WORST_CASE(?,O(n^2))
* Step 1: NaturalPI 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:
        NaturalPI {shape = Quadratic, restrict = NoRestrict, uargs = UArgs, urules = URules, selector = Nothing}
    + Details:
        We apply a polynomial interpretation of kind constructor-based(quadratic):
        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) = 1                          
           p(false) = 2                          
             p(gcd) = 1 + 2*x1 + x1^2 + x2 + x2^2
          p(if_gcd) = x1 + x2 + x2^2 + x3 + x3^2 
              p(le) = 2 + x2                     
           p(minus) = 1 + x1                     
               p(s) = 2 + x1                     
            p(true) = 0                          
        
        Following rules are strictly oriented:
                       gcd(0(),y) = 4 + y + y^2               
                                  > y                         
                                  = y                         
        
                    gcd(s(x),0()) = 11 + 6*x + x^2            
                                  > 2 + x                     
                                  = s(x)                      
        
                   gcd(s(x),s(y)) = 15 + 6*x + x^2 + 5*y + y^2
                                  > 14 + 6*x + x^2 + 5*y + y^2
                                  = if_gcd(le(y,x),s(x),s(y)) 
        
        if_gcd(false(),s(x),s(y)) = 14 + 5*x + x^2 + 5*y + y^2
                                  > 10 + 5*x + x^2 + 4*y + y^2
                                  = gcd(minus(y,x),s(x))      
        
         if_gcd(true(),s(x),s(y)) = 12 + 5*x + x^2 + 5*y + y^2
                                  > 10 + 4*x + x^2 + 5*y + y^2
                                  = gcd(minus(x,y),s(y))      
        
                        le(0(),y) = 2 + y                     
                                  > 0                         
                                  = true()                    
        
                     le(s(x),0()) = 3                         
                                  > 2                         
                                  = false()                   
        
                    le(s(x),s(y)) = 4 + y                     
                                  > 2 + y                     
                                  = le(x,y)                   
        
                     minus(x,0()) = 1 + x                     
                                  > x                         
                                  = x                         
        
                 minus(s(x),s(y)) = 3 + x                     
                                  > 1 + x                     
                                  = minus(x,y)                
        
        
        Following rules are (at-least) weakly oriented:
        

WORST_CASE(?,O(n^2))