WORST_CASE(?,O(n^2))
* Step 1: NaturalMI WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            a__div(X1,X2) -> div(X1,X2)
            a__div(0(),s(Y)) -> 0()
            a__div(s(X),s(Y)) -> a__if(a__geq(X,Y),s(div(minus(X,Y),s(Y))),0())
            a__geq(X,0()) -> true()
            a__geq(X1,X2) -> geq(X1,X2)
            a__geq(0(),s(Y)) -> false()
            a__geq(s(X),s(Y)) -> a__geq(X,Y)
            a__if(X1,X2,X3) -> if(X1,X2,X3)
            a__if(false(),X,Y) -> mark(Y)
            a__if(true(),X,Y) -> mark(X)
            a__minus(X1,X2) -> minus(X1,X2)
            a__minus(0(),Y) -> 0()
            a__minus(s(X),s(Y)) -> a__minus(X,Y)
            mark(0()) -> 0()
            mark(div(X1,X2)) -> a__div(mark(X1),X2)
            mark(false()) -> false()
            mark(geq(X1,X2)) -> a__geq(X1,X2)
            mark(if(X1,X2,X3)) -> a__if(mark(X1),X2,X3)
            mark(minus(X1,X2)) -> a__minus(X1,X2)
            mark(s(X)) -> s(mark(X))
            mark(true()) -> true()
        - Signature:
            {a__div/2,a__geq/2,a__if/3,a__minus/2,mark/1} / {0/0,div/2,false/0,geq/2,if/3,minus/2,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a__div,a__geq,a__if,a__minus,mark} and constructors {0
            ,div,false,geq,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(a__div) = {1},
          uargs(a__if) = {1},
          uargs(s) = {1}
        
        Following symbols are considered usable:
          {a__div,a__geq,a__if,a__minus,mark}
        TcT has computed the following interpretation:
                 p(0) = [0]                                 
                        [0]                                 
            p(a__div) = [1 3] x1 + [2]                      
                        [0 1]      [0]                      
            p(a__geq) = [1 0] x1 + [4]                      
                        [0 0]      [1]                      
             p(a__if) = [1 0] x1 + [4 0] x2 + [4 0] x3 + [2]
                        [0 0]      [0 1]      [0 1]      [0]
          p(a__minus) = [0 1] x1 + [1]                      
                        [0 0]      [0]                      
               p(div) = [1 2] x1 + [1]                      
                        [0 1]      [0]                      
             p(false) = [2]                                 
                        [0]                                 
               p(geq) = [1 0] x1 + [2]                      
                        [0 0]      [1]                      
                p(if) = [1 0] x1 + [1 0] x2 + [1 0] x3 + [1]
                        [0 0]      [0 1]      [0 1]      [0]
              p(mark) = [4 0] x1 + [2]                      
                        [0 1]      [0]                      
             p(minus) = [0 1] x1 + [0]                      
                        [0 0]      [0]                      
                 p(s) = [1 2] x1 + [1]                      
                        [0 1]      [4]                      
              p(true) = [1]                                 
                        [0]                                 
        
        Following rules are strictly oriented:
              a__div(X1,X2) = [1 3] X1 + [2]                                
                              [0 1]      [0]                                
                            > [1 2] X1 + [1]                                
                              [0 1]      [0]                                
                            = div(X1,X2)                                    
        
           a__div(0(),s(Y)) = [2]                                           
                              [0]                                           
                            > [0]                                           
                              [0]                                           
                            = 0()                                           
        
          a__div(s(X),s(Y)) = [1 5] X + [15]                                
                              [0 1]     [4]                                 
                            > [1 4] X + [14]                                
                              [0 0]     [4]                                 
                            = a__if(a__geq(X,Y),s(div(minus(X,Y),s(Y))),0())
        
              a__geq(X,0()) = [1 0] X + [4]                                 
                              [0 0]     [1]                                 
                            > [1]                                           
                              [0]                                           
                            = true()                                        
        
              a__geq(X1,X2) = [1 0] X1 + [4]                                
                              [0 0]      [1]                                
                            > [1 0] X1 + [2]                                
                              [0 0]      [1]                                
                            = geq(X1,X2)                                    
        
           a__geq(0(),s(Y)) = [4]                                           
                              [1]                                           
                            > [2]                                           
                              [0]                                           
                            = false()                                       
        
          a__geq(s(X),s(Y)) = [1 2] X + [5]                                 
                              [0 0]     [1]                                 
                            > [1 0] X + [4]                                 
                              [0 0]     [1]                                 
                            = a__geq(X,Y)                                   
        
            a__if(X1,X2,X3) = [1 0] X1 + [4 0] X2 + [4 0] X3 + [2]          
                              [0 0]      [0 1]      [0 1]      [0]          
                            > [1 0] X1 + [1 0] X2 + [1 0] X3 + [1]          
                              [0 0]      [0 1]      [0 1]      [0]          
                            = if(X1,X2,X3)                                  
        
         a__if(false(),X,Y) = [4 0] X + [4 0] Y + [4]                       
                              [0 1]     [0 1]     [0]                       
                            > [4 0] Y + [2]                                 
                              [0 1]     [0]                                 
                            = mark(Y)                                       
        
          a__if(true(),X,Y) = [4 0] X + [4 0] Y + [3]                       
                              [0 1]     [0 1]     [0]                       
                            > [4 0] X + [2]                                 
                              [0 1]     [0]                                 
                            = mark(X)                                       
        
            a__minus(X1,X2) = [0 1] X1 + [1]                                
                              [0 0]      [0]                                
                            > [0 1] X1 + [0]                                
                              [0 0]      [0]                                
                            = minus(X1,X2)                                  
        
            a__minus(0(),Y) = [1]                                           
                              [0]                                           
                            > [0]                                           
                              [0]                                           
                            = 0()                                           
        
        a__minus(s(X),s(Y)) = [0 1] X + [5]                                 
                              [0 0]     [0]                                 
                            > [0 1] X + [1]                                 
                              [0 0]     [0]                                 
                            = a__minus(X,Y)                                 
        
                  mark(0()) = [2]                                           
                              [0]                                           
                            > [0]                                           
                              [0]                                           
                            = 0()                                           
        
           mark(div(X1,X2)) = [4 8] X1 + [6]                                
                              [0 1]      [0]                                
                            > [4 3] X1 + [4]                                
                              [0 1]      [0]                                
                            = a__div(mark(X1),X2)                           
        
              mark(false()) = [10]                                          
                              [0]                                           
                            > [2]                                           
                              [0]                                           
                            = false()                                       
        
           mark(geq(X1,X2)) = [4 0] X1 + [10]                               
                              [0 0]      [1]                                
                            > [1 0] X1 + [4]                                
                              [0 0]      [1]                                
                            = a__geq(X1,X2)                                 
        
         mark(if(X1,X2,X3)) = [4 0] X1 + [4 0] X2 + [4 0] X3 + [6]          
                              [0 0]      [0 1]      [0 1]      [0]          
                            > [4 0] X1 + [4 0] X2 + [4 0] X3 + [4]          
                              [0 0]      [0 1]      [0 1]      [0]          
                            = a__if(mark(X1),X2,X3)                         
        
         mark(minus(X1,X2)) = [0 4] X1 + [2]                                
                              [0 0]      [0]                                
                            > [0 1] X1 + [1]                                
                              [0 0]      [0]                                
                            = a__minus(X1,X2)                               
        
                 mark(s(X)) = [4 8] X + [6]                                 
                              [0 1]     [4]                                 
                            > [4 2] X + [3]                                 
                              [0 1]     [4]                                 
                            = s(mark(X))                                    
        
               mark(true()) = [6]                                           
                              [0]                                           
                            > [1]                                           
                              [0]                                           
                            = true()                                        
        
        
        Following rules are (at-least) weakly oriented:
        

WORST_CASE(?,O(n^2))