YES(?,O(1))
* Step 1: UnsatPaths WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A,B,C) -> f8(0,10,0)        True                   (1,1)
          1. f8(A,B,C) -> f8(2 + A,B,1 + C) [A + -1*C >= 0         (?,1)
                                             && C >= 0                  
                                             && -10 + B + C >= 0        
                                             && 10 + -1*B + C >= 0      
                                             && A + C >= 0              
                                             && 10 + -1*B >= 0          
                                             && 10 + A + -1*B >= 0      
                                             && -10 + B >= 0            
                                             && -10 + A + B >= 0        
                                             && A >= 0                  
                                             && B >= 1 + C]             
          2. f8(A,B,C) -> f6(A,B,C)         [A + -1*C >= 0         (?,1)
                                             && C >= 0                  
                                             && -10 + B + C >= 0        
                                             && 10 + -1*B + C >= 0      
                                             && A + C >= 0              
                                             && 10 + -1*B >= 0          
                                             && 10 + A + -1*B >= 0      
                                             && -10 + B >= 0            
                                             && -10 + A + B >= 0        
                                             && A >= 0                  
                                             && 2*B >= 1 + A            
                                             && C >= B]                 
          3. f8(A,B,C) -> f6(A,B,C)         [A + -1*C >= 0         (?,1)
                                             && C >= 0                  
                                             && -10 + B + C >= 0        
                                             && 10 + -1*B + C >= 0      
                                             && A + C >= 0              
                                             && 10 + -1*B >= 0          
                                             && 10 + A + -1*B >= 0      
                                             && -10 + B >= 0            
                                             && -10 + A + B >= 0        
                                             && A >= 0                  
                                             && A >= 2*B                
                                             && C >= B]                 
        Signature:
          {(f0,3);(f6,3);(f8,3)}
        Flow Graph:
          [0->{1,2,3},1->{1,2,3},2->{},3->{}]
        
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(0,2),(0,3)]
* Step 2: TrivialSCCs WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A,B,C) -> f8(0,10,0)        True                   (1,1)
          1. f8(A,B,C) -> f8(2 + A,B,1 + C) [A + -1*C >= 0         (?,1)
                                             && C >= 0                  
                                             && -10 + B + C >= 0        
                                             && 10 + -1*B + C >= 0      
                                             && A + C >= 0              
                                             && 10 + -1*B >= 0          
                                             && 10 + A + -1*B >= 0      
                                             && -10 + B >= 0            
                                             && -10 + A + B >= 0        
                                             && A >= 0                  
                                             && B >= 1 + C]             
          2. f8(A,B,C) -> f6(A,B,C)         [A + -1*C >= 0         (?,1)
                                             && C >= 0                  
                                             && -10 + B + C >= 0        
                                             && 10 + -1*B + C >= 0      
                                             && A + C >= 0              
                                             && 10 + -1*B >= 0          
                                             && 10 + A + -1*B >= 0      
                                             && -10 + B >= 0            
                                             && -10 + A + B >= 0        
                                             && A >= 0                  
                                             && 2*B >= 1 + A            
                                             && C >= B]                 
          3. f8(A,B,C) -> f6(A,B,C)         [A + -1*C >= 0         (?,1)
                                             && C >= 0                  
                                             && -10 + B + C >= 0        
                                             && 10 + -1*B + C >= 0      
                                             && A + C >= 0              
                                             && 10 + -1*B >= 0          
                                             && 10 + A + -1*B >= 0      
                                             && -10 + B >= 0            
                                             && -10 + A + B >= 0        
                                             && A >= 0                  
                                             && A >= 2*B                
                                             && C >= B]                 
        Signature:
          {(f0,3);(f6,3);(f8,3)}
        Flow Graph:
          [0->{1},1->{1,2,3},2->{},3->{}]
        
    + Applied Processor:
        TrivialSCCs
    + Details:
        All trivial SCCs of the transition graph admit timebound 1.
* Step 3: PolyRank WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A,B,C) -> f8(0,10,0)        True                   (1,1)
          1. f8(A,B,C) -> f8(2 + A,B,1 + C) [A + -1*C >= 0         (?,1)
                                             && C >= 0                  
                                             && -10 + B + C >= 0        
                                             && 10 + -1*B + C >= 0      
                                             && A + C >= 0              
                                             && 10 + -1*B >= 0          
                                             && 10 + A + -1*B >= 0      
                                             && -10 + B >= 0            
                                             && -10 + A + B >= 0        
                                             && A >= 0                  
                                             && B >= 1 + C]             
          2. f8(A,B,C) -> f6(A,B,C)         [A + -1*C >= 0         (1,1)
                                             && C >= 0                  
                                             && -10 + B + C >= 0        
                                             && 10 + -1*B + C >= 0      
                                             && A + C >= 0              
                                             && 10 + -1*B >= 0          
                                             && 10 + A + -1*B >= 0      
                                             && -10 + B >= 0            
                                             && -10 + A + B >= 0        
                                             && A >= 0                  
                                             && 2*B >= 1 + A            
                                             && C >= B]                 
          3. f8(A,B,C) -> f6(A,B,C)         [A + -1*C >= 0         (1,1)
                                             && C >= 0                  
                                             && -10 + B + C >= 0        
                                             && 10 + -1*B + C >= 0      
                                             && A + C >= 0              
                                             && 10 + -1*B >= 0          
                                             && 10 + A + -1*B >= 0      
                                             && -10 + B >= 0            
                                             && -10 + A + B >= 0        
                                             && A >= 0                  
                                             && A >= 2*B                
                                             && C >= B]                 
        Signature:
          {(f0,3);(f6,3);(f8,3)}
        Flow Graph:
          [0->{1},1->{1,2,3},2->{},3->{}]
        
    + Applied Processor:
        PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
    + Details:
        We apply a polynomial interpretation of shape linear:
          p(f0) = 10        
          p(f6) = x2 + -1*x3
          p(f8) = x2 + -1*x3
        
        Following rules are strictly oriented:
                [A + -1*C >= 0 ==>                  
                     && C >= 0                      
           && -10 + B + C >= 0                      
         && 10 + -1*B + C >= 0                      
                 && A + C >= 0                      
             && 10 + -1*B >= 0                      
         && 10 + A + -1*B >= 0                      
               && -10 + B >= 0                      
           && -10 + A + B >= 0                      
                     && A >= 0                      
                && B >= 1 + C]                      
                     f8(A,B,C)   = B + -1*C         
                                 > -1 + B + -1*C    
                                 = f8(2 + A,B,1 + C)
        
        
        Following rules are weakly oriented:
                          True ==>           
                     f0(A,B,C)   = 10        
                                >= 10        
                                 = f8(0,10,0)
        
                [A + -1*C >= 0 ==>           
                     && C >= 0               
           && -10 + B + C >= 0               
         && 10 + -1*B + C >= 0               
                 && A + C >= 0               
             && 10 + -1*B >= 0               
         && 10 + A + -1*B >= 0               
               && -10 + B >= 0               
           && -10 + A + B >= 0               
                     && A >= 0               
               && 2*B >= 1 + A               
                    && C >= B]               
                     f8(A,B,C)   = B + -1*C  
                                >= B + -1*C  
                                 = f6(A,B,C) 
        
                [A + -1*C >= 0 ==>           
                     && C >= 0               
           && -10 + B + C >= 0               
         && 10 + -1*B + C >= 0               
                 && A + C >= 0               
             && 10 + -1*B >= 0               
         && 10 + A + -1*B >= 0               
               && -10 + B >= 0               
           && -10 + A + B >= 0               
                     && A >= 0               
                   && A >= 2*B               
                    && C >= B]               
                     f8(A,B,C)   = B + -1*C  
                                >= B + -1*C  
                                 = f6(A,B,C) 
        
        
* Step 4: KnowledgePropagation WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A,B,C) -> f8(0,10,0)        True                   (1,1) 
          1. f8(A,B,C) -> f8(2 + A,B,1 + C) [A + -1*C >= 0         (10,1)
                                             && C >= 0                   
                                             && -10 + B + C >= 0         
                                             && 10 + -1*B + C >= 0       
                                             && A + C >= 0               
                                             && 10 + -1*B >= 0           
                                             && 10 + A + -1*B >= 0       
                                             && -10 + B >= 0             
                                             && -10 + A + B >= 0         
                                             && A >= 0                   
                                             && B >= 1 + C]              
          2. f8(A,B,C) -> f6(A,B,C)         [A + -1*C >= 0         (1,1) 
                                             && C >= 0                   
                                             && -10 + B + C >= 0         
                                             && 10 + -1*B + C >= 0       
                                             && A + C >= 0               
                                             && 10 + -1*B >= 0           
                                             && 10 + A + -1*B >= 0       
                                             && -10 + B >= 0             
                                             && -10 + A + B >= 0         
                                             && A >= 0                   
                                             && 2*B >= 1 + A             
                                             && C >= B]                  
          3. f8(A,B,C) -> f6(A,B,C)         [A + -1*C >= 0         (1,1) 
                                             && C >= 0                   
                                             && -10 + B + C >= 0         
                                             && 10 + -1*B + C >= 0       
                                             && A + C >= 0               
                                             && 10 + -1*B >= 0           
                                             && 10 + A + -1*B >= 0       
                                             && -10 + B >= 0             
                                             && -10 + A + B >= 0         
                                             && A >= 0                   
                                             && A >= 2*B                 
                                             && C >= B]                  
        Signature:
          {(f0,3);(f6,3);(f8,3)}
        Flow Graph:
          [0->{1},1->{1,2,3},2->{},3->{}]
        
    + Applied Processor:
        KnowledgePropagation
    + Details:
        The problem is already solved.

YES(?,O(1))