WORST_CASE(?,O(n^1))
* Step 1: LocalSizeboundsProc WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. eval0(A,B,C) -> eval1(A,B,C)        [A >= 1]                             (1,1)
          1. eval1(A,B,C) -> eval1(A,A + B,C)    [A >= 1 + B && C >= 1 + A && A >= 1] (?,1)
          2. eval1(A,B,C) -> eval1(A,B,-1*A + B) [A >= 1 + B && C >= 1 + A && A >= 1] (?,1)
        Signature:
          {(eval0,3);(eval1,3)}
        Flow Graph:
          [0->{1,2},1->{1,2},2->{1,2}]
        
    + Applied Processor:
        LocalSizeboundsProc
    + Details:
        LocalSizebounds generated; rvgraph
          (<0,0,A>, A, .= 0) (<0,0,B>,         B, .= 0) (<0,0,C>,         C, .= 0) 
          (<1,0,A>, A, .= 0) (<1,0,B>, 1 + A + B, .* 1) (<1,0,C>,         C, .= 0) 
          (<2,0,A>, A, .= 0) (<2,0,B>,         B, .= 0) (<2,0,C>, 1 + A + B, .* 1) 
* Step 2: SizeboundsProc WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. eval0(A,B,C) -> eval1(A,B,C)        [A >= 1]                             (1,1)
          1. eval1(A,B,C) -> eval1(A,A + B,C)    [A >= 1 + B && C >= 1 + A && A >= 1] (?,1)
          2. eval1(A,B,C) -> eval1(A,B,-1*A + B) [A >= 1 + B && C >= 1 + A && A >= 1] (?,1)
        Signature:
          {(eval0,3);(eval1,3)}
        Flow Graph:
          [0->{1,2},1->{1,2},2->{1,2}]
        Sizebounds:
          (<0,0,A>, ?) (<0,0,B>, ?) (<0,0,C>, ?) 
          (<1,0,A>, ?) (<1,0,B>, ?) (<1,0,C>, ?) 
          (<2,0,A>, ?) (<2,0,B>, ?) (<2,0,C>, ?) 
    + Applied Processor:
        SizeboundsProc
    + Details:
        Sizebounds computed:
          (<0,0,A>, A) (<0,0,B>, B) (<0,0,C>,               C) 
          (<1,0,A>, A) (<1,0,B>, A) (<1,0,C>, 1 + 2*A + B + C) 
          (<2,0,A>, A) (<2,0,B>, A) (<2,0,C>,     1 + 2*A + B) 
* Step 3: UnsatPaths WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. eval0(A,B,C) -> eval1(A,B,C)        [A >= 1]                             (1,1)
          1. eval1(A,B,C) -> eval1(A,A + B,C)    [A >= 1 + B && C >= 1 + A && A >= 1] (?,1)
          2. eval1(A,B,C) -> eval1(A,B,-1*A + B) [A >= 1 + B && C >= 1 + A && A >= 1] (?,1)
        Signature:
          {(eval0,3);(eval1,3)}
        Flow Graph:
          [0->{1,2},1->{1,2},2->{1,2}]
        Sizebounds:
          (<0,0,A>, A) (<0,0,B>, B) (<0,0,C>,               C) 
          (<1,0,A>, A) (<1,0,B>, A) (<1,0,C>, 1 + 2*A + B + C) 
          (<2,0,A>, A) (<2,0,B>, A) (<2,0,C>,     1 + 2*A + B) 
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(2,1),(2,2)]
* Step 4: LeafRules WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. eval0(A,B,C) -> eval1(A,B,C)        [A >= 1]                             (1,1)
          1. eval1(A,B,C) -> eval1(A,A + B,C)    [A >= 1 + B && C >= 1 + A && A >= 1] (?,1)
          2. eval1(A,B,C) -> eval1(A,B,-1*A + B) [A >= 1 + B && C >= 1 + A && A >= 1] (?,1)
        Signature:
          {(eval0,3);(eval1,3)}
        Flow Graph:
          [0->{1,2},1->{1,2},2->{}]
        Sizebounds:
          (<0,0,A>, A) (<0,0,B>, B) (<0,0,C>,               C) 
          (<1,0,A>, A) (<1,0,B>, A) (<1,0,C>, 1 + 2*A + B + C) 
          (<2,0,A>, A) (<2,0,B>, A) (<2,0,C>,     1 + 2*A + B) 
    + Applied Processor:
        LeafRules
    + Details:
        The following transitions are estimated by its predecessors and are removed [2]
* Step 5: PolyRank WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. eval0(A,B,C) -> eval1(A,B,C)     [A >= 1]                             (1,1)
          1. eval1(A,B,C) -> eval1(A,A + B,C) [A >= 1 + B && C >= 1 + A && A >= 1] (?,1)
        Signature:
          {(eval0,3);(eval1,3)}
        Flow Graph:
          [0->{1},1->{1}]
        Sizebounds:
          (<0,0,A>, A) (<0,0,B>, B) (<0,0,C>,               C) 
          (<1,0,A>, A) (<1,0,B>, A) (<1,0,C>, 1 + 2*A + B + C) 
    + Applied Processor:
        PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
    + Details:
        We apply a polynomial interpretation of shape linear:
          p(eval0) = x1 + -1*x2
          p(eval1) = x1 + -1*x2
        
        The following rules are strictly oriented:
        [A >= 1 + B && C >= 1 + A && A >= 1] ==>                 
                                eval1(A,B,C)   = A + -1*B        
                                               > -1*B            
                                               = eval1(A,A + B,C)
        
        
        The following rules are weakly oriented:
              [A >= 1] ==>             
          eval0(A,B,C)   = A + -1*B    
                        >= A + -1*B    
                         = eval1(A,B,C)
        
        
* Step 6: KnowledgePropagation WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. eval0(A,B,C) -> eval1(A,B,C)     [A >= 1]                             (1,1)    
          1. eval1(A,B,C) -> eval1(A,A + B,C) [A >= 1 + B && C >= 1 + A && A >= 1] (A + B,1)
        Signature:
          {(eval0,3);(eval1,3)}
        Flow Graph:
          [0->{1},1->{1}]
        Sizebounds:
          (<0,0,A>, A) (<0,0,B>, B) (<0,0,C>,               C) 
          (<1,0,A>, A) (<1,0,B>, A) (<1,0,C>, 1 + 2*A + B + C) 
    + Applied Processor:
        KnowledgePropagation
    + Details:
        The problem is already solved.

WORST_CASE(?,O(n^1))