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

WORST_CASE(?,O(n^1))