YES(?,O(1))
* Step 1: UnsatPaths WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A,B) -> f1(3000,B)     True                        (1,1)
          1. f1(A,B) -> f1(A,1000 + B) [889 + B >= 0 && 1999 >= A] (?,1)
        Signature:
          {(f0,2);(f1,2)}
        Flow Graph:
          [0->{1},1->{1}]
        
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(0,1)]
* Step 2: UnreachableRules WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A,B) -> f1(3000,B)     True                        (1,1)
          1. f1(A,B) -> f1(A,1000 + B) [889 + B >= 0 && 1999 >= A] (?,1)
        Signature:
          {(f0,2);(f1,2)}
        Flow Graph:
          [0->{},1->{1}]
        
    + Applied Processor:
        UnreachableRules
    + Details:
        Following transitions are not reachable from the starting states and are revomed: [1]
* Step 3: AddSinks WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A,B) -> f1(3000,B) True (1,1)
        Signature:
          {(f0,2);(f1,2)}
        Flow Graph:
          [0->{}]
        
    + Applied Processor:
        AddSinks
    + Details:
        ()
* Step 4: UnsatPaths WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A,B) -> f1(3000,B)     True (1,1)
          1. f0(A,B) -> exitus616(A,B) True (1,1)
        Signature:
          {(exitus616,2);(f0,2);(f1,2)}
        Flow Graph:
          [0->{},1->{}]
        
    + Applied Processor:
        UnsatPaths
    + Details:
        The problem is already solved.

YES(?,O(1))