YES
* Step 1: UnsatPaths YES
    + 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: FromIts YES
    + 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:
        FromIts
    + Details:
        ()
* Step 3: Decompose YES
    + Considered Problem:
        Rules:
          f0(A,B) -> f5(2,4)          True
          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]
          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]
        Signature:
          {(f0,2);(f5,2);(f8,2)}
        Rule Graph:
          [0->{1},1->{1,2},2->{}]
    + Applied Processor:
        Decompose NoGreedy
    + Details:
        We construct a looptree:
          P: [0,1,2]
          |
          `- p:[1] c: [1]
* Step 4: CloseWith YES
    + Considered Problem:
        (Rules:
          f0(A,B) -> f5(2,4)          True
          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]
          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]
        Signature:
          {(f0,2);(f5,2);(f8,2)}
        Rule Graph:
          [0->{1},1->{1,2},2->{}]
        ,We construct a looptree:
          P: [0,1,2]
          |
          `- p:[1] c: [1])
    + Applied Processor:
        CloseWith True
    + Details:
        ()

YES