WORST_CASE(?,O(n^1))
* Step 1: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            f0(x1,0(),x3,x4,x5) -> 0()
            f0(x1,S(x),x3,0(),x5) -> 0()
            f0(x1,S(x'),x3,S(x),x5) -> f1(x',S(x'),x,S(x),S(x))
            f1(x1,x2,x3,x4,0()) -> 0()
            f1(x1,x2,x3,x4,S(x)) -> f2(x2,x1,x3,x4,x)
            f2(x1,x2,0(),x4,x5) -> 0()
            f2(x1,x2,S(x),0(),0()) -> 0()
            f2(x1,x2,S(x'),0(),S(x)) -> f3(x1,x2,x',0(),x)
            f2(x1,x2,S(x'),S(x),0()) -> 0()
            f2(x1,x2,S(x''),S(x'),S(x)) -> f5(x1,x2,S(x''),x',x)
            f3(x1,x2,x3,x4,0()) -> 0()
            f3(x1,x2,x3,x4,S(x)) -> f4(x1,x2,x4,x3,x)
            f4(0(),x2,x3,x4,x5) -> 0()
            f4(S(x),0(),x3,x4,0()) -> 0()
            f4(S(x'),0(),x3,x4,S(x)) -> f3(x',0(),x3,x4,x)
            f4(S(x'),S(x),x3,x4,0()) -> 0()
            f4(S(x''),S(x'),x3,x4,S(x)) -> f2(S(x''),x',x3,x4,x)
            f5(x1,x2,x3,x4,0()) -> 0()
            f5(x1,x2,x3,x4,S(x)) -> f6(x2,x1,x3,x4,x)
            f6(x1,x2,x3,x4,0()) -> 0()
            f6(x1,x2,x3,x4,S(x)) -> f0(x1,x2,x4,x3,x)
        - Signature:
            {f0/5,f1/5,f2/5,f3/5,f4/5,f5/5,f6/5} / {0/0,S/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f0,f1,f2,f3,f4,f5,f6} and constructors {0,S}
    + Applied Processor:
        NaturalMI {miDimension = 1, miDegree = 1, 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:
          none
        
        Following symbols are considered usable:
          {f0,f1,f2,f3,f4,f5,f6}
        TcT has computed the following interpretation:
           p(0) = [0]                           
           p(S) = [1] x1 + [4]                  
          p(f0) = [1] x2 + [2] x4 + [1]         
          p(f1) = [1] x2 + [2] x3 + [5]         
          p(f2) = [1] x1 + [2] x3 + [4]         
          p(f3) = [1] x1 + [2] x3 + [2] x4 + [6]
          p(f4) = [1] x1 + [2] x3 + [2] x4 + [5]
          p(f5) = [1] x1 + [2] x3 + [3]         
          p(f6) = [1] x2 + [2] x3 + [2]         
        
        Following rules are strictly oriented:
                f0(x1,0(),x3,x4,x5) = [2] x4 + [1]                   
                                    > [0]                            
                                    = 0()                            
        
              f0(x1,S(x),x3,0(),x5) = [1] x + [5]                    
                                    > [0]                            
                                    = 0()                            
        
            f0(x1,S(x'),x3,S(x),x5) = [2] x + [1] x' + [13]          
                                    > [2] x + [1] x' + [9]           
                                    = f1(x',S(x'),x,S(x),S(x))       
        
                f1(x1,x2,x3,x4,0()) = [1] x2 + [2] x3 + [5]          
                                    > [0]                            
                                    = 0()                            
        
               f1(x1,x2,x3,x4,S(x)) = [1] x2 + [2] x3 + [5]          
                                    > [1] x2 + [2] x3 + [4]          
                                    = f2(x2,x1,x3,x4,x)              
        
                f2(x1,x2,0(),x4,x5) = [1] x1 + [4]                   
                                    > [0]                            
                                    = 0()                            
        
             f2(x1,x2,S(x),0(),0()) = [2] x + [1] x1 + [12]          
                                    > [0]                            
                                    = 0()                            
        
           f2(x1,x2,S(x'),0(),S(x)) = [2] x' + [1] x1 + [12]         
                                    > [2] x' + [1] x1 + [6]          
                                    = f3(x1,x2,x',0(),x)             
        
           f2(x1,x2,S(x'),S(x),0()) = [2] x' + [1] x1 + [12]         
                                    > [0]                            
                                    = 0()                            
        
        f2(x1,x2,S(x''),S(x'),S(x)) = [2] x'' + [1] x1 + [12]        
                                    > [2] x'' + [1] x1 + [11]        
                                    = f5(x1,x2,S(x''),x',x)          
        
                f3(x1,x2,x3,x4,0()) = [1] x1 + [2] x3 + [2] x4 + [6] 
                                    > [0]                            
                                    = 0()                            
        
               f3(x1,x2,x3,x4,S(x)) = [1] x1 + [2] x3 + [2] x4 + [6] 
                                    > [1] x1 + [2] x3 + [2] x4 + [5] 
                                    = f4(x1,x2,x4,x3,x)              
        
                f4(0(),x2,x3,x4,x5) = [2] x3 + [2] x4 + [5]          
                                    > [0]                            
                                    = 0()                            
        
             f4(S(x),0(),x3,x4,0()) = [1] x + [2] x3 + [2] x4 + [9]  
                                    > [0]                            
                                    = 0()                            
        
           f4(S(x'),0(),x3,x4,S(x)) = [1] x' + [2] x3 + [2] x4 + [9] 
                                    > [1] x' + [2] x3 + [2] x4 + [6] 
                                    = f3(x',0(),x3,x4,x)             
        
           f4(S(x'),S(x),x3,x4,0()) = [1] x' + [2] x3 + [2] x4 + [9] 
                                    > [0]                            
                                    = 0()                            
        
        f4(S(x''),S(x'),x3,x4,S(x)) = [1] x'' + [2] x3 + [2] x4 + [9]
                                    > [1] x'' + [2] x3 + [8]         
                                    = f2(S(x''),x',x3,x4,x)          
        
                f5(x1,x2,x3,x4,0()) = [1] x1 + [2] x3 + [3]          
                                    > [0]                            
                                    = 0()                            
        
               f5(x1,x2,x3,x4,S(x)) = [1] x1 + [2] x3 + [3]          
                                    > [1] x1 + [2] x3 + [2]          
                                    = f6(x2,x1,x3,x4,x)              
        
                f6(x1,x2,x3,x4,0()) = [1] x2 + [2] x3 + [2]          
                                    > [0]                            
                                    = 0()                            
        
               f6(x1,x2,x3,x4,S(x)) = [1] x2 + [2] x3 + [2]          
                                    > [1] x2 + [2] x3 + [1]          
                                    = f0(x1,x2,x4,x3,x)              
        
        
        Following rules are (at-least) weakly oriented:
        

WORST_CASE(?,O(n^1))