WORST_CASE(?,O(1))
* Step 1: LocalSizeboundsProc WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A) -> f3(0)     True                    (1,1)
          1. f3(A) -> f3(1 + A) [9 >= A]                (?,1)
          2. f3(A) -> f11(A)    [A >= 10 && 0 >= 1 + B] (?,1)
          3. f3(A) -> f11(A)    [A >= 10]               (?,1)
        Signature:
          {(f0,1);(f11,1);(f3,1)}
        Flow Graph:
          [0->{1,2,3},1->{1,2,3},2->{},3->{}]
        
    + Applied Processor:
        LocalSizeboundsProc
    + Details:
        LocalSizebounds generated; rvgraph
          (<0,0,A>,     0, .= 0) 
          (<1,0,A>, 1 + A, .+ 1) 
          (<2,0,A>,     A, .= 0) 
          (<3,0,A>,     A, .= 0) 
* Step 2: SizeboundsProc WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A) -> f3(0)     True                    (1,1)
          1. f3(A) -> f3(1 + A) [9 >= A]                (?,1)
          2. f3(A) -> f11(A)    [A >= 10 && 0 >= 1 + B] (?,1)
          3. f3(A) -> f11(A)    [A >= 10]               (?,1)
        Signature:
          {(f0,1);(f11,1);(f3,1)}
        Flow Graph:
          [0->{1,2,3},1->{1,2,3},2->{},3->{}]
        Sizebounds:
          (<0,0,A>, ?) 
          (<1,0,A>, ?) 
          (<2,0,A>, ?) 
          (<3,0,A>, ?) 
    + Applied Processor:
        SizeboundsProc
    + Details:
        Sizebounds computed:
          (<0,0,A>,  0) 
          (<1,0,A>, 10) 
          (<2,0,A>, 10) 
          (<3,0,A>, 10) 
* Step 3: UnsatPaths WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A) -> f3(0)     True                    (1,1)
          1. f3(A) -> f3(1 + A) [9 >= A]                (?,1)
          2. f3(A) -> f11(A)    [A >= 10 && 0 >= 1 + B] (?,1)
          3. f3(A) -> f11(A)    [A >= 10]               (?,1)
        Signature:
          {(f0,1);(f11,1);(f3,1)}
        Flow Graph:
          [0->{1,2,3},1->{1,2,3},2->{},3->{}]
        Sizebounds:
          (<0,0,A>,  0) 
          (<1,0,A>, 10) 
          (<2,0,A>, 10) 
          (<3,0,A>, 10) 
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(0,2),(0,3)]
* Step 4: LeafRules WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A) -> f3(0)     True                    (1,1)
          1. f3(A) -> f3(1 + A) [9 >= A]                (?,1)
          2. f3(A) -> f11(A)    [A >= 10 && 0 >= 1 + B] (?,1)
          3. f3(A) -> f11(A)    [A >= 10]               (?,1)
        Signature:
          {(f0,1);(f11,1);(f3,1)}
        Flow Graph:
          [0->{1},1->{1,2,3},2->{},3->{}]
        Sizebounds:
          (<0,0,A>,  0) 
          (<1,0,A>, 10) 
          (<2,0,A>, 10) 
          (<3,0,A>, 10) 
    + Applied Processor:
        LeafRules
    + Details:
        The following transitions are estimated by its predecessors and are removed [2,3]
* Step 5: PolyRank WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A) -> f3(0)     True     (1,1)
          1. f3(A) -> f3(1 + A) [9 >= A] (?,1)
        Signature:
          {(f0,1);(f11,1);(f3,1)}
        Flow Graph:
          [0->{1},1->{1}]
        Sizebounds:
          (<0,0,A>,  0) 
          (<1,0,A>, 10) 
    + Applied Processor:
        PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
    + Details:
        We apply a polynomial interpretation of shape linear:
          p(f0) = 10        
          p(f3) = 10 + -1*x1
        
        The following rules are strictly oriented:
        [9 >= A] ==>          
           f3(A)   = 10 + -1*A
                   > 9 + -1*A 
                   = f3(1 + A)
        
        
        The following rules are weakly oriented:
           True ==>      
          f0(A)   = 10   
                 >= 10   
                  = f3(0)
        
        
* Step 6: KnowledgePropagation WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A) -> f3(0)     True     (1,1) 
          1. f3(A) -> f3(1 + A) [9 >= A] (10,1)
        Signature:
          {(f0,1);(f11,1);(f3,1)}
        Flow Graph:
          [0->{1},1->{1}]
        Sizebounds:
          (<0,0,A>,  0) 
          (<1,0,A>, 10) 
    + Applied Processor:
        KnowledgePropagation
    + Details:
        The problem is already solved.

WORST_CASE(?,O(1))