YES(?,O(1))
* Step 1: UnreachableRules WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A,B,C,D) -> f4(A,E,C,D)     [A >= 10]         (?,1)
          1. f0(A,B,C,D) -> f0(1 + A,B,A,D) [9 >= A]          (?,1)
          2. f1(A,B,C,D) -> f0(1,B,C,D)     [9 >= E && A = 0] (?,1)
          3. f2(A,B,C,D) -> f0(2,B,C,2)     [9 >= A]          (?,1)
          4. f3(A,B,C,D) -> f0(0,B,C,D)     True              (1,1)
        Signature:
          {(f0,4);(f1,4);(f2,4);(f3,4);(f4,4)}
        Flow Graph:
          [0->{},1->{0,1},2->{0,1},3->{0,1},4->{0,1}]
        
    + Applied Processor:
        UnreachableRules
    + Details:
        Following transitions are not reachable from the starting states and are revomed: [2,3]
* Step 2: UnsatPaths WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A,B,C,D) -> f4(A,E,C,D)     [A >= 10] (?,1)
          1. f0(A,B,C,D) -> f0(1 + A,B,A,D) [9 >= A]  (?,1)
          4. f3(A,B,C,D) -> f0(0,B,C,D)     True      (1,1)
        Signature:
          {(f0,4);(f1,4);(f2,4);(f3,4);(f4,4)}
        Flow Graph:
          [0->{},1->{0,1},4->{0,1}]
        
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(4,0)]
* Step 3: TrivialSCCs WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A,B,C,D) -> f4(A,E,C,D)     [A >= 10] (?,1)
          1. f0(A,B,C,D) -> f0(1 + A,B,A,D) [9 >= A]  (?,1)
          4. f3(A,B,C,D) -> f0(0,B,C,D)     True      (1,1)
        Signature:
          {(f0,4);(f1,4);(f2,4);(f3,4);(f4,4)}
        Flow Graph:
          [0->{},1->{0,1},4->{1}]
        
    + Applied Processor:
        TrivialSCCs
    + Details:
        All trivial SCCs of the transition graph admit timebound 1.
* Step 4: PolyRank WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A,B,C,D) -> f4(A,E,C,D)     [A >= 10] (1,1)
          1. f0(A,B,C,D) -> f0(1 + A,B,A,D) [9 >= A]  (?,1)
          4. f3(A,B,C,D) -> f0(0,B,C,D)     True      (1,1)
        Signature:
          {(f0,4);(f1,4);(f2,4);(f3,4);(f4,4)}
        Flow Graph:
          [0->{},1->{0,1},4->{1}]
        
    + Applied Processor:
        PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
    + Details:
        We apply a polynomial interpretation of shape linear:
          p(f0) = 10 + -1*x1
          p(f3) = 10        
          p(f4) = 10 + -1*x1
        
        Following rules are strictly oriented:
             [9 >= A] ==>                
          f0(A,B,C,D)   = 10 + -1*A      
                        > 9 + -1*A       
                        = f0(1 + A,B,A,D)
        
        
        Following rules are weakly oriented:
            [A >= 10] ==>            
          f0(A,B,C,D)   = 10 + -1*A  
                       >= 10 + -1*A  
                        = f4(A,E,C,D)
        
                 True ==>            
          f3(A,B,C,D)   = 10         
                       >= 10         
                        = f0(0,B,C,D)
        
        
* Step 5: KnowledgePropagation WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A,B,C,D) -> f4(A,E,C,D)     [A >= 10] (1,1) 
          1. f0(A,B,C,D) -> f0(1 + A,B,A,D) [9 >= A]  (10,1)
          4. f3(A,B,C,D) -> f0(0,B,C,D)     True      (1,1) 
        Signature:
          {(f0,4);(f1,4);(f2,4);(f3,4);(f4,4)}
        Flow Graph:
          [0->{},1->{0,1},4->{1}]
        
    + Applied Processor:
        KnowledgePropagation
    + Details:
        The problem is already solved.

YES(?,O(1))