WORST_CASE(?,O(1))
* Step 1: RestrictVarsProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A,B,C,D,E) -> f7(F,F,10,0,E)    True         (1,1)
          1. f7(A,B,C,D,E) -> f7(A,B,C,1 + D,F) [C >= 1 + D] (?,1)
          2. f7(A,B,C,D,E) -> f19(A,B,C,D,E)    [D >= C]     (?,1)
        Signature:
          {(f0,5);(f19,5);(f7,5)}
        Flow Graph:
          [0->{1,2},1->{1,2},2->{}]
        
    + Applied Processor:
        RestrictVarsProcessor
    + Details:
        We removed the arguments [A,B,E] .
* Step 2: LocalSizeboundsProc WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(C,D) -> f7(10,0)    True         (1,1)
          1. f7(C,D) -> f7(C,1 + D) [C >= 1 + D] (?,1)
          2. f7(C,D) -> f19(C,D)    [D >= C]     (?,1)
        Signature:
          {(f0,2);(f19,2);(f7,2)}
        Flow Graph:
          [0->{1,2},1->{1,2},2->{}]
        
    + Applied Processor:
        LocalSizeboundsProc
    + Details:
        LocalSizebounds generated; rvgraph
          (<0,0,C>, 10, .= 10) (<0,0,D>,     0, .= 0) 
          (<1,0,C>,  C,  .= 0) (<1,0,D>, 1 + D, .+ 1) 
          (<2,0,C>,  C,  .= 0) (<2,0,D>,     D, .= 0) 
* Step 3: SizeboundsProc WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(C,D) -> f7(10,0)    True         (1,1)
          1. f7(C,D) -> f7(C,1 + D) [C >= 1 + D] (?,1)
          2. f7(C,D) -> f19(C,D)    [D >= C]     (?,1)
        Signature:
          {(f0,2);(f19,2);(f7,2)}
        Flow Graph:
          [0->{1,2},1->{1,2},2->{}]
        Sizebounds:
          (<0,0,C>, ?) (<0,0,D>, ?) 
          (<1,0,C>, ?) (<1,0,D>, ?) 
          (<2,0,C>, ?) (<2,0,D>, ?) 
    + Applied Processor:
        SizeboundsProc
    + Details:
        Sizebounds computed:
          (<0,0,C>, 10) (<0,0,D>,  0) 
          (<1,0,C>, 10) (<1,0,D>, 10) 
          (<2,0,C>, 10) (<2,0,D>, 10) 
* Step 4: UnsatPaths WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(C,D) -> f7(10,0)    True         (1,1)
          1. f7(C,D) -> f7(C,1 + D) [C >= 1 + D] (?,1)
          2. f7(C,D) -> f19(C,D)    [D >= C]     (?,1)
        Signature:
          {(f0,2);(f19,2);(f7,2)}
        Flow Graph:
          [0->{1,2},1->{1,2},2->{}]
        Sizebounds:
          (<0,0,C>, 10) (<0,0,D>,  0) 
          (<1,0,C>, 10) (<1,0,D>, 10) 
          (<2,0,C>, 10) (<2,0,D>, 10) 
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(0,2)]
* Step 5: LeafRules WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(C,D) -> f7(10,0)    True         (1,1)
          1. f7(C,D) -> f7(C,1 + D) [C >= 1 + D] (?,1)
          2. f7(C,D) -> f19(C,D)    [D >= C]     (?,1)
        Signature:
          {(f0,2);(f19,2);(f7,2)}
        Flow Graph:
          [0->{1},1->{1,2},2->{}]
        Sizebounds:
          (<0,0,C>, 10) (<0,0,D>,  0) 
          (<1,0,C>, 10) (<1,0,D>, 10) 
          (<2,0,C>, 10) (<2,0,D>, 10) 
    + Applied Processor:
        LeafRules
    + Details:
        The following transitions are estimated by its predecessors and are removed [2]
* Step 6: PolyRank WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(C,D) -> f7(10,0)    True         (1,1)
          1. f7(C,D) -> f7(C,1 + D) [C >= 1 + D] (?,1)
        Signature:
          {(f0,2);(f19,2);(f7,2)}
        Flow Graph:
          [0->{1},1->{1}]
        Sizebounds:
          (<0,0,C>, 10) (<0,0,D>,  0) 
          (<1,0,C>, 10) (<1,0,D>, 10) 
    + Applied Processor:
        PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
    + Details:
        We apply a polynomial interpretation of shape linear:
          p(f0) = 10        
          p(f7) = x1 + -1*x2
        
        The following rules are strictly oriented:
        [C >= 1 + D] ==>              
             f7(C,D)   = C + -1*D     
                       > -1 + C + -1*D
                       = f7(C,1 + D)  
        
        
        The following rules are weakly oriented:
             True ==>         
          f0(C,D)   = 10      
                   >= 10      
                    = f7(10,0)
        
        
* Step 7: KnowledgePropagation WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(C,D) -> f7(10,0)    True         (1,1) 
          1. f7(C,D) -> f7(C,1 + D) [C >= 1 + D] (10,1)
        Signature:
          {(f0,2);(f19,2);(f7,2)}
        Flow Graph:
          [0->{1},1->{1}]
        Sizebounds:
          (<0,0,C>, 10) (<0,0,D>,  0) 
          (<1,0,C>, 10) (<1,0,D>, 10) 
    + Applied Processor:
        KnowledgePropagation
    + Details:
        The problem is already solved.

WORST_CASE(?,O(1))