YES
* Step 1: UnsatPaths YES
    + Considered Problem:
        Rules:
          0. f0(A,B,C,D,E,F,G,H)  -> f10(I,0,C,D,E,F,G,H)     True         (1,1)
          1. f10(A,B,C,D,E,F,G,H) -> f10(A,1 + B,C,D,E,F,G,H) [C >= 1 + B] (?,1)
          2. f18(A,B,C,D,E,F,G,H) -> f22(A,B,C,D,E,E,1 + E,H) [D >= 2 + E] (?,1)
          3. f22(A,B,C,D,E,F,G,H) -> f22(A,B,C,D,E,F,1 + G,H) [D >= 1 + G] (?,1)
          4. f22(A,B,C,D,E,F,G,H) -> f22(A,B,C,D,E,G,1 + G,H) [D >= 1 + G] (?,1)
          5. f34(A,B,C,D,E,F,G,H) -> f34(A,B,C,D,1 + E,F,G,H) [D >= 2 + E] (?,1)
          6. f34(A,B,C,D,E,F,G,H) -> f43(A,B,C,D,E,F,G,H)     [1 + E >= D] (?,1)
          7. f22(A,B,C,D,E,F,G,H) -> f18(A,B,C,D,1 + E,F,G,I) [G >= D]     (?,1)
          8. f18(A,B,C,D,E,F,G,H) -> f34(A,B,C,D,0,F,G,H)     [1 + E >= D] (?,1)
          9. f10(A,B,C,D,E,F,G,H) -> f18(A,B,C,C,0,F,G,H)     [B >= C]     (?,1)
        Signature:
          {(f0,8);(f10,8);(f18,8);(f22,8);(f34,8);(f43,8)}
        Flow Graph:
          [0->{1,9},1->{1,9},2->{3,4,7},3->{3,4,7},4->{3,4,7},5->{5,6},6->{},7->{2,8},8->{5,6},9->{2,8}]
        
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(2,7)]
* Step 2: FromIts YES
    + Considered Problem:
        Rules:
          0. f0(A,B,C,D,E,F,G,H)  -> f10(I,0,C,D,E,F,G,H)     True         (1,1)
          1. f10(A,B,C,D,E,F,G,H) -> f10(A,1 + B,C,D,E,F,G,H) [C >= 1 + B] (?,1)
          2. f18(A,B,C,D,E,F,G,H) -> f22(A,B,C,D,E,E,1 + E,H) [D >= 2 + E] (?,1)
          3. f22(A,B,C,D,E,F,G,H) -> f22(A,B,C,D,E,F,1 + G,H) [D >= 1 + G] (?,1)
          4. f22(A,B,C,D,E,F,G,H) -> f22(A,B,C,D,E,G,1 + G,H) [D >= 1 + G] (?,1)
          5. f34(A,B,C,D,E,F,G,H) -> f34(A,B,C,D,1 + E,F,G,H) [D >= 2 + E] (?,1)
          6. f34(A,B,C,D,E,F,G,H) -> f43(A,B,C,D,E,F,G,H)     [1 + E >= D] (?,1)
          7. f22(A,B,C,D,E,F,G,H) -> f18(A,B,C,D,1 + E,F,G,I) [G >= D]     (?,1)
          8. f18(A,B,C,D,E,F,G,H) -> f34(A,B,C,D,0,F,G,H)     [1 + E >= D] (?,1)
          9. f10(A,B,C,D,E,F,G,H) -> f18(A,B,C,C,0,F,G,H)     [B >= C]     (?,1)
        Signature:
          {(f0,8);(f10,8);(f18,8);(f22,8);(f34,8);(f43,8)}
        Flow Graph:
          [0->{1,9},1->{1,9},2->{3,4},3->{3,4,7},4->{3,4,7},5->{5,6},6->{},7->{2,8},8->{5,6},9->{2,8}]
        
    + Applied Processor:
        FromIts
    + Details:
        ()
* Step 3: Decompose YES
    + Considered Problem:
        Rules:
          f0(A,B,C,D,E,F,G,H)  -> f10(I,0,C,D,E,F,G,H)      True
          f10(A,B,C,D,E,F,G,H) -> f10(A,1 + B,C,D,E,F,G,H)  [C >= 1 + B]
          f18(A,B,C,D,E,F,G,H) -> f22(A,B,C,D,E,E,1 + E,H)  [D >= 2 + E]
          f22(A,B,C,D,E,F,G,H) -> f22(A,B,C,D,E,F,1 + G,H)  [D >= 1 + G]
          f22(A,B,C,D,E,F,G,H) -> f22(A,B,C,D,E,G,1 + G,H)  [D >= 1 + G]
          f34(A,B,C,D,E,F,G,H) -> f34(A,B,C,D,1 + E,F,G,H)  [D >= 2 + E]
          f34(A,B,C,D,E,F,G,H) -> f43(A,B,C,D,E,F,G,H)      [1 + E >= D]
          f22(A,B,C,D,E,F,G,H) -> f18(A,B,C,D,1 + E,F,G,I)  [G >= D]
          f18(A,B,C,D,E,F,G,H) -> f34(A,B,C,D,0,F,G,H)      [1 + E >= D]
          f10(A,B,C,D,E,F,G,H) -> f18(A,B,C,C,0,F,G,H)      [B >= C]
        Signature:
          {(f0,8);(f10,8);(f18,8);(f22,8);(f34,8);(f43,8)}
        Rule Graph:
          [0->{1,9},1->{1,9},2->{3,4},3->{3,4,7},4->{3,4,7},5->{5,6},6->{},7->{2,8},8->{5,6},9->{2,8}]
    + Applied Processor:
        Decompose NoGreedy
    + Details:
        We construct a looptree:
          P: [0,1,2,3,4,5,6,7,8,9]
          |
          +- p:[1] c: [1]
          |
          +- p:[2,7,3,4] c: [2,7]
          |  |
          |  `- p:[3,4] c: [4]
          |     |
          |     `- p:[3] c: [3]
          |
          `- p:[5] c: [5]
* Step 4: CloseWith YES
    + Considered Problem:
        (Rules:
          f0(A,B,C,D,E,F,G,H)  -> f10(I,0,C,D,E,F,G,H)      True
          f10(A,B,C,D,E,F,G,H) -> f10(A,1 + B,C,D,E,F,G,H)  [C >= 1 + B]
          f18(A,B,C,D,E,F,G,H) -> f22(A,B,C,D,E,E,1 + E,H)  [D >= 2 + E]
          f22(A,B,C,D,E,F,G,H) -> f22(A,B,C,D,E,F,1 + G,H)  [D >= 1 + G]
          f22(A,B,C,D,E,F,G,H) -> f22(A,B,C,D,E,G,1 + G,H)  [D >= 1 + G]
          f34(A,B,C,D,E,F,G,H) -> f34(A,B,C,D,1 + E,F,G,H)  [D >= 2 + E]
          f34(A,B,C,D,E,F,G,H) -> f43(A,B,C,D,E,F,G,H)      [1 + E >= D]
          f22(A,B,C,D,E,F,G,H) -> f18(A,B,C,D,1 + E,F,G,I)  [G >= D]
          f18(A,B,C,D,E,F,G,H) -> f34(A,B,C,D,0,F,G,H)      [1 + E >= D]
          f10(A,B,C,D,E,F,G,H) -> f18(A,B,C,C,0,F,G,H)      [B >= C]
        Signature:
          {(f0,8);(f10,8);(f18,8);(f22,8);(f34,8);(f43,8)}
        Rule Graph:
          [0->{1,9},1->{1,9},2->{3,4},3->{3,4,7},4->{3,4,7},5->{5,6},6->{},7->{2,8},8->{5,6},9->{2,8}]
        ,We construct a looptree:
          P: [0,1,2,3,4,5,6,7,8,9]
          |
          +- p:[1] c: [1]
          |
          +- p:[2,7,3,4] c: [2,7]
          |  |
          |  `- p:[3,4] c: [4]
          |     |
          |     `- p:[3] c: [3]
          |
          `- p:[5] c: [5])
    + Applied Processor:
        CloseWith True
    + Details:
        ()

YES