WORST_CASE(?,O(n^1))
* Step 1: RestrictVarsProcessor WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. f0(A,B,C,D) -> f1(A,B,2,D)           [A >= 0 && 3 >= A && 3 >= B && B >= 0]       (1,1)
          1. f1(A,B,C,D) -> f1(A,1 + B,C,1 + B)   [A + C >= 1 + 2*B && 0 >= 2]                 (?,1)
          2. f1(A,B,C,D) -> f1(A,1 + B,C,1 + B)   [A + C >= 1 + 2*B]                           (?,1)
          3. f1(A,B,C,D) -> f1(A,-1 + B,C,-1 + B) [2*B >= 2 + A + C]                           (?,1)
          4. f1(A,B,C,D) -> f1(A,-1 + B,C,-1 + B) [2*B >= 2 + A + C && 0 >= 2]                 (?,1)
          5. f1(A,B,C,D) -> f1(A,B,C,B)           [0 >= 1 && 2*B >= A + C && 1 + A + C >= 2*B] (?,1)
          6. f1(A,B,C,D) -> f1(A,B,C,B)           [0 >= 1 && 2*B >= A + C && 1 + A + C >= 2*B] (?,1)
        Signature:
          {(f0,4);(f1,4)}
        Flow Graph:
          [0->{1,2,3,4,5,6},1->{1,2,3,4,5,6},2->{1,2,3,4,5,6},3->{1,2,3,4,5,6},4->{1,2,3,4,5,6},5->{1,2,3,4,5,6}
          ,6->{1,2,3,4,5,6}]
        
    + Applied Processor:
        RestrictVarsProcessor
    + Details:
        We removed the arguments [D] .
* Step 2: UnsatRules WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. f0(A,B,C) -> f1(A,B,2)      [A >= 0 && 3 >= A && 3 >= B && B >= 0]       (1,1)
          1. f1(A,B,C) -> f1(A,1 + B,C)  [A + C >= 1 + 2*B && 0 >= 2]                 (?,1)
          2. f1(A,B,C) -> f1(A,1 + B,C)  [A + C >= 1 + 2*B]                           (?,1)
          3. f1(A,B,C) -> f1(A,-1 + B,C) [2*B >= 2 + A + C]                           (?,1)
          4. f1(A,B,C) -> f1(A,-1 + B,C) [2*B >= 2 + A + C && 0 >= 2]                 (?,1)
          5. f1(A,B,C) -> f1(A,B,C)      [0 >= 1 && 2*B >= A + C && 1 + A + C >= 2*B] (?,1)
          6. f1(A,B,C) -> f1(A,B,C)      [0 >= 1 && 2*B >= A + C && 1 + A + C >= 2*B] (?,1)
        Signature:
          {(f0,3);(f1,3)}
        Flow Graph:
          [0->{1,2,3,4,5,6},1->{1,2,3,4,5,6},2->{1,2,3,4,5,6},3->{1,2,3,4,5,6},4->{1,2,3,4,5,6},5->{1,2,3,4,5,6}
          ,6->{1,2,3,4,5,6}]
        
    + Applied Processor:
        UnsatRules
    + Details:
        The following transitions have unsatisfiable constraints and are removed:  [1,4,5,6]
* Step 3: LocalSizeboundsProc WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. f0(A,B,C) -> f1(A,B,2)      [A >= 0 && 3 >= A && 3 >= B && B >= 0] (1,1)
          2. f1(A,B,C) -> f1(A,1 + B,C)  [A + C >= 1 + 2*B]                     (?,1)
          3. f1(A,B,C) -> f1(A,-1 + B,C) [2*B >= 2 + A + C]                     (?,1)
        Signature:
          {(f0,3);(f1,3)}
        Flow Graph:
          [0->{2,3},2->{2,3},3->{2,3}]
        
    + Applied Processor:
        LocalSizeboundsProc
    + Details:
        LocalSizebounds generated; rvgraph
          (<0,0,A>, A, .= 0) (<0,0,B>,     B, .= 0) (<0,0,C>, 2, .= 2) 
          (<2,0,A>, A, .= 0) (<2,0,B>, 1 + B, .+ 1) (<2,0,C>, C, .= 0) 
          (<3,0,A>, A, .= 0) (<3,0,B>, 1 + B, .+ 1) (<3,0,C>, C, .= 0) 
* Step 4: SizeboundsProc WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. f0(A,B,C) -> f1(A,B,2)      [A >= 0 && 3 >= A && 3 >= B && B >= 0] (1,1)
          2. f1(A,B,C) -> f1(A,1 + B,C)  [A + C >= 1 + 2*B]                     (?,1)
          3. f1(A,B,C) -> f1(A,-1 + B,C) [2*B >= 2 + A + C]                     (?,1)
        Signature:
          {(f0,3);(f1,3)}
        Flow Graph:
          [0->{2,3},2->{2,3},3->{2,3}]
        Sizebounds:
          (<0,0,A>, ?) (<0,0,B>, ?) (<0,0,C>, ?) 
          (<2,0,A>, ?) (<2,0,B>, ?) (<2,0,C>, ?) 
          (<3,0,A>, ?) (<3,0,B>, ?) (<3,0,C>, ?) 
    + Applied Processor:
        SizeboundsProc
    + Details:
        Sizebounds computed:
          (<0,0,A>, A) (<0,0,B>,     B) (<0,0,C>, 2) 
          (<2,0,A>, A) (<2,0,B>, 2 + A) (<2,0,C>, 2) 
          (<3,0,A>, A) (<3,0,B>,     ?) (<3,0,C>, 2) 
* Step 5: UnsatPaths WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. f0(A,B,C) -> f1(A,B,2)      [A >= 0 && 3 >= A && 3 >= B && B >= 0] (1,1)
          2. f1(A,B,C) -> f1(A,1 + B,C)  [A + C >= 1 + 2*B]                     (?,1)
          3. f1(A,B,C) -> f1(A,-1 + B,C) [2*B >= 2 + A + C]                     (?,1)
        Signature:
          {(f0,3);(f1,3)}
        Flow Graph:
          [0->{2,3},2->{2,3},3->{2,3}]
        Sizebounds:
          (<0,0,A>, A) (<0,0,B>,     B) (<0,0,C>, 2) 
          (<2,0,A>, A) (<2,0,B>, 2 + A) (<2,0,C>, 2) 
          (<3,0,A>, A) (<3,0,B>,     ?) (<3,0,C>, 2) 
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(2,3),(3,2)]
* Step 6: LocationConstraintsProc WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. f0(A,B,C) -> f1(A,B,2)      [A >= 0 && 3 >= A && 3 >= B && B >= 0] (1,1)
          2. f1(A,B,C) -> f1(A,1 + B,C)  [A + C >= 1 + 2*B]                     (?,1)
          3. f1(A,B,C) -> f1(A,-1 + B,C) [2*B >= 2 + A + C]                     (?,1)
        Signature:
          {(f0,3);(f1,3)}
        Flow Graph:
          [0->{2,3},2->{2},3->{3}]
        Sizebounds:
          (<0,0,A>, A) (<0,0,B>,     B) (<0,0,C>, 2) 
          (<2,0,A>, A) (<2,0,B>, 2 + A) (<2,0,C>, 2) 
          (<3,0,A>, A) (<3,0,B>,     ?) (<3,0,C>, 2) 
    + Applied Processor:
        LocationConstraintsProc
    + Details:
        We computed the location constraints  0 :  True 2 :  [B >= 0 && A >= 0] 3 :  [3 >= B && A >= 0] .
* Step 7: PolyRank WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. f0(A,B,C) -> f1(A,B,2)      [A >= 0 && 3 >= A && 3 >= B && B >= 0] (1,1)
          2. f1(A,B,C) -> f1(A,1 + B,C)  [A + C >= 1 + 2*B]                     (?,1)
          3. f1(A,B,C) -> f1(A,-1 + B,C) [2*B >= 2 + A + C]                     (?,1)
        Signature:
          {(f0,3);(f1,3)}
        Flow Graph:
          [0->{2,3},2->{2},3->{3}]
        Sizebounds:
          (<0,0,A>, A) (<0,0,B>,     B) (<0,0,C>, 2) 
          (<2,0,A>, A) (<2,0,B>, 2 + A) (<2,0,C>, 2) 
          (<3,0,A>, A) (<3,0,B>,     ?) (<3,0,C>, 2) 
    + Applied Processor:
        PolyRank {useFarkas = True, withSizebounds = [3], shape = Linear}
    + Details:
        We apply a polynomial interpretation of shape linear:
          p(f1) = -1 + -1*x1 + 2*x2 + -1*x3
        
        The following rules are strictly oriented:
        [2*B >= 2 + A + C] ==>                       
                 f1(A,B,C)   = -1 + -1*A + 2*B + -1*C
                             > -3 + -1*A + 2*B + -1*C
                             = f1(A,-1 + B,C)        
        
        
        The following rules are weakly oriented:
        
        We use the following global sizebounds:
        (<0,0,A>, A) (<0,0,B>,     B) (<0,0,C>, 2) 
        (<2,0,A>, A) (<2,0,B>, 2 + A) (<2,0,C>, 2) 
        (<3,0,A>, A) (<3,0,B>,     ?) (<3,0,C>, 2) 
* Step 8: PolyRank WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. f0(A,B,C) -> f1(A,B,2)      [A >= 0 && 3 >= A && 3 >= B && B >= 0] (1,1)          
          2. f1(A,B,C) -> f1(A,1 + B,C)  [A + C >= 1 + 2*B]                     (?,1)          
          3. f1(A,B,C) -> f1(A,-1 + B,C) [2*B >= 2 + A + C]                     (3 + A + 2*B,1)
        Signature:
          {(f0,3);(f1,3)}
        Flow Graph:
          [0->{2,3},2->{2},3->{3}]
        Sizebounds:
          (<0,0,A>, A) (<0,0,B>,     B) (<0,0,C>, 2) 
          (<2,0,A>, A) (<2,0,B>, 2 + A) (<2,0,C>, 2) 
          (<3,0,A>, A) (<3,0,B>,     ?) (<3,0,C>, 2) 
    + Applied Processor:
        PolyRank {useFarkas = True, withSizebounds = [2], shape = Linear}
    + Details:
        We apply a polynomial interpretation of shape linear:
          p(f1) = x1 + -2*x2 + x3
        
        The following rules are strictly oriented:
        [A + C >= 1 + 2*B] ==>                  
                 f1(A,B,C)   = A + -2*B + C     
                             > -2 + A + -2*B + C
                             = f1(A,1 + B,C)    
        
        
        The following rules are weakly oriented:
        
        We use the following global sizebounds:
        (<0,0,A>, A) (<0,0,B>,     B) (<0,0,C>, 2) 
        (<2,0,A>, A) (<2,0,B>, 2 + A) (<2,0,C>, 2) 
        (<3,0,A>, A) (<3,0,B>,     ?) (<3,0,C>, 2) 
* Step 9: KnowledgePropagation WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. f0(A,B,C) -> f1(A,B,2)      [A >= 0 && 3 >= A && 3 >= B && B >= 0] (1,1)          
          2. f1(A,B,C) -> f1(A,1 + B,C)  [A + C >= 1 + 2*B]                     (2 + A + 2*B,1)
          3. f1(A,B,C) -> f1(A,-1 + B,C) [2*B >= 2 + A + C]                     (3 + A + 2*B,1)
        Signature:
          {(f0,3);(f1,3)}
        Flow Graph:
          [0->{2,3},2->{2},3->{3}]
        Sizebounds:
          (<0,0,A>, A) (<0,0,B>,     B) (<0,0,C>, 2) 
          (<2,0,A>, A) (<2,0,B>, 2 + A) (<2,0,C>, 2) 
          (<3,0,A>, A) (<3,0,B>,     ?) (<3,0,C>, 2) 
    + Applied Processor:
        KnowledgePropagation
    + Details:
        The problem is already solved.

WORST_CASE(?,O(n^1))