WORST_CASE(?,O(1))
* Step 1: LocalSizeboundsProc WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f4(A)  -> f5(A)     [0 >= 1 + B] (?,1)
          1. f4(A)  -> f5(A)     True         (?,1)
          2. f0(A)  -> f4(0)     True         (1,1)
          3. f5(A)  -> f11(A)    [A >= 3]     (?,1)
          4. f4(A)  -> f11(A)    True         (?,1)
          5. f5(A)  -> f4(1 + A) [2 >= A]     (?,1)
          6. f11(A) -> f14(A)    [1 >= A]     (?,1)
          7. f11(A) -> f14(A)    [A >= 2]     (?,1)
        Signature:
          {(f0,1);(f11,1);(f14,1);(f4,1);(f5,1)}
        Flow Graph:
          [0->{3,5},1->{3,5},2->{0,1,4},3->{6,7},4->{6,7},5->{0,1,4},6->{},7->{}]
        
    + Applied Processor:
        LocalSizeboundsProc
    + Details:
        LocalSizebounds generated; rvgraph
          (<0,0,A>,     A, .= 0) 
          (<1,0,A>,     A, .= 0) 
          (<2,0,A>,     0, .= 0) 
          (<3,0,A>,     A, .= 0) 
          (<4,0,A>,     A, .= 0) 
          (<5,0,A>, 1 + A, .+ 1) 
          (<6,0,A>,     A, .= 0) 
          (<7,0,A>,     A, .= 0) 
* Step 2: SizeboundsProc WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f4(A)  -> f5(A)     [0 >= 1 + B] (?,1)
          1. f4(A)  -> f5(A)     True         (?,1)
          2. f0(A)  -> f4(0)     True         (1,1)
          3. f5(A)  -> f11(A)    [A >= 3]     (?,1)
          4. f4(A)  -> f11(A)    True         (?,1)
          5. f5(A)  -> f4(1 + A) [2 >= A]     (?,1)
          6. f11(A) -> f14(A)    [1 >= A]     (?,1)
          7. f11(A) -> f14(A)    [A >= 2]     (?,1)
        Signature:
          {(f0,1);(f11,1);(f14,1);(f4,1);(f5,1)}
        Flow Graph:
          [0->{3,5},1->{3,5},2->{0,1,4},3->{6,7},4->{6,7},5->{0,1,4},6->{},7->{}]
        Sizebounds:
          (<0,0,A>, ?) 
          (<1,0,A>, ?) 
          (<2,0,A>, ?) 
          (<3,0,A>, ?) 
          (<4,0,A>, ?) 
          (<5,0,A>, ?) 
          (<6,0,A>, ?) 
          (<7,0,A>, ?) 
    + Applied Processor:
        SizeboundsProc
    + Details:
        Sizebounds computed:
          (<0,0,A>, 3) 
          (<1,0,A>, 3) 
          (<2,0,A>, 0) 
          (<3,0,A>, 3) 
          (<4,0,A>, 3) 
          (<5,0,A>, 3) 
          (<6,0,A>, 3) 
          (<7,0,A>, 3) 
* Step 3: UnsatPaths WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f4(A)  -> f5(A)     [0 >= 1 + B] (?,1)
          1. f4(A)  -> f5(A)     True         (?,1)
          2. f0(A)  -> f4(0)     True         (1,1)
          3. f5(A)  -> f11(A)    [A >= 3]     (?,1)
          4. f4(A)  -> f11(A)    True         (?,1)
          5. f5(A)  -> f4(1 + A) [2 >= A]     (?,1)
          6. f11(A) -> f14(A)    [1 >= A]     (?,1)
          7. f11(A) -> f14(A)    [A >= 2]     (?,1)
        Signature:
          {(f0,1);(f11,1);(f14,1);(f4,1);(f5,1)}
        Flow Graph:
          [0->{3,5},1->{3,5},2->{0,1,4},3->{6,7},4->{6,7},5->{0,1,4},6->{},7->{}]
        Sizebounds:
          (<0,0,A>, 3) 
          (<1,0,A>, 3) 
          (<2,0,A>, 0) 
          (<3,0,A>, 3) 
          (<4,0,A>, 3) 
          (<5,0,A>, 3) 
          (<6,0,A>, 3) 
          (<7,0,A>, 3) 
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(3,6)]
* Step 4: LeafRules WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f4(A)  -> f5(A)     [0 >= 1 + B] (?,1)
          1. f4(A)  -> f5(A)     True         (?,1)
          2. f0(A)  -> f4(0)     True         (1,1)
          3. f5(A)  -> f11(A)    [A >= 3]     (?,1)
          4. f4(A)  -> f11(A)    True         (?,1)
          5. f5(A)  -> f4(1 + A) [2 >= A]     (?,1)
          6. f11(A) -> f14(A)    [1 >= A]     (?,1)
          7. f11(A) -> f14(A)    [A >= 2]     (?,1)
        Signature:
          {(f0,1);(f11,1);(f14,1);(f4,1);(f5,1)}
        Flow Graph:
          [0->{3,5},1->{3,5},2->{0,1,4},3->{7},4->{6,7},5->{0,1,4},6->{},7->{}]
        Sizebounds:
          (<0,0,A>, 3) 
          (<1,0,A>, 3) 
          (<2,0,A>, 0) 
          (<3,0,A>, 3) 
          (<4,0,A>, 3) 
          (<5,0,A>, 3) 
          (<6,0,A>, 3) 
          (<7,0,A>, 3) 
    + Applied Processor:
        LeafRules
    + Details:
        The following transitions are estimated by its predecessors and are removed [3,4,6,7]
* Step 5: PolyRank WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f4(A) -> f5(A)     [0 >= 1 + B] (?,1)
          1. f4(A) -> f5(A)     True         (?,1)
          2. f0(A) -> f4(0)     True         (1,1)
          5. f5(A) -> f4(1 + A) [2 >= A]     (?,1)
        Signature:
          {(f0,1);(f11,1);(f14,1);(f4,1);(f5,1)}
        Flow Graph:
          [0->{5},1->{5},2->{0,1},5->{0,1}]
        Sizebounds:
          (<0,0,A>, 3) 
          (<1,0,A>, 3) 
          (<2,0,A>, 0) 
          (<5,0,A>, 3) 
    + Applied Processor:
        PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
    + Details:
        We apply a polynomial interpretation of shape linear:
          p(f0) = 3        
          p(f4) = 3 + -1*x1
          p(f5) = 3 + -1*x1
        
        The following rules are strictly oriented:
        [2 >= A] ==>          
           f5(A)   = 3 + -1*A 
                   > 2 + -1*A 
                   = f4(1 + A)
        
        
        The following rules are weakly oriented:
        [0 >= 1 + B] ==>         
               f4(A)   = 3 + -1*A
                      >= 3 + -1*A
                       = f5(A)   
        
                True ==>         
               f4(A)   = 3 + -1*A
                      >= 3 + -1*A
                       = f5(A)   
        
                True ==>         
               f0(A)   = 3       
                      >= 3       
                       = f4(0)   
        
        
* Step 6: KnowledgePropagation WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f4(A) -> f5(A)     [0 >= 1 + B] (?,1)
          1. f4(A) -> f5(A)     True         (?,1)
          2. f0(A) -> f4(0)     True         (1,1)
          5. f5(A) -> f4(1 + A) [2 >= A]     (3,1)
        Signature:
          {(f0,1);(f11,1);(f14,1);(f4,1);(f5,1)}
        Flow Graph:
          [0->{5},1->{5},2->{0,1},5->{0,1}]
        Sizebounds:
          (<0,0,A>, 3) 
          (<1,0,A>, 3) 
          (<2,0,A>, 0) 
          (<5,0,A>, 3) 
    + Applied Processor:
        KnowledgePropagation
    + Details:
        We propagate bounds from predecessors.
* Step 7: LocalSizeboundsProc WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f4(A) -> f5(A)     [0 >= 1 + B] (4,1)
          1. f4(A) -> f5(A)     True         (4,1)
          2. f0(A) -> f4(0)     True         (1,1)
          5. f5(A) -> f4(1 + A) [2 >= A]     (3,1)
        Signature:
          {(f0,1);(f11,1);(f14,1);(f4,1);(f5,1)}
        Flow Graph:
          [0->{5},1->{5},2->{0,1},5->{0,1}]
        Sizebounds:
          (<0,0,A>, 3) 
          (<1,0,A>, 3) 
          (<2,0,A>, 0) 
          (<5,0,A>, 3) 
    + Applied Processor:
        LocalSizeboundsProc
    + Details:
        The problem is already solved.

WORST_CASE(?,O(1))