YES
* Step 1: UnsatPaths YES
    + Considered Problem:
        Rules:
          0. f12(A,B,C,D,E,F) -> f5(4,0,0,D,E,F)     True                                                                                                    (1,1)
          1. f5(A,B,C,D,E,F)  -> f5(A,1 + B,G,H,E,G) [B >= 0 && -4 + A + B >= 0 && 4 + -1*A + B >= 0 && 4 + -1*A >= 0 && -4 + A >= 0 && A >= 1 + B && C = 0] (?,1)
          2. f5(A,B,C,D,E,F)  -> f10(A,B,C,C,C,F)    [B >= 0 && -4 + A + B >= 0 && 4 + -1*A + B >= 0 && 4 + -1*A >= 0 && -4 + A >= 0 && 0 >= 1 + C]          (?,1)
          3. f5(A,B,C,D,E,F)  -> f10(A,B,C,C,C,F)    [B >= 0 && -4 + A + B >= 0 && 4 + -1*A + B >= 0 && 4 + -1*A >= 0 && -4 + A >= 0 && C >= 1]              (?,1)
          4. f5(A,B,C,D,E,F)  -> f11(A,B,0,0,0,F)    [B >= 0 && -4 + A + B >= 0 && 4 + -1*A + B >= 0 && 4 + -1*A >= 0 && -4 + A >= 0 && B >= A && C = 0]     (?,1)
        Signature:
          {(f10,6);(f11,6);(f12,6);(f5,6)}
        Flow Graph:
          [0->{1,2,3,4},1->{1,2,3,4},2->{},3->{},4->{}]
        
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(0,2),(0,3),(0,4)]
* Step 2: FromIts YES
    + Considered Problem:
        Rules:
          0. f12(A,B,C,D,E,F) -> f5(4,0,0,D,E,F)     True                                                                                                    (1,1)
          1. f5(A,B,C,D,E,F)  -> f5(A,1 + B,G,H,E,G) [B >= 0 && -4 + A + B >= 0 && 4 + -1*A + B >= 0 && 4 + -1*A >= 0 && -4 + A >= 0 && A >= 1 + B && C = 0] (?,1)
          2. f5(A,B,C,D,E,F)  -> f10(A,B,C,C,C,F)    [B >= 0 && -4 + A + B >= 0 && 4 + -1*A + B >= 0 && 4 + -1*A >= 0 && -4 + A >= 0 && 0 >= 1 + C]          (?,1)
          3. f5(A,B,C,D,E,F)  -> f10(A,B,C,C,C,F)    [B >= 0 && -4 + A + B >= 0 && 4 + -1*A + B >= 0 && 4 + -1*A >= 0 && -4 + A >= 0 && C >= 1]              (?,1)
          4. f5(A,B,C,D,E,F)  -> f11(A,B,0,0,0,F)    [B >= 0 && -4 + A + B >= 0 && 4 + -1*A + B >= 0 && 4 + -1*A >= 0 && -4 + A >= 0 && B >= A && C = 0]     (?,1)
        Signature:
          {(f10,6);(f11,6);(f12,6);(f5,6)}
        Flow Graph:
          [0->{1},1->{1,2,3,4},2->{},3->{},4->{}]
        
    + Applied Processor:
        FromIts
    + Details:
        ()
* Step 3: Decompose YES
    + Considered Problem:
        Rules:
          f12(A,B,C,D,E,F) -> f5(4,0,0,D,E,F)      True
          f5(A,B,C,D,E,F)  -> f5(A,1 + B,G,H,E,G)  [B >= 0
                                                    && -4 + A + B >= 0
                                                    && 4 + -1*A + B >= 0
                                                    && 4 + -1*A >= 0
                                                    && -4 + A >= 0
                                                    && A >= 1 + B
                                                    && C = 0]
          f5(A,B,C,D,E,F)  -> f10(A,B,C,C,C,F)     [B >= 0
                                                    && -4 + A + B >= 0
                                                    && 4 + -1*A + B >= 0
                                                    && 4 + -1*A >= 0
                                                    && -4 + A >= 0
                                                    && 0 >= 1 + C]
          f5(A,B,C,D,E,F)  -> f10(A,B,C,C,C,F)     [B >= 0
                                                    && -4 + A + B >= 0
                                                    && 4 + -1*A + B >= 0
                                                    && 4 + -1*A >= 0
                                                    && -4 + A >= 0
                                                    && C >= 1]
          f5(A,B,C,D,E,F)  -> f11(A,B,0,0,0,F)     [B >= 0
                                                    && -4 + A + B >= 0
                                                    && 4 + -1*A + B >= 0
                                                    && 4 + -1*A >= 0
                                                    && -4 + A >= 0
                                                    && B >= A
                                                    && C = 0]
        Signature:
          {(f10,6);(f11,6);(f12,6);(f5,6)}
        Rule Graph:
          [0->{1},1->{1,2,3,4},2->{},3->{},4->{}]
    + Applied Processor:
        Decompose NoGreedy
    + Details:
        We construct a looptree:
          P: [0,1,2,3,4]
          |
          `- p:[1] c: [1]
* Step 4: CloseWith YES
    + Considered Problem:
        (Rules:
          f12(A,B,C,D,E,F) -> f5(4,0,0,D,E,F)      True
          f5(A,B,C,D,E,F)  -> f5(A,1 + B,G,H,E,G)  [B >= 0
                                                    && -4 + A + B >= 0
                                                    && 4 + -1*A + B >= 0
                                                    && 4 + -1*A >= 0
                                                    && -4 + A >= 0
                                                    && A >= 1 + B
                                                    && C = 0]
          f5(A,B,C,D,E,F)  -> f10(A,B,C,C,C,F)     [B >= 0
                                                    && -4 + A + B >= 0
                                                    && 4 + -1*A + B >= 0
                                                    && 4 + -1*A >= 0
                                                    && -4 + A >= 0
                                                    && 0 >= 1 + C]
          f5(A,B,C,D,E,F)  -> f10(A,B,C,C,C,F)     [B >= 0
                                                    && -4 + A + B >= 0
                                                    && 4 + -1*A + B >= 0
                                                    && 4 + -1*A >= 0
                                                    && -4 + A >= 0
                                                    && C >= 1]
          f5(A,B,C,D,E,F)  -> f11(A,B,0,0,0,F)     [B >= 0
                                                    && -4 + A + B >= 0
                                                    && 4 + -1*A + B >= 0
                                                    && 4 + -1*A >= 0
                                                    && -4 + A >= 0
                                                    && B >= A
                                                    && C = 0]
        Signature:
          {(f10,6);(f11,6);(f12,6);(f5,6)}
        Rule Graph:
          [0->{1},1->{1,2,3,4},2->{},3->{},4->{}]
        ,We construct a looptree:
          P: [0,1,2,3,4]
          |
          `- p:[1] c: [1])
    + Applied Processor:
        CloseWith True
    + Details:
        ()

YES