YES(?,POLY)
* Step 1: FromIts WORST_CASE(?,POLY)
    + Considered Problem:
        Rules:
          0. start(A) -> a(A) [A >= 1]                                 (1,1)
          1. start(A) -> a(A) [A >= 2]                                 (1,1)
          2. start(A) -> a(A) [A >= 4]                                 (1,1)
          3. a(A)     -> a(B) [-1 + A >= 0 && 2*B >= 2 && A = 2*B]     (?,1)
          4. a(A)     -> a(B) [-1 + A >= 0 && 2*B >= 1 && A = 1 + 2*B] (?,1)
        Signature:
          {(a,1);(start,1)}
        Flow Graph:
          [0->{3,4},1->{3,4},2->{3,4},3->{3,4},4->{3,4}]
        
    + Applied Processor:
        FromIts
    + Details:
        ()
* Step 2: AddSinks WORST_CASE(?,POLY)
    + Considered Problem:
        Rules:
          start(A) -> a(A)  [A >= 1]
          start(A) -> a(A)  [A >= 2]
          start(A) -> a(A)  [A >= 4]
          a(A)     -> a(B)  [-1 + A >= 0 && 2*B >= 2 && A = 2*B]
          a(A)     -> a(B)  [-1 + A >= 0 && 2*B >= 1 && A = 1 + 2*B]
        Signature:
          {(a,1);(start,1)}
        Rule Graph:
          [0->{3,4},1->{3,4},2->{3,4},3->{3,4},4->{3,4}]
    + Applied Processor:
        AddSinks
    + Details:
        ()
* Step 3: Decompose WORST_CASE(?,POLY)
    + Considered Problem:
        Rules:
          start(A) -> a(A)          [A >= 1]
          start(A) -> a(A)          [A >= 2]
          start(A) -> a(A)          [A >= 4]
          a(A)     -> a(B)          [-1 + A >= 0 && 2*B >= 2 && A = 2*B]
          a(A)     -> a(B)          [-1 + A >= 0 && 2*B >= 1 && A = 1 + 2*B]
          a(A)     -> exitus616(A)  True
          a(A)     -> exitus616(A)  True
          a(A)     -> exitus616(A)  True
          a(A)     -> exitus616(A)  True
          a(A)     -> exitus616(A)  True
          a(A)     -> exitus616(A)  True
        Signature:
          {(a,1);(exitus616,1);(start,1)}
        Rule Graph:
          [0->{3,4},1->{3,4},2->{3,4},3->{3,4,5,7,9},4->{3,4,6,8,10}]
    + Applied Processor:
        Decompose Greedy
    + Details:
        We construct a looptree:
          P: [0,1,2,3,4,5,6,7,8,9,10]
          |
          `- p:[3,4] c: [3,4]
* Step 4: AbstractSize WORST_CASE(?,POLY)
    + Considered Problem:
        (Rules:
          start(A) -> a(A)          [A >= 1]
          start(A) -> a(A)          [A >= 2]
          start(A) -> a(A)          [A >= 4]
          a(A)     -> a(B)          [-1 + A >= 0 && 2*B >= 2 && A = 2*B]
          a(A)     -> a(B)          [-1 + A >= 0 && 2*B >= 1 && A = 1 + 2*B]
          a(A)     -> exitus616(A)  True
          a(A)     -> exitus616(A)  True
          a(A)     -> exitus616(A)  True
          a(A)     -> exitus616(A)  True
          a(A)     -> exitus616(A)  True
          a(A)     -> exitus616(A)  True
        Signature:
          {(a,1);(exitus616,1);(start,1)}
        Rule Graph:
          [0->{3,4},1->{3,4},2->{3,4},3->{3,4,5,7,9},4->{3,4,6,8,10}]
        ,We construct a looptree:
          P: [0,1,2,3,4,5,6,7,8,9,10]
          |
          `- p:[3,4] c: [3,4])
    + Applied Processor:
        AbstractSize Minimize
    + Details:
        ()
* Step 5: AbstractFlow WORST_CASE(?,POLY)
    + Considered Problem:
        Program:
          Domain: [A,0.0]
           start  ~>  a           [A <= A]
           start  ~>  a           [A <= A]
           start  ~>  a           [A <= A]
           a      ~>  a           [A <= unknown]
           a      ~>  a           [A <= unknown]
           a      ~>  exitus616   [A <= A]
           a      ~>  exitus616   [A <= A]
           a      ~>  exitus616   [A <= A]
           a      ~>  exitus616   [A <= A]
           a      ~>  exitus616   [A <= A]
           a      ~>  exitus616   [A <= A]
          + Loop: [0.0 <= 2*K + 2*A]
               a  ~>  a   [A <= unknown]
               a  ~>  a   [A <= unknown]
    + Applied Processor:
        AbstractFlow
    + Details:
        ()
* Step 6: Lare WORST_CASE(?,POLY)
    + Considered Problem:
        Program:
          Domain: [tick,huge,K,A,0.0]
           start  ~>  a           []
           start  ~>  a           []
           start  ~>  a           []
           a      ~>  a           [huge ~=> A]
           a      ~>  a           [huge ~=> A]
           a      ~>  exitus616   []
           a      ~>  exitus616   []
           a      ~>  exitus616   []
           a      ~>  exitus616   []
           a      ~>  exitus616   []
           a      ~>  exitus616   []
          + Loop: [A ~*> 0.0,K ~*> 0.0]
               a  ~>  a   [huge ~=> A]
               a  ~>  a   [huge ~=> A]
    + Applied Processor:
        Lare
    + Details:
         start  ~>  exitus616   [huge ~=> A,tick ~+> tick,A ~*> 0.0,A ~*> tick,K ~*> 0.0,K ~*> tick]
        + <a  ~>  a>  [huge ~=> A,tick ~+> tick,A ~*> 0.0,A ~*> tick,K ~*> 0.0,K ~*> tick]

YES(?,POLY)