YES
* Step 1: 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. f1(A,B,C,D,E,F,G) -> f0(-1 + A,B,-1 + C,D,C,A,G) [A >= 1 && C >= 1] (?,1)
          3. f2(A,B,C,D,E,F,G) -> f4(A,B,C,D,E,F,H)           [0 >= C]           (?,1)
          4. f2(A,B,C,D,E,F,G) -> f0(H,B,C,D,E,F,G)           [H >= 1 && C >= 1] (?,1)
          5. f3(A,B,C,D,E,F,G) -> f2(H,B,I,D,E,F,G)           True               (1,1)
        Signature:
          {(f0,7);(f1,7);(f2,7);(f3,7);(f4,7)}
        Flow Graph:
          [0->{3,4},1->{0,1},2->{0,1},3->{},4->{0,1},5->{3,4}]
        
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(4,0)]
* Step 2: UnreachableRules 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. f1(A,B,C,D,E,F,G) -> f0(-1 + A,B,-1 + C,D,C,A,G) [A >= 1 && C >= 1] (?,1)
          3. f2(A,B,C,D,E,F,G) -> f4(A,B,C,D,E,F,H)           [0 >= C]           (?,1)
          4. f2(A,B,C,D,E,F,G) -> f0(H,B,C,D,E,F,G)           [H >= 1 && C >= 1] (?,1)
          5. f3(A,B,C,D,E,F,G) -> f2(H,B,I,D,E,F,G)           True               (1,1)
        Signature:
          {(f0,7);(f1,7);(f2,7);(f3,7);(f4,7)}
        Flow Graph:
          [0->{3,4},1->{0,1},2->{0,1},3->{},4->{1},5->{3,4}]
        
    + Applied Processor:
        UnreachableRules
    + Details:
        Following transitions are not reachable from the starting states and are revomed: [2]
* Step 3: FromIts 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)
          3. f2(A,B,C,D,E,F,G) -> f4(A,B,C,D,E,F,H)           [0 >= C]           (?,1)
          4. f2(A,B,C,D,E,F,G) -> f0(H,B,C,D,E,F,G)           [H >= 1 && C >= 1] (?,1)
          5. f3(A,B,C,D,E,F,G) -> f2(H,B,I,D,E,F,G)           True               (1,1)
        Signature:
          {(f0,7);(f1,7);(f2,7);(f3,7);(f4,7)}
        Flow Graph:
          [0->{3,4},1->{0,1},3->{},4->{1},5->{3,4}]
        
    + Applied Processor:
        FromIts
    + Details:
        ()
* Step 4: Decompose YES
    + Considered Problem:
        Rules:
          f0(A,B,C,D,E,F,G) -> f2(A,B,C,D,E,F,G)            [0 >= A]
          f0(A,B,C,D,E,F,G) -> f0(-1 + A,C,-1 + C,A,E,F,G)  [A >= 1]
          f2(A,B,C,D,E,F,G) -> f4(A,B,C,D,E,F,H)            [0 >= C]
          f2(A,B,C,D,E,F,G) -> f0(H,B,C,D,E,F,G)            [H >= 1 && C >= 1]
          f3(A,B,C,D,E,F,G) -> f2(H,B,I,D,E,F,G)            True
        Signature:
          {(f0,7);(f1,7);(f2,7);(f3,7);(f4,7)}
        Rule Graph:
          [0->{3,4},1->{0,1},3->{},4->{1},5->{3,4}]
    + Applied Processor:
        Decompose NoGreedy
    + Details:
        We construct a looptree:
          P: [0,1,3,4,5]
          |
          `- p:[0,1,4] c: [0,4]
             |
             `- p:[1] c: [1]
* Step 5: CloseWith YES
    + Considered Problem:
        (Rules:
          f0(A,B,C,D,E,F,G) -> f2(A,B,C,D,E,F,G)            [0 >= A]
          f0(A,B,C,D,E,F,G) -> f0(-1 + A,C,-1 + C,A,E,F,G)  [A >= 1]
          f2(A,B,C,D,E,F,G) -> f4(A,B,C,D,E,F,H)            [0 >= C]
          f2(A,B,C,D,E,F,G) -> f0(H,B,C,D,E,F,G)            [H >= 1 && C >= 1]
          f3(A,B,C,D,E,F,G) -> f2(H,B,I,D,E,F,G)            True
        Signature:
          {(f0,7);(f1,7);(f2,7);(f3,7);(f4,7)}
        Rule Graph:
          [0->{3,4},1->{0,1},3->{},4->{1},5->{3,4}]
        ,We construct a looptree:
          P: [0,1,3,4,5]
          |
          `- p:[0,1,4] c: [0,4]
             |
             `- p:[1] c: [1])
    + Applied Processor:
        CloseWith True
    + Details:
        ()

YES