WORST_CASE(?,O(n^1))
* Step 1: RestrictVarsProcessor WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. f2(A,B,C) -> f1(A,B,C)     True                   (1,1)
          1. f1(A,B,C) -> f1(1 + A,B,C) [B >= 1 + A]           (?,1)
          2. f1(A,B,C) -> f1(1 + A,A,C) [B >= D && A = B]      (?,1)
          3. f1(A,B,C) -> f300(A,B,D)   [A >= B && A >= 1 + B] (?,1)
          4. f1(A,B,C) -> f300(A,B,D)   [A >= B && B >= 1 + A] (?,1)
        Signature:
          {(f1,3);(f2,3);(f300,3)}
        Flow Graph:
          [0->{1,2,3,4},1->{1,2,3,4},2->{1,2,3,4},3->{},4->{}]
        
    + Applied Processor:
        RestrictVarsProcessor
    + Details:
        We removed the arguments [C] .
* Step 2: UnsatRules WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. f2(A,B) -> f1(A,B)     True                   (1,1)
          1. f1(A,B) -> f1(1 + A,B) [B >= 1 + A]           (?,1)
          2. f1(A,B) -> f1(1 + A,A) [B >= D && A = B]      (?,1)
          3. f1(A,B) -> f300(A,B)   [A >= B && A >= 1 + B] (?,1)
          4. f1(A,B) -> f300(A,B)   [A >= B && B >= 1 + A] (?,1)
        Signature:
          {(f1,2);(f2,2);(f300,2)}
        Flow Graph:
          [0->{1,2,3,4},1->{1,2,3,4},2->{1,2,3,4},3->{},4->{}]
        
    + Applied Processor:
        UnsatRules
    + Details:
        The following transitions have unsatisfiable constraints and are removed:  [4]
* Step 3: LocalSizeboundsProc WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. f2(A,B) -> f1(A,B)     True                   (1,1)
          1. f1(A,B) -> f1(1 + A,B) [B >= 1 + A]           (?,1)
          2. f1(A,B) -> f1(1 + A,A) [B >= D && A = B]      (?,1)
          3. f1(A,B) -> f300(A,B)   [A >= B && A >= 1 + B] (?,1)
        Signature:
          {(f1,2);(f2,2);(f300,2)}
        Flow Graph:
          [0->{1,2,3},1->{1,2,3},2->{1,2,3},3->{}]
        
    + Applied Processor:
        LocalSizeboundsProc
    + Details:
        LocalSizebounds generated; rvgraph
          (<0,0,A>,     A, .= 0) (<0,0,B>, B, .= 0) 
          (<1,0,A>, 1 + A, .+ 1) (<1,0,B>, B, .= 0) 
          (<2,0,A>, 1 + A, .+ 1) (<2,0,B>, A, .= 0) 
          (<3,0,A>,     A, .= 0) (<3,0,B>, B, .= 0) 
* Step 4: SizeboundsProc WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. f2(A,B) -> f1(A,B)     True                   (1,1)
          1. f1(A,B) -> f1(1 + A,B) [B >= 1 + A]           (?,1)
          2. f1(A,B) -> f1(1 + A,A) [B >= D && A = B]      (?,1)
          3. f1(A,B) -> f300(A,B)   [A >= B && A >= 1 + B] (?,1)
        Signature:
          {(f1,2);(f2,2);(f300,2)}
        Flow Graph:
          [0->{1,2,3},1->{1,2,3},2->{1,2,3},3->{}]
        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>, A) (<0,0,B>, B) 
          (<1,0,A>, ?) (<1,0,B>, ?) 
          (<2,0,A>, ?) (<2,0,B>, ?) 
          (<3,0,A>, ?) (<3,0,B>, ?) 
* Step 5: UnsatPaths WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. f2(A,B) -> f1(A,B)     True                   (1,1)
          1. f1(A,B) -> f1(1 + A,B) [B >= 1 + A]           (?,1)
          2. f1(A,B) -> f1(1 + A,A) [B >= D && A = B]      (?,1)
          3. f1(A,B) -> f300(A,B)   [A >= B && A >= 1 + B] (?,1)
        Signature:
          {(f1,2);(f2,2);(f300,2)}
        Flow Graph:
          [0->{1,2,3},1->{1,2,3},2->{1,2,3},3->{}]
        Sizebounds:
          (<0,0,A>, A) (<0,0,B>, B) 
          (<1,0,A>, ?) (<1,0,B>, ?) 
          (<2,0,A>, ?) (<2,0,B>, ?) 
          (<3,0,A>, ?) (<3,0,B>, ?) 
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(1,3),(2,1),(2,2)]
* Step 6: LeafRules WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. f2(A,B) -> f1(A,B)     True                   (1,1)
          1. f1(A,B) -> f1(1 + A,B) [B >= 1 + A]           (?,1)
          2. f1(A,B) -> f1(1 + A,A) [B >= D && A = B]      (?,1)
          3. f1(A,B) -> f300(A,B)   [A >= B && A >= 1 + B] (?,1)
        Signature:
          {(f1,2);(f2,2);(f300,2)}
        Flow Graph:
          [0->{1,2,3},1->{1,2},2->{3},3->{}]
        Sizebounds:
          (<0,0,A>, A) (<0,0,B>, B) 
          (<1,0,A>, ?) (<1,0,B>, ?) 
          (<2,0,A>, ?) (<2,0,B>, ?) 
          (<3,0,A>, ?) (<3,0,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. f2(A,B) -> f1(A,B)     True         (1,1)
          1. f1(A,B) -> f1(1 + A,B) [B >= 1 + A] (?,1)
        Signature:
          {(f1,2);(f2,2);(f300,2)}
        Flow Graph:
          [0->{1},1->{1}]
        Sizebounds:
          (<0,0,A>, A) (<0,0,B>, B) 
          (<1,0,A>, ?) (<1,0,B>, ?) 
    + Applied Processor:
        PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
    + Details:
        We apply a polynomial interpretation of shape linear:
          p(f1) = -1*x1 + x2
          p(f2) = -1*x1 + x2
        
        The following rules are strictly oriented:
        [B >= 1 + A] ==>              
             f1(A,B)   = -1*A + B     
                       > -1 + -1*A + B
                       = f1(1 + A,B)  
        
        
        The following rules are weakly oriented:
             True ==>         
          f2(A,B)   = -1*A + B
                   >= -1*A + B
                    = f1(A,B) 
        
        
* Step 8: KnowledgePropagation WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. f2(A,B) -> f1(A,B)     True         (1,1)    
          1. f1(A,B) -> f1(1 + A,B) [B >= 1 + A] (A + B,1)
        Signature:
          {(f1,2);(f2,2);(f300,2)}
        Flow Graph:
          [0->{1},1->{1}]
        Sizebounds:
          (<0,0,A>, A) (<0,0,B>, B) 
          (<1,0,A>, ?) (<1,0,B>, ?) 
    + Applied Processor:
        KnowledgePropagation
    + Details:
        The problem is already solved.

WORST_CASE(?,O(n^1))