YES(?,POLY)
* Step 1: UnsatPaths WORST_CASE(?,POLY)
    + Considered Problem:
        Rules:
          0. f1(A,B,C) -> f1(A,1 + B,C) [-1 + B + -1*C >= 0 && A >= 1 + B]           (?,1)
          1. f3(A,B,C) -> f1(A,B,C)     [B >= 1 + C]                                 (1,1)
          2. f1(A,B,C) -> f1(A,B,1 + C) [-1 + B + -1*C >= 0 && B >= 2 + C && B >= A] (?,1)
        Signature:
          {(f1,3);(f3,3)}
        Flow Graph:
          [0->{0,2},1->{0,2},2->{0,2}]
        
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(2,0)]
* Step 2: FromIts WORST_CASE(?,POLY)
    + Considered Problem:
        Rules:
          0. f1(A,B,C) -> f1(A,1 + B,C) [-1 + B + -1*C >= 0 && A >= 1 + B]           (?,1)
          1. f3(A,B,C) -> f1(A,B,C)     [B >= 1 + C]                                 (1,1)
          2. f1(A,B,C) -> f1(A,B,1 + C) [-1 + B + -1*C >= 0 && B >= 2 + C && B >= A] (?,1)
        Signature:
          {(f1,3);(f3,3)}
        Flow Graph:
          [0->{0,2},1->{0,2},2->{2}]
        
    + Applied Processor:
        FromIts
    + Details:
        ()
* Step 3: Unfold WORST_CASE(?,POLY)
    + Considered Problem:
        Rules:
          f1(A,B,C) -> f1(A,1 + B,C)  [-1 + B + -1*C >= 0 && A >= 1 + B]
          f3(A,B,C) -> f1(A,B,C)      [B >= 1 + C]
          f1(A,B,C) -> f1(A,B,1 + C)  [-1 + B + -1*C >= 0 && B >= 2 + C && B >= A]
        Signature:
          {(f1,3);(f3,3)}
        Rule Graph:
          [0->{0,2},1->{0,2},2->{2}]
    + Applied Processor:
        Unfold
    + Details:
        ()
* Step 4: AddSinks WORST_CASE(?,POLY)
    + Considered Problem:
        Rules:
          f1.0(A,B,C) -> f1.0(A,1 + B,C)  [-1 + B + -1*C >= 0 && A >= 1 + B]
          f1.0(A,B,C) -> f1.2(A,1 + B,C)  [-1 + B + -1*C >= 0 && A >= 1 + B]
          f3.1(A,B,C) -> f1.0(A,B,C)      [B >= 1 + C]
          f3.1(A,B,C) -> f1.2(A,B,C)      [B >= 1 + C]
          f1.2(A,B,C) -> f1.2(A,B,1 + C)  [-1 + B + -1*C >= 0 && B >= 2 + C && B >= A]
        Signature:
          {(f1.0,3);(f1.2,3);(f3.1,3)}
        Rule Graph:
          [0->{0,1},1->{4},2->{0,1},3->{4},4->{4}]
    + Applied Processor:
        AddSinks
    + Details:
        ()
* Step 5: Decompose WORST_CASE(?,POLY)
    + Considered Problem:
        Rules:
          f1.0(A,B,C) -> f1.0(A,1 + B,C)   [-1 + B + -1*C >= 0 && A >= 1 + B]
          f1.0(A,B,C) -> f1.2(A,1 + B,C)   [-1 + B + -1*C >= 0 && A >= 1 + B]
          f3.1(A,B,C) -> f1.0(A,B,C)       [B >= 1 + C]
          f3.1(A,B,C) -> f1.2(A,B,C)       [B >= 1 + C]
          f1.2(A,B,C) -> f1.2(A,B,1 + C)   [-1 + B + -1*C >= 0 && B >= 2 + C && B >= A]
          f1.2(A,B,C) -> exitus616(A,B,C)  True
          f1.2(A,B,C) -> exitus616(A,B,C)  True
        Signature:
          {(exitus616,3);(f1.0,3);(f1.2,3);(f3.1,3)}
        Rule Graph:
          [0->{0,1},1->{4},2->{0,1},3->{4},4->{4,5,6}]
    + Applied Processor:
        Decompose Greedy
    + Details:
        We construct a looptree:
          P: [0,1,2,3,4,5,6]
          |
          +- p:[0] c: [0]
          |
          `- p:[4] c: [4]
* Step 6: AbstractSize WORST_CASE(?,POLY)
    + Considered Problem:
        (Rules:
          f1.0(A,B,C) -> f1.0(A,1 + B,C)   [-1 + B + -1*C >= 0 && A >= 1 + B]
          f1.0(A,B,C) -> f1.2(A,1 + B,C)   [-1 + B + -1*C >= 0 && A >= 1 + B]
          f3.1(A,B,C) -> f1.0(A,B,C)       [B >= 1 + C]
          f3.1(A,B,C) -> f1.2(A,B,C)       [B >= 1 + C]
          f1.2(A,B,C) -> f1.2(A,B,1 + C)   [-1 + B + -1*C >= 0 && B >= 2 + C && B >= A]
          f1.2(A,B,C) -> exitus616(A,B,C)  True
          f1.2(A,B,C) -> exitus616(A,B,C)  True
        Signature:
          {(exitus616,3);(f1.0,3);(f1.2,3);(f3.1,3)}
        Rule Graph:
          [0->{0,1},1->{4},2->{0,1},3->{4},4->{4,5,6}]
        ,We construct a looptree:
          P: [0,1,2,3,4,5,6]
          |
          +- p:[0] c: [0]
          |
          `- p:[4] c: [4])
    + Applied Processor:
        AbstractSize Minimize
    + Details:
        ()
* Step 7: AbstractFlow WORST_CASE(?,POLY)
    + Considered Problem:
        Program:
          Domain: [A,B,C,0.0,0.1]
           f1.0  ~>  f1.0        [A <= A, B <= K + B, C <= C]
           f1.0  ~>  f1.2        [A <= A, B <= K + B, C <= C]
           f3.1  ~>  f1.0        [A <= A, B <= B, C <= C]
           f3.1  ~>  f1.2        [A <= A, B <= B, C <= C]
           f1.2  ~>  f1.2        [A <= A, B <= B, C <= B + C]
           f1.2  ~>  exitus616   [A <= A, B <= B, C <= C]
           f1.2  ~>  exitus616   [A <= A, B <= B, C <= C]
          + Loop: [0.0 <= K + A + B]
               f1.0  ~>  f1.0   [A <= A, B <= K + B, C <= C]
          + Loop: [0.1 <= 2*K + B + C]
               f1.2  ~>  f1.2   [A <= A, B <= B, C <= B + C]
    + Applied Processor:
        AbstractFlow
    + Details:
        ()
* Step 8: Lare WORST_CASE(?,POLY)
    + Considered Problem:
        Program:
          Domain: [tick,huge,K,A,B,C,0.0,0.1]
           f1.0  ~>  f1.0        [B ~+> B,K ~+> B]
           f1.0  ~>  f1.2        [B ~+> B,K ~+> B]
           f3.1  ~>  f1.0        []
           f3.1  ~>  f1.2        []
           f1.2  ~>  f1.2        [B ~+> C,C ~+> C]
           f1.2  ~>  exitus616   []
           f1.2  ~>  exitus616   []
          + Loop: [A ~+> 0.0,B ~+> 0.0,K ~+> 0.0]
               f1.0  ~>  f1.0   [B ~+> B,K ~+> B]
          + Loop: [B ~+> 0.1,C ~+> 0.1,K ~*> 0.1]
               f1.2  ~>  f1.2   [B ~+> C,C ~+> C]
    + Applied Processor:
        Lare
    + Details:
         f3.1  ~>  exitus616   [A ~+> 0.0
                               ,A ~+> tick
                               ,B ~+> B
                               ,B ~+> C
                               ,B ~+> 0.0
                               ,B ~+> 0.1
                               ,B ~+> tick
                               ,C ~+> C
                               ,C ~+> 0.1
                               ,C ~+> tick
                               ,tick ~+> tick
                               ,K ~+> B
                               ,K ~+> C
                               ,K ~+> 0.0
                               ,K ~+> 0.1
                               ,K ~+> tick
                               ,A ~*> B
                               ,A ~*> C
                               ,A ~*> 0.1
                               ,A ~*> tick
                               ,B ~*> B
                               ,B ~*> C
                               ,B ~*> 0.1
                               ,B ~*> tick
                               ,C ~*> C
                               ,K ~*> B
                               ,K ~*> C
                               ,K ~*> 0.1
                               ,K ~*> tick]
        + <f1.0  ~>  f1.0>  [A ~+> 0.0
                            ,A ~+> tick
                            ,B ~+> B
                            ,B ~+> 0.0
                            ,B ~+> tick
                            ,tick ~+> tick
                            ,K ~+> B
                            ,K ~+> 0.0
                            ,K ~+> tick
                            ,A ~*> B
                            ,B ~*> B
                            ,K ~*> B]
        + <f1.2  ~>  f1.2>  [B ~+> C
                            ,B ~+> 0.1
                            ,B ~+> tick
                            ,C ~+> C
                            ,C ~+> 0.1
                            ,C ~+> tick
                            ,tick ~+> tick
                            ,B ~*> C
                            ,C ~*> C
                            ,K ~*> C
                            ,K ~*> 0.1
                            ,K ~*> tick]

YES(?,POLY)