YES
* Step 1: UnsatPaths YES
    + Considered Problem:
        Rules:
          0. f0(A,B,C,D) -> f4(A,E,C,D)     [A >= 10]         (?,1)
          1. f0(A,B,C,D) -> f0(1 + A,B,A,D) [9 >= A]          (?,1)
          2. f1(A,B,C,D) -> f0(1,B,C,D)     [9 >= E && A = 0] (?,1)
          3. f2(A,B,C,D) -> f0(2,B,C,2)     [9 >= A]          (?,1)
          4. f3(A,B,C,D) -> f0(0,B,C,D)     True              (1,1)
        Signature:
          {(f0,4);(f1,4);(f2,4);(f3,4);(f4,4)}
        Flow Graph:
          [0->{},1->{0,1},2->{0,1},3->{0,1},4->{0,1}]
        
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(2,0),(3,0),(4,0)]
* Step 2: UnreachableRules YES
    + Considered Problem:
        Rules:
          0. f0(A,B,C,D) -> f4(A,E,C,D)     [A >= 10]         (?,1)
          1. f0(A,B,C,D) -> f0(1 + A,B,A,D) [9 >= A]          (?,1)
          2. f1(A,B,C,D) -> f0(1,B,C,D)     [9 >= E && A = 0] (?,1)
          3. f2(A,B,C,D) -> f0(2,B,C,2)     [9 >= A]          (?,1)
          4. f3(A,B,C,D) -> f0(0,B,C,D)     True              (1,1)
        Signature:
          {(f0,4);(f1,4);(f2,4);(f3,4);(f4,4)}
        Flow Graph:
          [0->{},1->{0,1},2->{1},3->{1},4->{1}]
        
    + Applied Processor:
        UnreachableRules
    + Details:
        Following transitions are not reachable from the starting states and are revomed: [2,3]
* Step 3: FromIts YES
    + Considered Problem:
        Rules:
          0. f0(A,B,C,D) -> f4(A,E,C,D)     [A >= 10] (?,1)
          1. f0(A,B,C,D) -> f0(1 + A,B,A,D) [9 >= A]  (?,1)
          4. f3(A,B,C,D) -> f0(0,B,C,D)     True      (1,1)
        Signature:
          {(f0,4);(f1,4);(f2,4);(f3,4);(f4,4)}
        Flow Graph:
          [0->{},1->{0,1},4->{1}]
        
    + Applied Processor:
        FromIts
    + Details:
        ()
* Step 4: Decompose YES
    + Considered Problem:
        Rules:
          f0(A,B,C,D) -> f4(A,E,C,D)      [A >= 10]
          f0(A,B,C,D) -> f0(1 + A,B,A,D)  [9 >= A]
          f3(A,B,C,D) -> f0(0,B,C,D)      True
        Signature:
          {(f0,4);(f1,4);(f2,4);(f3,4);(f4,4)}
        Rule Graph:
          [0->{},1->{0,1},4->{1}]
    + Applied Processor:
        Decompose NoGreedy
    + Details:
        We construct a looptree:
          P: [0,1,4]
          |
          `- p:[1] c: [1]
* Step 5: CloseWith YES
    + Considered Problem:
        (Rules:
          f0(A,B,C,D) -> f4(A,E,C,D)      [A >= 10]
          f0(A,B,C,D) -> f0(1 + A,B,A,D)  [9 >= A]
          f3(A,B,C,D) -> f0(0,B,C,D)      True
        Signature:
          {(f0,4);(f1,4);(f2,4);(f3,4);(f4,4)}
        Rule Graph:
          [0->{},1->{0,1},4->{1}]
        ,We construct a looptree:
          P: [0,1,4]
          |
          `- p:[1] c: [1])
    + Applied Processor:
        CloseWith True
    + Details:
        ()

YES