WORST_CASE(?,O(n^1))
* Step 1: RestrictVarsProcessor WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. f300(A,B,C) -> f300(-1 + A,-2 + A,C) [A >= 1 && A + B >= 1 && B >= 1] (?,1)
          1. f300(A,B,C) -> f1(A,B,D)             [A >= 1 && 0 >= A + B && B >= 1] (?,1)
          2. f300(A,B,C) -> f1(A,B,D)             [B >= 1 && 0 >= A]               (?,1)
          3. f300(A,B,C) -> f1(A,B,D)             [0 >= B]                         (?,1)
          4. f2(A,B,C)   -> f300(A,B,C)           True                             (1,1)
        Signature:
          {(f1,3);(f2,3);(f300,3)}
        Flow Graph:
          [0->{0,1,2,3},1->{},2->{},3->{},4->{0,1,2,3}]
        
    + Applied Processor:
        RestrictVarsProcessor
    + Details:
        We removed the arguments [C] .
* Step 2: UnsatRules WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. f300(A,B) -> f300(-1 + A,-2 + A) [A >= 1 && A + B >= 1 && B >= 1] (?,1)
          1. f300(A,B) -> f1(A,B)             [A >= 1 && 0 >= A + B && B >= 1] (?,1)
          2. f300(A,B) -> f1(A,B)             [B >= 1 && 0 >= A]               (?,1)
          3. f300(A,B) -> f1(A,B)             [0 >= B]                         (?,1)
          4. f2(A,B)   -> f300(A,B)           True                             (1,1)
        Signature:
          {(f1,2);(f2,2);(f300,2)}
        Flow Graph:
          [0->{0,1,2,3},1->{},2->{},3->{},4->{0,1,2,3}]
        
    + Applied Processor:
        UnsatRules
    + Details:
        The following transitions have unsatisfiable constraints and are removed:  [1]
* Step 3: LocalSizeboundsProc WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. f300(A,B) -> f300(-1 + A,-2 + A) [A >= 1 && A + B >= 1 && B >= 1] (?,1)
          2. f300(A,B) -> f1(A,B)             [B >= 1 && 0 >= A]               (?,1)
          3. f300(A,B) -> f1(A,B)             [0 >= B]                         (?,1)
          4. f2(A,B)   -> f300(A,B)           True                             (1,1)
        Signature:
          {(f1,2);(f2,2);(f300,2)}
        Flow Graph:
          [0->{0,2,3},2->{},3->{},4->{0,2,3}]
        
    + Applied Processor:
        LocalSizeboundsProc
    + Details:
        LocalSizebounds generated; rvgraph
          (<0,0,A>, 1 + A, .+ 1) (<0,0,B>, 2 + A, .+ 2) 
          (<2,0,A>,     A, .= 0) (<2,0,B>,     B, .= 0) 
          (<3,0,A>,     A, .= 0) (<3,0,B>,     B, .= 0) 
          (<4,0,A>,     A, .= 0) (<4,0,B>,     B, .= 0) 
* Step 4: SizeboundsProc WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. f300(A,B) -> f300(-1 + A,-2 + A) [A >= 1 && A + B >= 1 && B >= 1] (?,1)
          2. f300(A,B) -> f1(A,B)             [B >= 1 && 0 >= A]               (?,1)
          3. f300(A,B) -> f1(A,B)             [0 >= B]                         (?,1)
          4. f2(A,B)   -> f300(A,B)           True                             (1,1)
        Signature:
          {(f1,2);(f2,2);(f300,2)}
        Flow Graph:
          [0->{0,2,3},2->{},3->{},4->{0,2,3}]
        Sizebounds:
          (<0,0,A>, ?) (<0,0,B>, ?) 
          (<2,0,A>, ?) (<2,0,B>, ?) 
          (<3,0,A>, ?) (<3,0,B>, ?) 
          (<4,0,A>, ?) (<4,0,B>, ?) 
    + Applied Processor:
        SizeboundsProc
    + Details:
        Sizebounds computed:
          (<0,0,A>, ?) (<0,0,B>, ?) 
          (<2,0,A>, ?) (<2,0,B>, ?) 
          (<3,0,A>, ?) (<3,0,B>, ?) 
          (<4,0,A>, A) (<4,0,B>, B) 
* Step 5: UnsatPaths WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. f300(A,B) -> f300(-1 + A,-2 + A) [A >= 1 && A + B >= 1 && B >= 1] (?,1)
          2. f300(A,B) -> f1(A,B)             [B >= 1 && 0 >= A]               (?,1)
          3. f300(A,B) -> f1(A,B)             [0 >= B]                         (?,1)
          4. f2(A,B)   -> f300(A,B)           True                             (1,1)
        Signature:
          {(f1,2);(f2,2);(f300,2)}
        Flow Graph:
          [0->{0,2,3},2->{},3->{},4->{0,2,3}]
        Sizebounds:
          (<0,0,A>, ?) (<0,0,B>, ?) 
          (<2,0,A>, ?) (<2,0,B>, ?) 
          (<3,0,A>, ?) (<3,0,B>, ?) 
          (<4,0,A>, A) (<4,0,B>, B) 
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(0,2)]
* Step 6: LeafRules WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. f300(A,B) -> f300(-1 + A,-2 + A) [A >= 1 && A + B >= 1 && B >= 1] (?,1)
          2. f300(A,B) -> f1(A,B)             [B >= 1 && 0 >= A]               (?,1)
          3. f300(A,B) -> f1(A,B)             [0 >= B]                         (?,1)
          4. f2(A,B)   -> f300(A,B)           True                             (1,1)
        Signature:
          {(f1,2);(f2,2);(f300,2)}
        Flow Graph:
          [0->{0,3},2->{},3->{},4->{0,2,3}]
        Sizebounds:
          (<0,0,A>, ?) (<0,0,B>, ?) 
          (<2,0,A>, ?) (<2,0,B>, ?) 
          (<3,0,A>, ?) (<3,0,B>, ?) 
          (<4,0,A>, A) (<4,0,B>, B) 
    + Applied Processor:
        LeafRules
    + Details:
        The following transitions are estimated by its predecessors and are removed [2,3]
* Step 7: PolyRank WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. f300(A,B) -> f300(-1 + A,-2 + A) [A >= 1 && A + B >= 1 && B >= 1] (?,1)
          4. f2(A,B)   -> f300(A,B)           True                             (1,1)
        Signature:
          {(f1,2);(f2,2);(f300,2)}
        Flow Graph:
          [0->{0},4->{0}]
        Sizebounds:
          (<0,0,A>, ?) (<0,0,B>, ?) 
          (<4,0,A>, A) (<4,0,B>, B) 
    + Applied Processor:
        PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
    + Details:
        We apply a polynomial interpretation of shape linear:
            p(f2) = x1
          p(f300) = x1
        
        The following rules are strictly oriented:
        [A >= 1 && A + B >= 1 && B >= 1] ==>                    
                               f300(A,B)   = A                  
                                           > -1 + A             
                                           = f300(-1 + A,-2 + A)
        
        
        The following rules are weakly oriented:
             True ==>          
          f2(A,B)   = A        
                   >= A        
                    = f300(A,B)
        
        
* Step 8: KnowledgePropagation WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. f300(A,B) -> f300(-1 + A,-2 + A) [A >= 1 && A + B >= 1 && B >= 1] (A,1)
          4. f2(A,B)   -> f300(A,B)           True                             (1,1)
        Signature:
          {(f1,2);(f2,2);(f300,2)}
        Flow Graph:
          [0->{0},4->{0}]
        Sizebounds:
          (<0,0,A>, ?) (<0,0,B>, ?) 
          (<4,0,A>, A) (<4,0,B>, B) 
    + Applied Processor:
        KnowledgePropagation
    + Details:
        The problem is already solved.

WORST_CASE(?,O(n^1))