0]                      
          p(false) = [2]                                 
                     [0]                                 
              p(g) = [2 0] x1 + [1 0] x2 + [0]           
                     [0 1]      [1 0]      [0]           
             p(if) = [1 4] x1 + [1 0] x2 + [1 0] x3 + [0]
                     [0 0]      [0 1]      [0 1]      [0]
              p(s) = [0 1] x1 + [2]                      
                     [0 1]      [2]                      
           p(true) = [6]                                 
                     [0]                                 
        
        Following rules are strictly oriented:
                 f(0()) = [7]                    
                          [0]                    
                        > [6]                    
                          [0]                    
                        = true()                 
        
                 f(1()) = [6]                    
                          [0]                    
                        > [2]                    
                          [0]                    
                        = false()                
        
                f(s(x)) = [0 1] x + [2]          
                          [0 0]     [0]          
                        > [0 1] x + [0]          
                          [0 0]     [0]          
                        = f(x)                   
        
              g(x,c(y)) = [2 0] x + [1 0] y + [7]
                          [0 1]     [1 0]     [7]
                        > [2 0] x + [1 0] y + [6]
                          [0 1]     [1 0]     [6]
                        = g(x,g(s(c(y)),y))      
        
           g(s(x),s(y)) = [0 2] x + [0 1] y + [6]
                          [0 1]     [0 1]     [4]
                        > [0 2] x + [0 1] y + [4]
                          [0 1]     [0 1]     [4]
                        = if(f(x),s(x),s(y))     
        
        if(false(),x,y) = [1 0] x + [1 0] y + [2]
                          [0 1]     [0 1]     [0]
                        > [1 0] y + [0]          
                          [0 1]     [0]          
                        = y                      
        
         if(true(),x,y) = [1 0] x + [1 0] y + [6]
                          [0 1]     [0 1]     [0]
                        > [1 0] x + [0]          
                          [0 1]     [0]          
                        = x                      
        
        
        Following rules are (at-least) weakly oriented:
        

WORST_CASE(?,O(n^2))