WORST_CASE(?,O(1))
* Step 1: RestrictVarsProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A,B) -> f5(2,4)         True      (1,1)
          1. f5(A,B) -> f5(2 + A,4 + A) [19 >= A] (?,1)
          2. f5(A,B) -> f8(A,B)         [A >= 20] (?,1)
        Signature:
          {(f0,2);(f5,2);(f8,2)}
        Flow Graph:
          [0->{1,2},1->{1,2},2->{}]
        
    + Applied Processor:
        RestrictVarsProcessor
    + Details:
        We removed the arguments [B] .
* Step 2: LocalSizeboundsProc WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A) -> f5(2)     True      (1,1)
          1. f5(A) -> f5(2 + A) [19 >= A] (?,1)
          2. f5(A) -> f8(A)     [A >= 20] (?,1)
        Signature:
          {(f0,1);(f5,1);(f8,1)}
        Flow Graph:
          [0->{1,2},1->{1,2},2->{}]
        
    + Applied Processor:
        LocalSizeboundsProc
    + Details:
        LocalSizebounds generated; rvgraph
          (<0,0,A>,     2, .= 2) 
          (<1,0,A>, 2 + A, .+ 2) 
          (<2,0,A>,     A, .= 0) 
* Step 3: SizeboundsProc WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A) -> f5(2)     True      (1,1)
          1. f5(A) -> f5(2 + A) [19 >= A] (?,1)
          2. f5(A) -> f8(A)     [A >= 20] (?,1)
        Signature:
          {(f0,1);(f5,1);(f8,1)}
        Flow Graph:
          [0->{1,2},1->{1,2},2->{}]
        Sizebounds:
          (<0,0,A>, ?) 
          (<1,0,A>, ?) 
          (<2,0,A>, ?) 
    + Applied Processor:
        SizeboundsProc
    + Details:
        Sizebounds computed:
          (<0,0,A>,  2) 
          (<1,0,A>, 21) 
          (<2,0,A>, 21) 
* Step 4: UnsatPaths WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A) -> f5(2)     True      (1,1)
          1. f5(A) -> f5(2 + A) [19 >= A] (?,1)
          2. f5(A) -> f8(A)     [A >= 20] (?,1)
        Signature:
          {(f0,1);(f5,1);(f8,1)}
        Flow Graph:
          [0->{1,2},1->{1,2},2->{}]
        Sizebounds:
          (<0,0,A>,  2) 
          (<1,0,A>, 21) 
          (<2,0,A>, 21) 
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(0,2)]
* Step 5: LeafRules WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A) -> f5(2)     True      (1,1)
          1. f5(A) -> f5(2 + A) [19 >= A] (?,1)
          2. f5(A) -> f8(A)     [A >= 20] (?,1)
        Signature:
          {(f0,1);(f5,1);(f8,1)}
        Flow Graph:
          [0->{1},1->{1,2},2->{}]
        Sizebounds:
          (<0,0,A>,  2) 
          (<1,0,A>, 21) 
          (<2,0,A>, 21) 
    + Applied Processor:
        LeafRules
    + Details:
        The following transitions are estimated by its predecessors and are removed [2]
* Step 6: PolyRank WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A) -> f5(2)     True      (1,1)
          1. f5(A) -> f5(2 + A) [19 >= A] (?,1)
        Signature:
          {(f0,1);(f5,1);(f8,1)}
        Flow Graph:
          [0->{1},1->{1}]
        Sizebounds:
          (<0,0,A>,  2) 
          (<1,0,A>, 21) 
    + Applied Processor:
        PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
    + Details:
        We apply a polynomial interpretation of shape linear:
          p(f0) = 18        
          p(f5) = 20 + -1*x1
        
        The following rules are strictly oriented:
        [19 >= A] ==>          
            f5(A)   = 20 + -1*A
                    > 18 + -1*A
                    = f5(2 + A)
        
        
        The following rules are weakly oriented:
           True ==>      
          f0(A)   = 18   
                 >= 18   
                  = f5(2)
        
        
* Step 7: KnowledgePropagation WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A) -> f5(2)     True      (1,1) 
          1. f5(A) -> f5(2 + A) [19 >= A] (18,1)
        Signature:
          {(f0,1);(f5,1);(f8,1)}
        Flow Graph:
          [0->{1},1->{1}]
        Sizebounds:
          (<0,0,A>,  2) 
          (<1,0,A>, 21) 
    + Applied Processor:
        KnowledgePropagation
    + Details:
        The problem is already solved.

WORST_CASE(?,O(1))