WORST_CASE(?,O(n^2))
* Step 1: NaturalMI WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            div_active(x,y) -> div(x,y)
            div_active(0(),s(y)) -> 0()
            div_active(s(x),s(y)) -> if_active(ge_active(x,y),s(div(minus(x,y),s(y))),0())
            ge_active(x,y) -> ge(x,y)
            ge_active(x,0()) -> true()
            ge_active(0(),s(y)) -> false()
            ge_active(s(x),s(y)) -> ge_active(x,y)
            if_active(x,y,z) -> if(x,y,z)
            if_active(false(),x,y) -> mark(y)
            if_active(true(),x,y) -> mark(x)
            mark(0()) -> 0()
            mark(div(x,y)) -> div_active(mark(x),y)
            mark(ge(x,y)) -> ge_active(x,y)
            mark(if(x,y,z)) -> if_active(mark(x),y,z)
            mark(minus(x,y)) -> minus_active(x,y)
            mark(s(x)) -> s(mark(x))
            minus_active(x,y) -> minus(x,y)
            minus_active(0(),y) -> 0()
            minus_active(s(x),s(y)) -> minus_active(x,y)
        - Signature:
            {div_active/2,ge_active/2,if_active/3,mark/1,minus_active/2} / {0/0,div/2,false/0,ge/2,if/3,minus/2,s/1
            ,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {div_active,ge_active,if_active,mark
            ,minus_active} and constructors {0,div,false,ge,if,minus,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(div_active) = {1},
          uargs(if_active) = {1},
          uargs(s) = {1}
        
        Following symbols are considered usable:
          {div_active,ge_active,if_active,mark,minus_active}
        TcT has computed the following interpretation:
                     p(0) = [0]                                 
                            [0]                                 
                   p(div) = [1 4] x1 + [0]                      
                            [0 1]      [1]                      
            p(div_active) = [1 7] x1 + [1]                      
                            [0 1]      [1]                      
                 p(false) = [1]                                 
                            [0]                                 
                    p(ge) = [1 1] x1 + [3]                      
                            [0 0]      [0]                      
             p(ge_active) = [1 1] x1 + [4]                      
                            [0 0]      [0]                      
                    p(if) = [1 0] x1 + [1 0] x2 + [1 1] x3 + [3]
                            [0 1]      [0 1]      [0 1]      [0]
             p(if_active) = [1 0] x1 + [2 2] x2 + [2 2] x3 + [4]
                            [0 1]      [0 1]      [0 1]      [0]
                  p(mark) = [2 2] x1 + [2]                      
                            [0 1]      [0]                      
                 p(minus) = [0 1] x1 + [0]                      
                            [0 0]      [0]                      
          p(minus_active) = [0 1] x1 + [1]                      
                            [0 0]      [0]                      
                     p(s) = [1 0] x1 + [0]                      
                            [0 1]      [2]                      
                  p(true) = [2]                                 
                            [0]                                 
        
        Following rules are strictly oriented:
                div_active(x,y) = [1 7] x + [1]                                        
                                  [0 1]     [1]                                        
                                > [1 4] x + [0]                                        
                                  [0 1]     [1]                                        
                                = div(x,y)                                             
        
           div_active(0(),s(y)) = [1]                                                  
                                  [1]                                                  
                                > [0]                                                  
                                  [0]                                                  
                                = 0()                                                  
        
          div_active(s(x),s(y)) = [1 7] x + [15]                                       
                                  [0 1]     [3]                                        
                                > [1 3] x + [14]                                       
                                  [0 0]     [3]                                        
                                = if_active(ge_active(x,y),s(div(minus(x,y),s(y))),0())
        
                 ge_active(x,y) = [1 1] x + [4]                                        
                                  [0 0]     [0]                                        
                                > [1 1] x + [3]                                        
                                  [0 0]     [0]                                        
                                = ge(x,y)                                              
        
               ge_active(x,0()) = [1 1] x + [4]                                        
                                  [0 0]     [0]                                        
                                > [2]                                                  
                                  [0]                                                  
                                = true()                                               
        
            ge_active(0(),s(y)) = [4]                                                  
                                  [0]                                                  
                                > [1]                                                  
                                  [0]                                                  
                                = false()                                              
        
           ge_active(s(x),s(y)) = [1 1] x + [6]                                        
                                  [0 0]     [0]                                        
                                > [1 1] x + [4]                                        
                                  [0 0]     [0]                                        
                                = ge_active(x,y)                                       
        
               if_active(x,y,z) = [1 0] x + [2 2] y + [2 2] z + [4]                    
                                  [0 1]     [0 1]     [0 1]     [0]                    
                                > [1 0] x + [1 0] y + [1 1] z + [3]                    
                                  [0 1]     [0 1]     [0 1]     [0]                    
                                = if(x,y,z)                                            
        
         if_active(false(),x,y) = [2 2] x + [2 2] y + [5]                              
                                  [0 1]     [0 1]     [0]                              
                                > [2 2] y + [2]                                        
                                  [0 1]     [0]                                        
                                = mark(y)                                              
        
          if_active(true(),x,y) = [2 2] x + [2 2] y + [6]                              
                                  [0 1]     [0 1]     [0]                              
                                > [2 2] x + [2]                                        
                                  [0 1]     [0]                                        
                                = mark(x)                                              
        
                      mark(0()) = [2]                                                  
                                  [0]                                                  
                                > [0]                                                  
                                  [0]                                                  
                                = 0()                                                  
        
                 mark(div(x,y)) = [2 10] x + [4]                                       
                                  [0  1]     [1]                                       
                                > [2 9] x + [3]                                        
                                  [0 1]     [1]                                        
                                = div_active(mark(x),y)                                
        
                  mark(ge(x,y)) = [2 2] x + [8]                                        
                                  [0 0]     [0]                                        
                                > [1 1] x + [4]                                        
                                  [0 0]     [0]                                        
                                = ge_active(x,y)                                       
        
                mark(if(x,y,z)) = [2 2] x + [2 2] y + [2 4] z + [8]                    
                                  [0 1]     [0 1]     [0 1]     [0]                    
                                > [2 2] x + [2 2] y + [2 2] z + [6]                    
                                  [0 1]     [0 1]     [0 1]     [0]                    
                                = if_active(mark(x),y,z)                               
        
               mark(minus(x,y)) = [0 2] x + [2]                                        
                                  [0 0]     [0]                                        
                                > [0 1] x + [1]                                        
                                  [0 0]     [0]                                        
                                = minus_active(x,y)                                    
        
                     mark(s(x)) = [2 2] x + [6]                                        
                                  [0 1]     [2]                                        
                                > [2 2] x + [2]                                        
                                  [0 1]     [2]                                        
                                = s(mark(x))                                           
        
              minus_active(x,y) = [0 1] x + [1]                                        
                                  [0 0]     [0]                                        
                                > [0 1] x + [0]                                        
                                  [0 0]     [0]                                        
                                = minus(x,y)                                           
        
            minus_active(0(),y) = [1]                                                  
                                  [0]                                                  
                                > [0]                                                  
                                  [0]                                                  
                                = 0()                                                  
        
        minus_active(s(x),s(y)) = [0 1] x + [3]                                        
                                  [0 0]     [0]                                        
                                > [0 1] x + [1]                                        
                                  [0 0]     [0]                                        
                                = minus_active(x,y)                                    
        
        
        Following rules are (at-least) weakly oriented:
        

WORST_CASE(?,O(n^2))