YES(?,POLY)
* Step 1: UnsatPaths WORST_CASE(?,POLY)
    + Considered Problem:
        Rules:
          0. f1(A,B) -> f3(A,A)           [A >= 1]                                           (1,1)
          1. f3(A,B) -> f3(A,-1 + B)      [A + -1*B >= 0 && -1 + A >= 0 && B >= 1]           (?,1)
          2. f3(A,B) -> f3(-1 + A,-1 + A) [A + -1*B >= 0 && -1 + A >= 0 && 0 >= B && A >= 2] (?,1)
        Signature:
          {(f1,2);(f3,2)}
        Flow Graph:
          [0->{1,2},1->{1,2},2->{1,2}]
        
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(0,2),(2,2)]
* Step 2: FromIts WORST_CASE(?,POLY)
    + Considered Problem:
        Rules:
          0. f1(A,B) -> f3(A,A)           [A >= 1]                                           (1,1)
          1. f3(A,B) -> f3(A,-1 + B)      [A + -1*B >= 0 && -1 + A >= 0 && B >= 1]           (?,1)
          2. f3(A,B) -> f3(-1 + A,-1 + A) [A + -1*B >= 0 && -1 + A >= 0 && 0 >= B && A >= 2] (?,1)
        Signature:
          {(f1,2);(f3,2)}
        Flow Graph:
          [0->{1},1->{1,2},2->{1}]
        
    + Applied Processor:
        FromIts
    + Details:
        ()
* Step 3: AddSinks WORST_CASE(?,POLY)
    + Considered Problem:
        Rules:
          f1(A,B) -> f3(A,A)            [A >= 1]
          f3(A,B) -> f3(A,-1 + B)       [A + -1*B >= 0 && -1 + A >= 0 && B >= 1]
          f3(A,B) -> f3(-1 + A,-1 + A)  [A + -1*B >= 0 && -1 + A >= 0 && 0 >= B && A >= 2]
        Signature:
          {(f1,2);(f3,2)}
        Rule Graph:
          [0->{1},1->{1,2},2->{1}]
    + Applied Processor:
        AddSinks
    + Details:
        ()
* Step 4: Decompose WORST_CASE(?,POLY)
    + Considered Problem:
        Rules:
          f1(A,B) -> f3(A,A)            [A >= 1]
          f3(A,B) -> f3(A,-1 + B)       [A + -1*B >= 0 && -1 + A >= 0 && B >= 1]
          f3(A,B) -> f3(-1 + A,-1 + A)  [A + -1*B >= 0 && -1 + A >= 0 && 0 >= B && A >= 2]
          f3(A,B) -> exitus616(A,B)     True
          f3(A,B) -> exitus616(A,B)     True
        Signature:
          {(exitus616,2);(f1,2);(f3,2)}
        Rule Graph:
          [0->{1},1->{1,2,3},2->{1,4}]
    + Applied Processor:
        Decompose Greedy
    + Details:
        We construct a looptree:
          P: [0,1,2,3,4]
          |
          `- p:[1,2] c: [2]
             |
             `- p:[1] c: [1]
* Step 5: AbstractSize WORST_CASE(?,POLY)
    + Considered Problem:
        (Rules:
          f1(A,B) -> f3(A,A)            [A >= 1]
          f3(A,B) -> f3(A,-1 + B)       [A + -1*B >= 0 && -1 + A >= 0 && B >= 1]
          f3(A,B) -> f3(-1 + A,-1 + A)  [A + -1*B >= 0 && -1 + A >= 0 && 0 >= B && A >= 2]
          f3(A,B) -> exitus616(A,B)     True
          f3(A,B) -> exitus616(A,B)     True
        Signature:
          {(exitus616,2);(f1,2);(f3,2)}
        Rule Graph:
          [0->{1},1->{1,2,3},2->{1,4}]
        ,We construct a looptree:
          P: [0,1,2,3,4]
          |
          `- p:[1,2] c: [2]
             |
             `- p:[1] c: [1])
    + Applied Processor:
        AbstractSize Minimize
    + Details:
        ()
* Step 6: AbstractFlow WORST_CASE(?,POLY)
    + Considered Problem:
        Program:
          Domain: [A,B,0.0,0.0.0]
           f1  ~>  f3          [A <= A, B <= A]
           f3  ~>  f3          [A <= A, B <= B]
           f3  ~>  f3          [A <= A, B <= A]
           f3  ~>  exitus616   [A <= A, B <= B]
           f3  ~>  exitus616   [A <= A, B <= B]
          + Loop: [0.0 <= A]
               f3  ~>  f3   [A <= A, B <= B]
               f3  ~>  f3   [A <= A, B <= A]
            + Loop: [0.0.0 <= K + B]
                 f3  ~>  f3   [A <= A, B <= B]
    + Applied Processor:
        AbstractFlow
    + Details:
        ()
* Step 7: Lare WORST_CASE(?,POLY)
    + Considered Problem:
        Program:
          Domain: [tick,huge,K,A,B,0.0,0.0.0]
           f1  ~>  f3          [A ~=> B]
           f3  ~>  f3          []
           f3  ~>  f3          [A ~=> B]
           f3  ~>  exitus616   []
           f3  ~>  exitus616   []
          + Loop: [A ~=> 0.0]
               f3  ~>  f3   []
               f3  ~>  f3   [A ~=> B]
            + Loop: [B ~+> 0.0.0,K ~+> 0.0.0]
                 f3  ~>  f3   []
    + Applied Processor:
        Lare
    + Details:
         f1  ~>  exitus616   [A ~=> B
                             ,A ~=> 0.0
                             ,A ~+> 0.0.0
                             ,A ~+> tick
                             ,tick ~+> tick
                             ,K ~+> 0.0.0
                             ,K ~+> tick
                             ,A ~*> tick
                             ,K ~*> tick]
        + <f3  ~>  f3>  [A ~=> B
                        ,A ~=> 0.0
                        ,A ~+> 0.0.0
                        ,A ~+> tick
                        ,B ~+> 0.0.0
                        ,B ~+> tick
                        ,tick ~+> tick
                        ,K ~+> 0.0.0
                        ,K ~+> tick
                        ,A ~*> tick
                        ,B ~*> tick
                        ,K ~*> tick]
          + <f3  ~>  f3>  [B ~+> 0.0.0,B ~+> tick,tick ~+> tick,K ~+> 0.0.0,K ~+> tick]

YES(?,POLY)