YES
* Step 1: TrivialSCCs YES
    + Considered Problem:
        Rules:
          0. f0(A,B,C,D,E,F,G) -> f2(A,B,C,D,E,F,G)           [0 >= A]           (?,1)
          1. f0(A,B,C,D,E,F,G) -> f0(-1 + A,C,-1 + C,A,E,F,G) [A >= 1]           (?,1)
          2. f2(A,B,C,D,E,F,G) -> f4(A,B,C,D,E,F,H)           [0 >= C]           (?,1)
          3. f2(A,B,C,D,E,F,G) -> f0(H,B,C,D,E,F,G)           [H >= 1 && C >= 1] (?,1)
          4. f3(A,B,C,D,E,F,G) -> f2(H,B,I,D,E,F,G)           True               (1,1)
        Signature:
          {(f0,7);(f2,7);(f3,7);(f4,7)}
        Flow Graph:
          [0->{2,3},1->{0,1},2->{},3->{0,1},4->{2,3}]
        
    + Applied Processor:
        TrivialSCCs
    + Details:
        All trivial SCCs of the transition graph admit timebound 1.
* Step 2: UnsatPaths YES
    + Considered Problem:
        Rules:
          0. f0(A,B,C,D,E,F,G) -> f2(A,B,C,D,E,F,G)           [0 >= A]           (?,1)
          1. f0(A,B,C,D,E,F,G) -> f0(-1 + A,C,-1 + C,A,E,F,G) [A >= 1]           (?,1)
          2. f2(A,B,C,D,E,F,G) -> f4(A,B,C,D,E,F,H)           [0 >= C]           (1,1)
          3. f2(A,B,C,D,E,F,G) -> f0(H,B,C,D,E,F,G)           [H >= 1 && C >= 1] (?,1)
          4. f3(A,B,C,D,E,F,G) -> f2(H,B,I,D,E,F,G)           True               (1,1)
        Signature:
          {(f0,7);(f2,7);(f3,7);(f4,7)}
        Flow Graph:
          [0->{2,3},1->{0,1},2->{},3->{0,1},4->{2,3}]
        
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(3,0)]
* Step 3: Looptree YES
    + Considered Problem:
        Rules:
          0. f0(A,B,C,D,E,F,G) -> f2(A,B,C,D,E,F,G)           [0 >= A]           (?,1)
          1. f0(A,B,C,D,E,F,G) -> f0(-1 + A,C,-1 + C,A,E,F,G) [A >= 1]           (?,1)
          2. f2(A,B,C,D,E,F,G) -> f4(A,B,C,D,E,F,H)           [0 >= C]           (1,1)
          3. f2(A,B,C,D,E,F,G) -> f0(H,B,C,D,E,F,G)           [H >= 1 && C >= 1] (?,1)
          4. f3(A,B,C,D,E,F,G) -> f2(H,B,I,D,E,F,G)           True               (1,1)
        Signature:
          {(f0,7);(f2,7);(f3,7);(f4,7)}
        Flow Graph:
          [0->{2,3},1->{0,1},2->{},3->{1},4->{2,3}]
        
    + Applied Processor:
        Looptree
    + Details:
        We construct a looptree:
          P: [0,1,2,3,4]
          |
          `- p:[0,1,3] c: [3]
             |
             `- p:[1] c: [1]

YES