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

WORST_CASE(?,O(n^1))