WORST_CASE(?,O(1))
* Step 1: RestrictVarsProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A,B,C) -> f5(A,0,C)         [A >= 128] (1,1)
          1. f0(A,B,C) -> f7(A,0,D)         [127 >= A] (1,1)
          2. f7(A,B,C) -> f7(A,1 + B,1 + C) [35 >= B]  (?,1)
          3. f7(A,B,C) -> f5(A,B,C)         [B >= 36]  (?,1)
        Signature:
          {(f0,3);(f5,3);(f7,3)}
        Flow Graph:
          [0->{},1->{2,3},2->{2,3},3->{}]
        
    + Applied Processor:
        RestrictVarsProcessor
    + Details:
        We removed the arguments [C] .
* Step 2: LocalSizeboundsProc WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A,B) -> f5(A,0)     [A >= 128] (1,1)
          1. f0(A,B) -> f7(A,0)     [127 >= A] (1,1)
          2. f7(A,B) -> f7(A,1 + B) [35 >= B]  (?,1)
          3. f7(A,B) -> f5(A,B)     [B >= 36]  (?,1)
        Signature:
          {(f0,2);(f5,2);(f7,2)}
        Flow Graph:
          [0->{},1->{2,3},2->{2,3},3->{}]
        
    + Applied Processor:
        LocalSizeboundsProc
    + Details:
        LocalSizebounds generated; rvgraph
          (<0,0,A>, A, .= 0) (<0,0,B>,     0, .= 0) 
          (<1,0,A>, A, .= 0) (<1,0,B>,     0, .= 0) 
          (<2,0,A>, A, .= 0) (<2,0,B>, 1 + B, .+ 1) 
          (<3,0,A>, A, .= 0) (<3,0,B>,     B, .= 0) 
* Step 3: SizeboundsProc WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A,B) -> f5(A,0)     [A >= 128] (1,1)
          1. f0(A,B) -> f7(A,0)     [127 >= A] (1,1)
          2. f7(A,B) -> f7(A,1 + B) [35 >= B]  (?,1)
          3. f7(A,B) -> f5(A,B)     [B >= 36]  (?,1)
        Signature:
          {(f0,2);(f5,2);(f7,2)}
        Flow Graph:
          [0->{},1->{2,3},2->{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>,  0) 
          (<1,0,A>, A) (<1,0,B>,  0) 
          (<2,0,A>, A) (<2,0,B>, 36) 
          (<3,0,A>, A) (<3,0,B>, 36) 
* Step 4: UnsatPaths WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A,B) -> f5(A,0)     [A >= 128] (1,1)
          1. f0(A,B) -> f7(A,0)     [127 >= A] (1,1)
          2. f7(A,B) -> f7(A,1 + B) [35 >= B]  (?,1)
          3. f7(A,B) -> f5(A,B)     [B >= 36]  (?,1)
        Signature:
          {(f0,2);(f5,2);(f7,2)}
        Flow Graph:
          [0->{},1->{2,3},2->{2,3},3->{}]
        Sizebounds:
          (<0,0,A>, A) (<0,0,B>,  0) 
          (<1,0,A>, A) (<1,0,B>,  0) 
          (<2,0,A>, A) (<2,0,B>, 36) 
          (<3,0,A>, A) (<3,0,B>, 36) 
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(1,3)]
* Step 5: LeafRules WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A,B) -> f5(A,0)     [A >= 128] (1,1)
          1. f0(A,B) -> f7(A,0)     [127 >= A] (1,1)
          2. f7(A,B) -> f7(A,1 + B) [35 >= B]  (?,1)
          3. f7(A,B) -> f5(A,B)     [B >= 36]  (?,1)
        Signature:
          {(f0,2);(f5,2);(f7,2)}
        Flow Graph:
          [0->{},1->{2},2->{2,3},3->{}]
        Sizebounds:
          (<0,0,A>, A) (<0,0,B>,  0) 
          (<1,0,A>, A) (<1,0,B>,  0) 
          (<2,0,A>, A) (<2,0,B>, 36) 
          (<3,0,A>, A) (<3,0,B>, 36) 
    + Applied Processor:
        LeafRules
    + Details:
        The following transitions are estimated by its predecessors and are removed [3]
* Step 6: PolyRank WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A,B) -> f5(A,0)     [A >= 128] (1,1)
          1. f0(A,B) -> f7(A,0)     [127 >= A] (1,1)
          2. f7(A,B) -> f7(A,1 + B) [35 >= B]  (?,1)
        Signature:
          {(f0,2);(f5,2);(f7,2)}
        Flow Graph:
          [0->{},1->{2},2->{2}]
        Sizebounds:
          (<0,0,A>, A) (<0,0,B>,  0) 
          (<1,0,A>, A) (<1,0,B>,  0) 
          (<2,0,A>, A) (<2,0,B>, 36) 
    + Applied Processor:
        PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
    + Details:
        We apply a polynomial interpretation of shape linear:
          p(f0) = 36        
          p(f5) = 36        
          p(f7) = 36 + -1*x2
        
        The following rules are strictly oriented:
        [35 >= B] ==>            
          f7(A,B)   = 36 + -1*B  
                    > 35 + -1*B  
                    = f7(A,1 + B)
        
        
        The following rules are weakly oriented:
        [A >= 128] ==>        
           f0(A,B)   = 36     
                    >= 36     
                     = f5(A,0)
        
        [127 >= A] ==>        
           f0(A,B)   = 36     
                    >= 36     
                     = f7(A,0)
        
        
* Step 7: KnowledgePropagation WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A,B) -> f5(A,0)     [A >= 128] (1,1) 
          1. f0(A,B) -> f7(A,0)     [127 >= A] (1,1) 
          2. f7(A,B) -> f7(A,1 + B) [35 >= B]  (36,1)
        Signature:
          {(f0,2);(f5,2);(f7,2)}
        Flow Graph:
          [0->{},1->{2},2->{2}]
        Sizebounds:
          (<0,0,A>, A) (<0,0,B>,  0) 
          (<1,0,A>, A) (<1,0,B>,  0) 
          (<2,0,A>, A) (<2,0,B>, 36) 
    + Applied Processor:
        KnowledgePropagation
    + Details:
        The problem is already solved.

WORST_CASE(?,O(1))