WORST_CASE(?,O(1))
* Step 1: RestrictVarsProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f300(A,B,C,D,E) -> f300(-1 + A,B,C,D,E) [A >= 101 && 9 >= B] (?,1)
          1. f300(A,B,C,D,E) -> f2(A,B,0,0,0)        [100 >= A && 9 >= B] (?,1)
          2. f300(A,B,C,D,E) -> f2(A,B,0,0,0)        [B >= 10]            (?,1)
          3. f1(A,B,C,D,E)   -> f300(1000,B,C,D,E)   True                 (1,1)
        Signature:
          {(f1,5);(f2,5);(f300,5)}
        Flow Graph:
          [0->{0,1,2},1->{},2->{},3->{0,1,2}]
        
    + Applied Processor:
        RestrictVarsProcessor
    + Details:
        We removed the arguments [C,D,E] .
* Step 2: LocalSizeboundsProc WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f300(A,B) -> f300(-1 + A,B) [A >= 101 && 9 >= B] (?,1)
          1. f300(A,B) -> f2(A,B)        [100 >= A && 9 >= B] (?,1)
          2. f300(A,B) -> f2(A,B)        [B >= 10]            (?,1)
          3. f1(A,B)   -> f300(1000,B)   True                 (1,1)
        Signature:
          {(f1,2);(f2,2);(f300,2)}
        Flow Graph:
          [0->{0,1,2},1->{},2->{},3->{0,1,2}]
        
    + Applied Processor:
        LocalSizeboundsProc
    + Details:
        LocalSizebounds generated; rvgraph
          (<0,0,A>, 1 + A,    .+ 1) (<0,0,B>, B, .= 0) 
          (<1,0,A>,     A,    .= 0) (<1,0,B>, B, .= 0) 
          (<2,0,A>,     A,    .= 0) (<2,0,B>, B, .= 0) 
          (<3,0,A>,  1000, .= 1000) (<3,0,B>, B, .= 0) 
* Step 3: SizeboundsProc WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f300(A,B) -> f300(-1 + A,B) [A >= 101 && 9 >= B] (?,1)
          1. f300(A,B) -> f2(A,B)        [100 >= A && 9 >= B] (?,1)
          2. f300(A,B) -> f2(A,B)        [B >= 10]            (?,1)
          3. f1(A,B)   -> f300(1000,B)   True                 (1,1)
        Signature:
          {(f1,2);(f2,2);(f300,2)}
        Flow Graph:
          [0->{0,1,2},1->{},2->{},3->{0,1,2}]
        Sizebounds:
          (<0,0,A>, ?) (<0,0,B>, ?) 
          (<1,0,A>, ?) (<1,0,B>, ?) 
          (<2,0,A>, ?) (<2,0,B>, ?) 
          (<3,0,A>, ?) (<3,0,B>, ?) 
    + Applied Processor:
        SizeboundsProc
    + Details:
        Sizebounds computed:
          (<0,0,A>,    ?) (<0,0,B>, B) 
          (<1,0,A>,    ?) (<1,0,B>, B) 
          (<2,0,A>,    ?) (<2,0,B>, B) 
          (<3,0,A>, 1000) (<3,0,B>, B) 
* Step 4: UnsatPaths WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f300(A,B) -> f300(-1 + A,B) [A >= 101 && 9 >= B] (?,1)
          1. f300(A,B) -> f2(A,B)        [100 >= A && 9 >= B] (?,1)
          2. f300(A,B) -> f2(A,B)        [B >= 10]            (?,1)
          3. f1(A,B)   -> f300(1000,B)   True                 (1,1)
        Signature:
          {(f1,2);(f2,2);(f300,2)}
        Flow Graph:
          [0->{0,1,2},1->{},2->{},3->{0,1,2}]
        Sizebounds:
          (<0,0,A>,    ?) (<0,0,B>, B) 
          (<1,0,A>,    ?) (<1,0,B>, B) 
          (<2,0,A>,    ?) (<2,0,B>, B) 
          (<3,0,A>, 1000) (<3,0,B>, B) 
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(0,2),(3,1)]
* Step 5: LeafRules WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f300(A,B) -> f300(-1 + A,B) [A >= 101 && 9 >= B] (?,1)
          1. f300(A,B) -> f2(A,B)        [100 >= A && 9 >= B] (?,1)
          2. f300(A,B) -> f2(A,B)        [B >= 10]            (?,1)
          3. f1(A,B)   -> f300(1000,B)   True                 (1,1)
        Signature:
          {(f1,2);(f2,2);(f300,2)}
        Flow Graph:
          [0->{0,1},1->{},2->{},3->{0,2}]
        Sizebounds:
          (<0,0,A>,    ?) (<0,0,B>, B) 
          (<1,0,A>,    ?) (<1,0,B>, B) 
          (<2,0,A>,    ?) (<2,0,B>, B) 
          (<3,0,A>, 1000) (<3,0,B>, B) 
    + Applied Processor:
        LeafRules
    + Details:
        The following transitions are estimated by its predecessors and are removed [1,2]
* Step 6: PolyRank WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f300(A,B) -> f300(-1 + A,B) [A >= 101 && 9 >= B] (?,1)
          3. f1(A,B)   -> f300(1000,B)   True                 (1,1)
        Signature:
          {(f1,2);(f2,2);(f300,2)}
        Flow Graph:
          [0->{0},3->{0}]
        Sizebounds:
          (<0,0,A>,    ?) (<0,0,B>, B) 
          (<3,0,A>, 1000) (<3,0,B>, B) 
    + Applied Processor:
        PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
    + Details:
        We apply a polynomial interpretation of shape linear:
            p(f1) = 900      
          p(f300) = -100 + x1
        
        The following rules are strictly oriented:
        [A >= 101 && 9 >= B] ==>               
                   f300(A,B)   = -100 + A      
                               > -101 + A      
                               = f300(-1 + A,B)
        
        
        The following rules are weakly oriented:
             True ==>             
          f1(A,B)   = 900         
                   >= 900         
                    = f300(1000,B)
        
        
* Step 7: KnowledgePropagation WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f300(A,B) -> f300(-1 + A,B) [A >= 101 && 9 >= B] (900,1)
          3. f1(A,B)   -> f300(1000,B)   True                 (1,1)  
        Signature:
          {(f1,2);(f2,2);(f300,2)}
        Flow Graph:
          [0->{0},3->{0}]
        Sizebounds:
          (<0,0,A>,    ?) (<0,0,B>, B) 
          (<3,0,A>, 1000) (<3,0,B>, B) 
    + Applied Processor:
        KnowledgePropagation
    + Details:
        The problem is already solved.

WORST_CASE(?,O(1))