YES(?,O(1))
* Step 1: UnsatPaths WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A,B) -> f5(2,4)         True                                                                                                  (1,1)
          1. f5(A,B) -> f5(2 + A,4 + A) [2 + A + -1*B >= 0 && -4 + B >= 0 && -6 + A + B >= 0 && -2 + -1*A + B >= 0 && -2 + A >= 0 && 19 >= A] (?,1)
          2. f5(A,B) -> f8(A,B)         [2 + A + -1*B >= 0 && -4 + B >= 0 && -6 + A + B >= 0 && -2 + -1*A + B >= 0 && -2 + A >= 0 && A >= 20] (?,1)
        Signature:
          {(f0,2);(f5,2);(f8,2)}
        Flow Graph:
          [0->{1,2},1->{1,2},2->{}]
        
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(0,2)]
* Step 2: TrivialSCCs WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A,B) -> f5(2,4)         True                                                                                                  (1,1)
          1. f5(A,B) -> f5(2 + A,4 + A) [2 + A + -1*B >= 0 && -4 + B >= 0 && -6 + A + B >= 0 && -2 + -1*A + B >= 0 && -2 + A >= 0 && 19 >= A] (?,1)
          2. f5(A,B) -> f8(A,B)         [2 + A + -1*B >= 0 && -4 + B >= 0 && -6 + A + B >= 0 && -2 + -1*A + B >= 0 && -2 + A >= 0 && A >= 20] (?,1)
        Signature:
          {(f0,2);(f5,2);(f8,2)}
        Flow Graph:
          [0->{1},1->{1,2},2->{}]
        
    + 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) -> f5(2,4)         True                                                                                                  (1,1)
          1. f5(A,B) -> f5(2 + A,4 + A) [2 + A + -1*B >= 0 && -4 + B >= 0 && -6 + A + B >= 0 && -2 + -1*A + B >= 0 && -2 + A >= 0 && 19 >= A] (?,1)
          2. f5(A,B) -> f8(A,B)         [2 + A + -1*B >= 0 && -4 + B >= 0 && -6 + A + B >= 0 && -2 + -1*A + B >= 0 && -2 + A >= 0 && A >= 20] (1,1)
        Signature:
          {(f0,2);(f5,2);(f8,2)}
        Flow Graph:
          [0->{1},1->{1,2},2->{}]
        
    + Applied Processor:
        PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
    + Details:
        We apply a polynomial interpretation of shape linear:
          p(f0) = 52        
          p(f5) = 54 + -1*x1
          p(f8) = 54 + -1*x1
        
        Following rules are strictly oriented:
        [2 + A + -1*B >= 0 && -4 + B >= 0 && -6 + A + B >= 0 && -2 + -1*A + B >= 0 && -2 + A >= 0 && 19 >= A] ==>                
                                                                                                      f5(A,B)   = 54 + -1*A      
                                                                                                                > 52 + -1*A      
                                                                                                                = f5(2 + A,4 + A)
        
        
        Following rules are weakly oriented:
                                                                                                         True ==>          
                                                                                                      f0(A,B)   = 52       
                                                                                                               >= 52       
                                                                                                                = f5(2,4)  
        
        [2 + A + -1*B >= 0 && -4 + B >= 0 && -6 + A + B >= 0 && -2 + -1*A + B >= 0 && -2 + A >= 0 && A >= 20] ==>          
                                                                                                      f5(A,B)   = 54 + -1*A
                                                                                                               >= 54 + -1*A
                                                                                                                = f8(A,B)  
        
        
* Step 4: KnowledgePropagation WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A,B) -> f5(2,4)         True                                                                                                  (1,1) 
          1. f5(A,B) -> f5(2 + A,4 + A) [2 + A + -1*B >= 0 && -4 + B >= 0 && -6 + A + B >= 0 && -2 + -1*A + B >= 0 && -2 + A >= 0 && 19 >= A] (52,1)
          2. f5(A,B) -> f8(A,B)         [2 + A + -1*B >= 0 && -4 + B >= 0 && -6 + A + B >= 0 && -2 + -1*A + B >= 0 && -2 + A >= 0 && A >= 20] (1,1) 
        Signature:
          {(f0,2);(f5,2);(f8,2)}
        Flow Graph:
          [0->{1},1->{1,2},2->{}]
        
    + Applied Processor:
        KnowledgePropagation
    + Details:
        The problem is already solved.

YES(?,O(1))