WORST_CASE(?,O(n^2))
* Step 1: LocalSizeboundsProc WORST_CASE(?,O(n^2))
    + Considered Problem:
        Rules:
          0. f4(A,B,C) -> f4(A,1 + B,C) [A >= 1 + B]           (?,1)
          1. f4(A,B,C) -> f4(1 + A,0,C) [C >= 2 + A && B >= A] (?,1)
          2. f0(A,B,C) -> f4(0,0,C)     [C >= 1]               (1,1)
        Signature:
          {(f0,3);(f4,3)}
        Flow Graph:
          [0->{0,1},1->{0,1},2->{0,1}]
        
    + Applied Processor:
        LocalSizeboundsProc
    + Details:
        LocalSizebounds generated; rvgraph
          (<0,0,A>,         A, .= 0) (<0,0,B>, 1 + B, .+ 1) (<0,0,C>, C, .= 0) 
          (<1,0,A>, 1 + A + C, .* 1) (<1,0,B>,     0, .= 0) (<1,0,C>, C, .= 0) 
          (<2,0,A>,         0, .= 0) (<2,0,B>,     0, .= 0) (<2,0,C>, C, .= 0) 
* Step 2: SizeboundsProc WORST_CASE(?,O(n^2))
    + Considered Problem:
        Rules:
          0. f4(A,B,C) -> f4(A,1 + B,C) [A >= 1 + B]           (?,1)
          1. f4(A,B,C) -> f4(1 + A,0,C) [C >= 2 + A && B >= A] (?,1)
          2. f0(A,B,C) -> f4(0,0,C)     [C >= 1]               (1,1)
        Signature:
          {(f0,3);(f4,3)}
        Flow Graph:
          [0->{0,1},1->{0,1},2->{0,1}]
        Sizebounds:
          (<0,0,A>, ?) (<0,0,B>, ?) (<0,0,C>, ?) 
          (<1,0,A>, ?) (<1,0,B>, ?) (<1,0,C>, ?) 
          (<2,0,A>, ?) (<2,0,B>, ?) (<2,0,C>, ?) 
    + Applied Processor:
        SizeboundsProc
    + Details:
        Sizebounds computed:
          (<0,0,A>, C) (<0,0,B>, C) (<0,0,C>, C) 
          (<1,0,A>, C) (<1,0,B>, 0) (<1,0,C>, C) 
          (<2,0,A>, 0) (<2,0,B>, 0) (<2,0,C>, C) 
* Step 3: UnsatPaths WORST_CASE(?,O(n^2))
    + Considered Problem:
        Rules:
          0. f4(A,B,C) -> f4(A,1 + B,C) [A >= 1 + B]           (?,1)
          1. f4(A,B,C) -> f4(1 + A,0,C) [C >= 2 + A && B >= A] (?,1)
          2. f0(A,B,C) -> f4(0,0,C)     [C >= 1]               (1,1)
        Signature:
          {(f0,3);(f4,3)}
        Flow Graph:
          [0->{0,1},1->{0,1},2->{0,1}]
        Sizebounds:
          (<0,0,A>, C) (<0,0,B>, C) (<0,0,C>, C) 
          (<1,0,A>, C) (<1,0,B>, 0) (<1,0,C>, C) 
          (<2,0,A>, 0) (<2,0,B>, 0) (<2,0,C>, C) 
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(2,0)]
* Step 4: PolyRank WORST_CASE(?,O(n^2))
    + Considered Problem:
        Rules:
          0. f4(A,B,C) -> f4(A,1 + B,C) [A >= 1 + B]           (?,1)
          1. f4(A,B,C) -> f4(1 + A,0,C) [C >= 2 + A && B >= A] (?,1)
          2. f0(A,B,C) -> f4(0,0,C)     [C >= 1]               (1,1)
        Signature:
          {(f0,3);(f4,3)}
        Flow Graph:
          [0->{0,1},1->{0,1},2->{1}]
        Sizebounds:
          (<0,0,A>, C) (<0,0,B>, C) (<0,0,C>, C) 
          (<1,0,A>, C) (<1,0,B>, 0) (<1,0,C>, C) 
          (<2,0,A>, 0) (<2,0,B>, 0) (<2,0,C>, C) 
    + Applied Processor:
        PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
    + Details:
        We apply a polynomial interpretation of shape linear:
          p(f0) = x3             
          p(f4) = -1 + -1*x1 + x3
        
        The following rules are strictly oriented:
        [C >= 2 + A && B >= A] ==>              
                     f4(A,B,C)   = -1 + -1*A + C
                                 > -2 + -1*A + C
                                 = f4(1 + A,0,C)
        
                      [C >= 1] ==>              
                     f0(A,B,C)   = C            
                                 > -1 + C       
                                 = f4(0,0,C)    
        
        
        The following rules are weakly oriented:
        [A >= 1 + B] ==>              
           f4(A,B,C)   = -1 + -1*A + C
                      >= -1 + -1*A + C
                       = f4(A,1 + B,C)
        
        
* Step 5: PolyRank WORST_CASE(?,O(n^2))
    + Considered Problem:
        Rules:
          0. f4(A,B,C) -> f4(A,1 + B,C) [A >= 1 + B]           (?,1)
          1. f4(A,B,C) -> f4(1 + A,0,C) [C >= 2 + A && B >= A] (C,1)
          2. f0(A,B,C) -> f4(0,0,C)     [C >= 1]               (1,1)
        Signature:
          {(f0,3);(f4,3)}
        Flow Graph:
          [0->{0,1},1->{0,1},2->{1}]
        Sizebounds:
          (<0,0,A>, C) (<0,0,B>, C) (<0,0,C>, C) 
          (<1,0,A>, C) (<1,0,B>, 0) (<1,0,C>, C) 
          (<2,0,A>, 0) (<2,0,B>, 0) (<2,0,C>, C) 
    + Applied Processor:
        PolyRank {useFarkas = True, withSizebounds = [0], shape = Linear}
    + Details:
        We apply a polynomial interpretation of shape linear:
          p(f4) = x1 + -1*x2
        
        The following rules are strictly oriented:
        [A >= 1 + B] ==>              
           f4(A,B,C)   = A + -1*B     
                       > -1 + A + -1*B
                       = f4(A,1 + B,C)
        
        
        The following rules are weakly oriented:
        
        We use the following global sizebounds:
        (<0,0,A>, C) (<0,0,B>, C) (<0,0,C>, C) 
        (<1,0,A>, C) (<1,0,B>, 0) (<1,0,C>, C) 
        (<2,0,A>, 0) (<2,0,B>, 0) (<2,0,C>, C) 
* Step 6: KnowledgePropagation WORST_CASE(?,O(n^2))
    + Considered Problem:
        Rules:
          0. f4(A,B,C) -> f4(A,1 + B,C) [A >= 1 + B]           (C^2,1)
          1. f4(A,B,C) -> f4(1 + A,0,C) [C >= 2 + A && B >= A] (C,1)  
          2. f0(A,B,C) -> f4(0,0,C)     [C >= 1]               (1,1)  
        Signature:
          {(f0,3);(f4,3)}
        Flow Graph:
          [0->{0,1},1->{0,1},2->{1}]
        Sizebounds:
          (<0,0,A>, C) (<0,0,B>, C) (<0,0,C>, C) 
          (<1,0,A>, C) (<1,0,B>, 0) (<1,0,C>, C) 
          (<2,0,A>, 0) (<2,0,B>, 0) (<2,0,C>, C) 
    + Applied Processor:
        KnowledgePropagation
    + Details:
        The problem is already solved.

WORST_CASE(?,O(n^2))