WORST_CASE(?,O(n^1))
* Step 1: LocalSizeboundsProc WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. sumto(A,B) -> end(A,B)       [A >= 1 + B] (?,1)
          1. sumto(A,B) -> sumto(1 + A,B) [B >= A]     (?,1)
          2. start(A,B) -> sumto(A,B)     True         (1,1)
        Signature:
          {(end,2);(start,2);(sumto,2)}
        Flow Graph:
          [0->{},1->{0,1},2->{0,1}]
        
    + 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>,     A, .= 0) (<2,0,B>, B, .= 0) 
* Step 2: SizeboundsProc WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. sumto(A,B) -> end(A,B)       [A >= 1 + B] (?,1)
          1. sumto(A,B) -> sumto(1 + A,B) [B >= A]     (?,1)
          2. start(A,B) -> sumto(A,B)     True         (1,1)
        Signature:
          {(end,2);(start,2);(sumto,2)}
        Flow Graph:
          [0->{},1->{0,1},2->{0,1}]
        Sizebounds:
          (<0,0,A>, ?) (<0,0,B>, ?) 
          (<1,0,A>, ?) (<1,0,B>, ?) 
          (<2,0,A>, ?) (<2,0,B>, ?) 
    + Applied Processor:
        SizeboundsProc
    + Details:
        Sizebounds computed:
          (<0,0,A>, 1 + A + B) (<0,0,B>, B) 
          (<1,0,A>,     1 + B) (<1,0,B>, B) 
          (<2,0,A>,         A) (<2,0,B>, B) 
* Step 3: LeafRules WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. sumto(A,B) -> end(A,B)       [A >= 1 + B] (?,1)
          1. sumto(A,B) -> sumto(1 + A,B) [B >= A]     (?,1)
          2. start(A,B) -> sumto(A,B)     True         (1,1)
        Signature:
          {(end,2);(start,2);(sumto,2)}
        Flow Graph:
          [0->{},1->{0,1},2->{0,1}]
        Sizebounds:
          (<0,0,A>, 1 + A + B) (<0,0,B>, B) 
          (<1,0,A>,     1 + B) (<1,0,B>, B) 
          (<2,0,A>,         A) (<2,0,B>, B) 
    + Applied Processor:
        LeafRules
    + Details:
        The following transitions are estimated by its predecessors and are removed [0]
* Step 4: PolyRank WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          1. sumto(A,B) -> sumto(1 + A,B) [B >= A] (?,1)
          2. start(A,B) -> sumto(A,B)     True     (1,1)
        Signature:
          {(end,2);(start,2);(sumto,2)}
        Flow Graph:
          [1->{1},2->{1}]
        Sizebounds:
          (<1,0,A>, 1 + B) (<1,0,B>, B) 
          (<2,0,A>,     A) (<2,0,B>, B) 
    + Applied Processor:
        PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
    + Details:
        We apply a polynomial interpretation of shape linear:
          p(start) = 1 + -1*x1 + x2
          p(sumto) = 1 + -1*x1 + x2
        
        The following rules are strictly oriented:
            [B >= A] ==>               
          sumto(A,B)   = 1 + -1*A + B  
                       > -1*A + B      
                       = sumto(1 + A,B)
        
        
        The following rules are weakly oriented:
                True ==>             
          start(A,B)   = 1 + -1*A + B
                      >= 1 + -1*A + B
                       = sumto(A,B)  
        
        
* Step 5: KnowledgePropagation WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          1. sumto(A,B) -> sumto(1 + A,B) [B >= A] (1 + A + B,1)
          2. start(A,B) -> sumto(A,B)     True     (1,1)        
        Signature:
          {(end,2);(start,2);(sumto,2)}
        Flow Graph:
          [1->{1},2->{1}]
        Sizebounds:
          (<1,0,A>, 1 + B) (<1,0,B>, B) 
          (<2,0,A>,     A) (<2,0,B>, B) 
    + Applied Processor:
        KnowledgePropagation
    + Details:
        The problem is already solved.

WORST_CASE(?,O(n^1))