WORST_CASE(?,O(n^1))
* Step 1: LocalSizeboundsProc WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. f(A,B,C)     -> f(A,1 + B,C) [A >= 1 + B && A >= 1 + C] (?,1)
          1. f(A,B,C)     -> f(A,B,1 + C) [A >= 1 + B && A >= 1 + C] (?,1)
          2. start(A,B,C) -> f(A,B,C)     True                       (1,1)
        Signature:
          {(f,3);(start,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>, A, .= 0) (<1,0,B>,     B, .= 0) (<1,0,C>, 1 + C, .+ 1) 
          (<2,0,A>, A, .= 0) (<2,0,B>,     B, .= 0) (<2,0,C>,     C, .= 0) 
* Step 2: SizeboundsProc WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. f(A,B,C)     -> f(A,1 + B,C) [A >= 1 + B && A >= 1 + C] (?,1)
          1. f(A,B,C)     -> f(A,B,1 + C) [A >= 1 + B && A >= 1 + C] (?,1)
          2. start(A,B,C) -> f(A,B,C)     True                       (1,1)
        Signature:
          {(f,3);(start,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>, A) (<0,0,B>, A) (<0,0,C>, A) 
          (<1,0,A>, A) (<1,0,B>, A) (<1,0,C>, A) 
          (<2,0,A>, A) (<2,0,B>, B) (<2,0,C>, C) 
* Step 3: PolyRank WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. f(A,B,C)     -> f(A,1 + B,C) [A >= 1 + B && A >= 1 + C] (?,1)
          1. f(A,B,C)     -> f(A,B,1 + C) [A >= 1 + B && A >= 1 + C] (?,1)
          2. start(A,B,C) -> f(A,B,C)     True                       (1,1)
        Signature:
          {(f,3);(start,3)}
        Flow Graph:
          [0->{0,1},1->{0,1},2->{0,1}]
        Sizebounds:
          (<0,0,A>, A) (<0,0,B>, A) (<0,0,C>, A) 
          (<1,0,A>, A) (<1,0,B>, A) (<1,0,C>, A) 
          (<2,0,A>, A) (<2,0,B>, B) (<2,0,C>, C) 
    + Applied Processor:
        PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
    + Details:
        We apply a polynomial interpretation of shape linear:
              p(f) = x1 + -1*x3
          p(start) = x1 + -1*x3
        
        The following rules are strictly oriented:
        [A >= 1 + B && A >= 1 + C] ==>              
                          f(A,B,C)   = A + -1*C     
                                     > -1 + A + -1*C
                                     = f(A,B,1 + C) 
        
        
        The following rules are weakly oriented:
        [A >= 1 + B && A >= 1 + C] ==>             
                          f(A,B,C)   = A + -1*C    
                                    >= A + -1*C    
                                     = f(A,1 + B,C)
        
                              True ==>             
                      start(A,B,C)   = A + -1*C    
                                    >= A + -1*C    
                                     = f(A,B,C)    
        
        
* Step 4: PolyRank WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. f(A,B,C)     -> f(A,1 + B,C) [A >= 1 + B && A >= 1 + C] (?,1)    
          1. f(A,B,C)     -> f(A,B,1 + C) [A >= 1 + B && A >= 1 + C] (A + C,1)
          2. start(A,B,C) -> f(A,B,C)     True                       (1,1)    
        Signature:
          {(f,3);(start,3)}
        Flow Graph:
          [0->{0,1},1->{0,1},2->{0,1}]
        Sizebounds:
          (<0,0,A>, A) (<0,0,B>, A) (<0,0,C>, A) 
          (<1,0,A>, A) (<1,0,B>, A) (<1,0,C>, A) 
          (<2,0,A>, A) (<2,0,B>, B) (<2,0,C>, C) 
    + Applied Processor:
        PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
    + Details:
        We apply a polynomial interpretation of shape linear:
              p(f) = x1 + -1*x2
          p(start) = x1 + -1*x2
        
        The following rules are strictly oriented:
        [A >= 1 + B && A >= 1 + C] ==>              
                          f(A,B,C)   = A + -1*B     
                                     > -1 + A + -1*B
                                     = f(A,1 + B,C) 
        
        
        The following rules are weakly oriented:
        [A >= 1 + B && A >= 1 + C] ==>             
                          f(A,B,C)   = A + -1*B    
                                    >= A + -1*B    
                                     = f(A,B,1 + C)
        
                              True ==>             
                      start(A,B,C)   = A + -1*B    
                                    >= A + -1*B    
                                     = f(A,B,C)    
        
        
* Step 5: KnowledgePropagation WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. f(A,B,C)     -> f(A,1 + B,C) [A >= 1 + B && A >= 1 + C] (A + B,1)
          1. f(A,B,C)     -> f(A,B,1 + C) [A >= 1 + B && A >= 1 + C] (A + C,1)
          2. start(A,B,C) -> f(A,B,C)     True                       (1,1)    
        Signature:
          {(f,3);(start,3)}
        Flow Graph:
          [0->{0,1},1->{0,1},2->{0,1}]
        Sizebounds:
          (<0,0,A>, A) (<0,0,B>, A) (<0,0,C>, A) 
          (<1,0,A>, A) (<1,0,B>, A) (<1,0,C>, A) 
          (<2,0,A>, A) (<2,0,B>, B) (<2,0,C>, C) 
    + Applied Processor:
        KnowledgePropagation
    + Details:
        The problem is already solved.

WORST_CASE(?,O(n^1))