YES
* Step 1: UnsatPaths YES
    + Considered Problem:
        Rules:
          0. f3(A,B,C,D) -> f0(0,B,C,D)     True                (1,1)
          1. f0(A,B,C,D) -> f0(1 + A,B,A,D) [A >= 0 && 9 >= A]  (?,1)
          2. f0(A,B,C,D) -> f4(A,E,C,D)     [A >= 0 && A >= 10] (?,1)
        Signature:
          {(f0,4);(f3,4);(f4,4)}
        Flow Graph:
          [0->{1,2},1->{1,2},2->{}]
        
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(0,2)]
* Step 2: FromIts YES
    + Considered Problem:
        Rules:
          0. f3(A,B,C,D) -> f0(0,B,C,D)     True                (1,1)
          1. f0(A,B,C,D) -> f0(1 + A,B,A,D) [A >= 0 && 9 >= A]  (?,1)
          2. f0(A,B,C,D) -> f4(A,E,C,D)     [A >= 0 && A >= 10] (?,1)
        Signature:
          {(f0,4);(f3,4);(f4,4)}
        Flow Graph:
          [0->{1},1->{1,2},2->{}]
        
    + Applied Processor:
        FromIts
    + Details:
        ()
* Step 3: Decompose YES
    + Considered Problem:
        Rules:
          f3(A,B,C,D) -> f0(0,B,C,D)      True
          f0(A,B,C,D) -> f0(1 + A,B,A,D)  [A >= 0 && 9 >= A]
          f0(A,B,C,D) -> f4(A,E,C,D)      [A >= 0 && A >= 10]
        Signature:
          {(f0,4);(f3,4);(f4,4)}
        Rule Graph:
          [0->{1},1->{1,2},2->{}]
    + Applied Processor:
        Decompose NoGreedy
    + Details:
        We construct a looptree:
          P: [0,1,2]
          |
          `- p:[1] c: [1]
* Step 4: CloseWith YES
    + Considered Problem:
        (Rules:
          f3(A,B,C,D) -> f0(0,B,C,D)      True
          f0(A,B,C,D) -> f0(1 + A,B,A,D)  [A >= 0 && 9 >= A]
          f0(A,B,C,D) -> f4(A,E,C,D)      [A >= 0 && A >= 10]
        Signature:
          {(f0,4);(f3,4);(f4,4)}
        Rule Graph:
          [0->{1},1->{1,2},2->{}]
        ,We construct a looptree:
          P: [0,1,2]
          |
          `- p:[1] c: [1])
    + Applied Processor:
        CloseWith True
    + Details:
        ()

YES