YES
* Step 1: UnsatRules YES
    + Considered Problem:
        Rules:
          0. f0(A,B,C,D) -> f1(A,B,2,D)           [A >= 0 && 3 >= A && 3 >= B && B >= 0]       (1,1)
          1. f1(A,B,C,D) -> f1(A,1 + B,C,1 + B)   [A + C >= 1 + 2*B && 0 >= 2]                 (?,1)
          2. f1(A,B,C,D) -> f1(A,1 + B,C,1 + B)   [A + C >= 1 + 2*B]                           (?,1)
          3. f1(A,B,C,D) -> f1(A,-1 + B,C,-1 + B) [2*B >= 2 + A + C]                           (?,1)
          4. f1(A,B,C,D) -> f1(A,-1 + B,C,-1 + B) [2*B >= 2 + A + C && 0 >= 2]                 (?,1)
          5. f1(A,B,C,D) -> f1(A,B,C,B)           [0 >= 1 && 2*B >= A + C && 1 + A + C >= 2*B] (?,1)
          6. f1(A,B,C,D) -> f1(A,B,C,B)           [0 >= 1 && 2*B >= A + C && 1 + A + C >= 2*B] (?,1)
        Signature:
          {(f0,4);(f1,4)}
        Flow Graph:
          [0->{1,2,3,4,5,6},1->{1,2,3,4,5,6},2->{1,2,3,4,5,6},3->{1,2,3,4,5,6},4->{1,2,3,4,5,6},5->{1,2,3,4,5,6}
          ,6->{1,2,3,4,5,6}]
        
    + Applied Processor:
        UnsatRules
    + Details:
        Following transitions have unsatisfiable constraints and are removed:  [1,4,5,6]
* Step 2: UnsatPaths YES
    + Considered Problem:
        Rules:
          0. f0(A,B,C,D) -> f1(A,B,2,D)           [A >= 0 && 3 >= A && 3 >= B && B >= 0] (1,1)
          2. f1(A,B,C,D) -> f1(A,1 + B,C,1 + B)   [A + C >= 1 + 2*B]                     (?,1)
          3. f1(A,B,C,D) -> f1(A,-1 + B,C,-1 + B) [2*B >= 2 + A + C]                     (?,1)
        Signature:
          {(f0,4);(f1,4)}
        Flow Graph:
          [0->{2,3},2->{2,3},3->{2,3}]
        
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(2,3),(3,2)]
* Step 3: FromIts YES
    + Considered Problem:
        Rules:
          0. f0(A,B,C,D) -> f1(A,B,2,D)           [A >= 0 && 3 >= A && 3 >= B && B >= 0] (1,1)
          2. f1(A,B,C,D) -> f1(A,1 + B,C,1 + B)   [A + C >= 1 + 2*B]                     (?,1)
          3. f1(A,B,C,D) -> f1(A,-1 + B,C,-1 + B) [2*B >= 2 + A + C]                     (?,1)
        Signature:
          {(f0,4);(f1,4)}
        Flow Graph:
          [0->{2,3},2->{2},3->{3}]
        
    + Applied Processor:
        FromIts
    + Details:
        ()
* Step 4: Decompose YES
    + Considered Problem:
        Rules:
          f0(A,B,C,D) -> f1(A,B,2,D)            [A >= 0 && 3 >= A && 3 >= B && B >= 0]
          f1(A,B,C,D) -> f1(A,1 + B,C,1 + B)    [A + C >= 1 + 2*B]
          f1(A,B,C,D) -> f1(A,-1 + B,C,-1 + B)  [2*B >= 2 + A + C]
        Signature:
          {(f0,4);(f1,4)}
        Rule Graph:
          [0->{2,3},2->{2},3->{3}]
    + Applied Processor:
        Decompose NoGreedy
    + Details:
        We construct a looptree:
          P: [0,2,3]
          |
          +- p:[3] c: [3]
          |
          `- p:[2] c: [2]
* Step 5: CloseWith YES
    + Considered Problem:
        (Rules:
          f0(A,B,C,D) -> f1(A,B,2,D)            [A >= 0 && 3 >= A && 3 >= B && B >= 0]
          f1(A,B,C,D) -> f1(A,1 + B,C,1 + B)    [A + C >= 1 + 2*B]
          f1(A,B,C,D) -> f1(A,-1 + B,C,-1 + B)  [2*B >= 2 + A + C]
        Signature:
          {(f0,4);(f1,4)}
        Rule Graph:
          [0->{2,3},2->{2},3->{3}]
        ,We construct a looptree:
          P: [0,2,3]
          |
          +- p:[3] c: [3]
          |
          `- p:[2] c: [2])
    + Applied Processor:
        CloseWith True
    + Details:
        ()

YES