YES
* Step 1: UnsatPaths YES
    + Considered Problem:
        Rules:
          0. f0(A,B,C) -> f1(A,B,2)      [A >= 0 && 3 >= A && 3 >= B && B >= 0] (1,1)
          1. f1(A,B,C) -> f1(A,1 + B,C)  [2 + -1*C >= 0                         (?,1)
                                          && 2 + B + -1*C >= 0                       
                                          && 5 + -1*B + -1*C >= 0                    
                                          && 2 + A + -1*C >= 0                       
                                          && 5 + -1*A + -1*C >= 0                    
                                          && -2 + C >= 0                             
                                          && -2 + B + C >= 0                         
                                          && 1 + -1*B + C >= 0                       
                                          && -2 + A + C >= 0                         
                                          && 1 + -1*A + C >= 0                       
                                          && 3 + -1*B >= 0                           
                                          && 3 + A + -1*B >= 0                       
                                          && 6 + -1*A + -1*B >= 0                    
                                          && B >= 0                                  
                                          && A + B >= 0                              
                                          && 3 + -1*A + B >= 0                       
                                          && 3 + -1*A >= 0                           
                                          && A >= 0                                  
                                          && A + C >= 1 + 2*B]                       
          2. f1(A,B,C) -> f1(A,-1 + B,C) [2 + -1*C >= 0                         (?,1)
                                          && 2 + B + -1*C >= 0                       
                                          && 5 + -1*B + -1*C >= 0                    
                                          && 2 + A + -1*C >= 0                       
                                          && 5 + -1*A + -1*C >= 0                    
                                          && -2 + C >= 0                             
                                          && -2 + B + C >= 0                         
                                          && 1 + -1*B + C >= 0                       
                                          && -2 + A + C >= 0                         
                                          && 1 + -1*A + C >= 0                       
                                          && 3 + -1*B >= 0                           
                                          && 3 + A + -1*B >= 0                       
                                          && 6 + -1*A + -1*B >= 0                    
                                          && B >= 0                                  
                                          && A + B >= 0                              
                                          && 3 + -1*A + B >= 0                       
                                          && 3 + -1*A >= 0                           
                                          && A >= 0                                  
                                          && 2*B >= 2 + A + C]                       
        Signature:
          {(f0,3);(f1,3)}
        Flow Graph:
          [0->{1,2},1->{1,2},2->{1,2}]
        
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(1,2),(2,1)]
* Step 2: Looptree YES
    + Considered Problem:
        Rules:
          0. f0(A,B,C) -> f1(A,B,2)      [A >= 0 && 3 >= A && 3 >= B && B >= 0] (1,1)
          1. f1(A,B,C) -> f1(A,1 + B,C)  [2 + -1*C >= 0                         (?,1)
                                          && 2 + B + -1*C >= 0                       
                                          && 5 + -1*B + -1*C >= 0                    
                                          && 2 + A + -1*C >= 0                       
                                          && 5 + -1*A + -1*C >= 0                    
                                          && -2 + C >= 0                             
                                          && -2 + B + C >= 0                         
                                          && 1 + -1*B + C >= 0                       
                                          && -2 + A + C >= 0                         
                                          && 1 + -1*A + C >= 0                       
                                          && 3 + -1*B >= 0                           
                                          && 3 + A + -1*B >= 0                       
                                          && 6 + -1*A + -1*B >= 0                    
                                          && B >= 0                                  
                                          && A + B >= 0                              
                                          && 3 + -1*A + B >= 0                       
                                          && 3 + -1*A >= 0                           
                                          && A >= 0                                  
                                          && A + C >= 1 + 2*B]                       
          2. f1(A,B,C) -> f1(A,-1 + B,C) [2 + -1*C >= 0                         (?,1)
                                          && 2 + B + -1*C >= 0                       
                                          && 5 + -1*B + -1*C >= 0                    
                                          && 2 + A + -1*C >= 0                       
                                          && 5 + -1*A + -1*C >= 0                    
                                          && -2 + C >= 0                             
                                          && -2 + B + C >= 0                         
                                          && 1 + -1*B + C >= 0                       
                                          && -2 + A + C >= 0                         
                                          && 1 + -1*A + C >= 0                       
                                          && 3 + -1*B >= 0                           
                                          && 3 + A + -1*B >= 0                       
                                          && 6 + -1*A + -1*B >= 0                    
                                          && B >= 0                                  
                                          && A + B >= 0                              
                                          && 3 + -1*A + B >= 0                       
                                          && 3 + -1*A >= 0                           
                                          && A >= 0                                  
                                          && 2*B >= 2 + A + C]                       
        Signature:
          {(f0,3);(f1,3)}
        Flow Graph:
          [0->{1,2},1->{1},2->{2}]
        
    + Applied Processor:
        Looptree
    + Details:
        We construct a looptree:
          P: [0,1,2]
          |
          +- p:[2] c: [2]
          |
          `- p:[1] c: [1]

YES