YES
* Step 1: FromIts YES
    + Considered Problem:
        Rules:
          0. f2(A,B,C,D,E,F) -> f4(A,B,C,D,E,H)                [B >= 1 && 0 >= A] (?,1)
          1. f2(A,B,C,D,E,F) -> f4(A,G,C,D,E,H)                [0 >= B && 0 >= G] (?,1)
          2. f3(A,B,C,D,E,F) -> f2(A,B,C,D,E,F)                True               (1,1)
          3. f2(A,B,C,D,E,F) -> f2(-1 + A,-1 + B,A,B,-2 + A,F) [A >= 1 && B >= 1] (?,1)
        Signature:
          {(f2,6);(f3,6);(f4,6)}
        Flow Graph:
          [0->{},1->{},2->{0,1,3},3->{0,1,3}]
        
    + Applied Processor:
        FromIts
    + Details:
        ()
* Step 2: Decompose YES
    + Considered Problem:
        Rules:
          f2(A,B,C,D,E,F) -> f4(A,B,C,D,E,H)                 [B >= 1 && 0 >= A]
          f2(A,B,C,D,E,F) -> f4(A,G,C,D,E,H)                 [0 >= B && 0 >= G]
          f3(A,B,C,D,E,F) -> f2(A,B,C,D,E,F)                 True
          f2(A,B,C,D,E,F) -> f2(-1 + A,-1 + B,A,B,-2 + A,F)  [A >= 1 && B >= 1]
        Signature:
          {(f2,6);(f3,6);(f4,6)}
        Rule Graph:
          [0->{},1->{},2->{0,1,3},3->{0,1,3}]
    + Applied Processor:
        Decompose NoGreedy
    + Details:
        We construct a looptree:
          P: [0,1,2,3]
          |
          `- p:[3] c: [3]
* Step 3: CloseWith YES
    + Considered Problem:
        (Rules:
          f2(A,B,C,D,E,F) -> f4(A,B,C,D,E,H)                 [B >= 1 && 0 >= A]
          f2(A,B,C,D,E,F) -> f4(A,G,C,D,E,H)                 [0 >= B && 0 >= G]
          f3(A,B,C,D,E,F) -> f2(A,B,C,D,E,F)                 True
          f2(A,B,C,D,E,F) -> f2(-1 + A,-1 + B,A,B,-2 + A,F)  [A >= 1 && B >= 1]
        Signature:
          {(f2,6);(f3,6);(f4,6)}
        Rule Graph:
          [0->{},1->{},2->{0,1,3},3->{0,1,3}]
        ,We construct a looptree:
          P: [0,1,2,3]
          |
          `- p:[3] c: [3])
    + Applied Processor:
        CloseWith True
    + Details:
        ()

YES