WORST_CASE(?,O(n^1))
* Step 1: NaturalPI 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:
        NaturalPI {shape = StronglyLinear, restrict = NoRestrict, uargs = UArgs, urules = URules, selector = Nothing}
    + Details:
        We apply a polynomial interpretation of kind constructor-based(stronglyLinear):
        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) = 6 + x1          
          p(f0) = 1 + x2 + x4     
          p(f1) = 6 + x2 + x3     
          p(f2) = 4 + x1 + x3     
          p(f3) = 7 + x1 + x3 + x4
          p(f4) = 6 + x1 + x3 + x4
          p(f5) = 3 + x1 + x3     
          p(f6) = 2 + x2 + x3     
        
        Following rules are strictly oriented:
                f0(x1,0(),x3,x4,x5) = 1 + x4                  
                                    > 0                       
                                    = 0()                     
        
              f0(x1,S(x),x3,0(),x5) = 7 + x                   
                                    > 0                       
                                    = 0()                     
        
            f0(x1,S(x'),x3,S(x),x5) = 13 + x + x'             
                                    > 12 + x + x'             
                                    = f1(x',S(x'),x,S(x),S(x))
        
                f1(x1,x2,x3,x4,0()) = 6 + x2 + x3             
                                    > 0                       
                                    = 0()                     
        
               f1(x1,x2,x3,x4,S(x)) = 6 + x2 + x3             
                                    > 4 + x2 + x3             
                                    = f2(x2,x1,x3,x4,x)       
        
                f2(x1,x2,0(),x4,x5) = 4 + x1                  
                                    > 0                       
                                    = 0()                     
        
             f2(x1,x2,S(x),0(),0()) = 10 + x + x1             
                                    > 0                       
                                    = 0()                     
        
           f2(x1,x2,S(x'),0(),S(x)) = 10 + x' + x1            
                                    > 7 + x' + x1             
                                    = f3(x1,x2,x',0(),x)      
        
           f2(x1,x2,S(x'),S(x),0()) = 10 + x' + x1            
                                    > 0                       
                                    = 0()                     
        
        f2(x1,x2,S(x''),S(x'),S(x)) = 10 + x'' + x1           
                                    > 9 + x'' + x1            
                                    = f5(x1,x2,S(x''),x',x)   
        
                f3(x1,x2,x3,x4,0()) = 7 + x1 + x3 + x4        
                                    > 0                       
                                    = 0()                     
        
               f3(x1,x2,x3,x4,S(x)) = 7 + x1 + x3 + x4        
                                    > 6 + x1 + x3 + x4        
                                    = f4(x1,x2,x4,x3,x)       
        
                f4(0(),x2,x3,x4,x5) = 6 + x3 + x4             
                                    > 0                       
                                    = 0()                     
        
             f4(S(x),0(),x3,x4,0()) = 12 + x + x3 + x4        
                                    > 0                       
                                    = 0()                     
        
           f4(S(x'),0(),x3,x4,S(x)) = 12 + x' + x3 + x4       
                                    > 7 + x' + x3 + x4        
                                    = f3(x',0(),x3,x4,x)      
        
           f4(S(x'),S(x),x3,x4,0()) = 12 + x' + x3 + x4       
                                    > 0                       
                                    = 0()                     
        
        f4(S(x''),S(x'),x3,x4,S(x)) = 12 + x'' + x3 + x4      
                                    > 10 + x'' + x3           
                                    = f2(S(x''),x',x3,x4,x)   
        
                f5(x1,x2,x3,x4,0()) = 3 + x1 + x3             
                                    > 0                       
                                    = 0()                     
        
               f5(x1,x2,x3,x4,S(x)) = 3 + x1 + x3             
                                    > 2 + x1 + x3             
                                    = f6(x2,x1,x3,x4,x)       
        
                f6(x1,x2,x3,x4,0()) = 2 + x2 + x3             
                                    > 0                       
                                    = 0()                     
        
               f6(x1,x2,x3,x4,S(x)) = 2 + x2 + x3             
                                    > 1 + x2 + x3             
                                    = f0(x1,x2,x4,x3,x)       
        
        
        Following rules are (at-least) weakly oriented:
        

WORST_CASE(?,O(n^1))