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

WORST_CASE(?,O(n^2))