YES(?,O(n^1))
* Step 1: UnreachableRules WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0.  f0(A,B,C) -> f3(-1*A,B,C)      True                   (?,1)
          1.  f3(A,B,C) -> f7(0,D,C)         [A = 0]                (?,1)
          2.  f4(A,B,C) -> f7(0,D,C)         [A = 0]                (?,1)
          3.  f6(A,B,C) -> f4(A,B,1)         [A >= 1]               (1,1)
          4.  f3(A,B,C) -> f4(-1 + -1*A,B,1) [0 >= 1 + A && 0 >= C] (?,1)
          5.  f3(A,B,C) -> f4(-1 + -1*A,B,1) [0 >= 1 + A && C >= 2] (?,1)
          6.  f3(A,B,C) -> f4(-1 + -1*A,B,1) [A >= 1 && 0 >= C]     (?,1)
          7.  f3(A,B,C) -> f4(-1 + -1*A,B,1) [A >= 1 && C >= 2]     (?,1)
          8.  f4(A,B,C) -> f3(1 + -1*A,B,0)  [0 >= 1 + A && C = 1]  (?,1)
          9.  f4(A,B,C) -> f3(1 + -1*A,B,0)  [A >= 1 && C = 1]      (?,1)
          10. f5(A,B,C) -> f3(1 + -1*A,B,0)  [0 >= 1 + A && C = 1]  (?,1)
          11. f5(A,B,C) -> f3(1 + -1*A,B,0)  [A >= 1 && C = 1]      (?,1)
        Signature:
          {(f0,3);(f3,3);(f4,3);(f5,3);(f6,3);(f7,3)}
        Flow Graph:
          [0->{1,4,5,6,7},1->{},2->{},3->{2,8,9},4->{2,8,9},5->{2,8,9},6->{2,8,9},7->{2,8,9},8->{1,4,5,6,7},9->{1,4
          ,5,6,7},10->{1,4,5,6,7},11->{1,4,5,6,7}]
        
    + Applied Processor:
        UnreachableRules
    + Details:
        Following transitions are not reachable from the starting states and are revomed: [0,10,11]
* Step 2: UnsatPaths WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          1. f3(A,B,C) -> f7(0,D,C)         [A = 0]                (?,1)
          2. f4(A,B,C) -> f7(0,D,C)         [A = 0]                (?,1)
          3. f6(A,B,C) -> f4(A,B,1)         [A >= 1]               (1,1)
          4. f3(A,B,C) -> f4(-1 + -1*A,B,1) [0 >= 1 + A && 0 >= C] (?,1)
          5. f3(A,B,C) -> f4(-1 + -1*A,B,1) [0 >= 1 + A && C >= 2] (?,1)
          6. f3(A,B,C) -> f4(-1 + -1*A,B,1) [A >= 1 && 0 >= C]     (?,1)
          7. f3(A,B,C) -> f4(-1 + -1*A,B,1) [A >= 1 && C >= 2]     (?,1)
          8. f4(A,B,C) -> f3(1 + -1*A,B,0)  [0 >= 1 + A && C = 1]  (?,1)
          9. f4(A,B,C) -> f3(1 + -1*A,B,0)  [A >= 1 && C = 1]      (?,1)
        Signature:
          {(f0,3);(f3,3);(f4,3);(f5,3);(f6,3);(f7,3)}
        Flow Graph:
          [1->{},2->{},3->{2,8,9},4->{2,8,9},5->{2,8,9},6->{2,8,9},7->{2,8,9},8->{1,4,5,6,7},9->{1,4,5,6,7}]
        
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(3,2)
                                                             ,(3,8)
                                                             ,(4,8)
                                                             ,(5,8)
                                                             ,(6,2)
                                                             ,(6,9)
                                                             ,(7,2)
                                                             ,(7,9)
                                                             ,(8,1)
                                                             ,(8,4)
                                                             ,(8,5)
                                                             ,(8,7)
                                                             ,(9,5)
                                                             ,(9,6)
                                                             ,(9,7)]
* Step 3: UnreachableRules WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          1. f3(A,B,C) -> f7(0,D,C)         [A = 0]                (?,1)
          2. f4(A,B,C) -> f7(0,D,C)         [A = 0]                (?,1)
          3. f6(A,B,C) -> f4(A,B,1)         [A >= 1]               (1,1)
          4. f3(A,B,C) -> f4(-1 + -1*A,B,1) [0 >= 1 + A && 0 >= C] (?,1)
          5. f3(A,B,C) -> f4(-1 + -1*A,B,1) [0 >= 1 + A && C >= 2] (?,1)
          6. f3(A,B,C) -> f4(-1 + -1*A,B,1) [A >= 1 && 0 >= C]     (?,1)
          7. f3(A,B,C) -> f4(-1 + -1*A,B,1) [A >= 1 && C >= 2]     (?,1)
          8. f4(A,B,C) -> f3(1 + -1*A,B,0)  [0 >= 1 + A && C = 1]  (?,1)
          9. f4(A,B,C) -> f3(1 + -1*A,B,0)  [A >= 1 && C = 1]      (?,1)
        Signature:
          {(f0,3);(f3,3);(f4,3);(f5,3);(f6,3);(f7,3)}
        Flow Graph:
          [1->{},2->{},3->{9},4->{2,9},5->{2,9},6->{8},7->{8},8->{6},9->{1,4}]
        
    + Applied Processor:
        UnreachableRules
    + Details:
        Following transitions are not reachable from the starting states and are revomed: [5,6,7,8]
* Step 4: TrivialSCCs WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          1. f3(A,B,C) -> f7(0,D,C)         [A = 0]                (?,1)
          2. f4(A,B,C) -> f7(0,D,C)         [A = 0]                (?,1)
          3. f6(A,B,C) -> f4(A,B,1)         [A >= 1]               (1,1)
          4. f3(A,B,C) -> f4(-1 + -1*A,B,1) [0 >= 1 + A && 0 >= C] (?,1)
          9. f4(A,B,C) -> f3(1 + -1*A,B,0)  [A >= 1 && C = 1]      (?,1)
        Signature:
          {(f0,3);(f3,3);(f4,3);(f5,3);(f6,3);(f7,3)}
        Flow Graph:
          [1->{},2->{},3->{9},4->{2,9},9->{1,4}]
        
    + Applied Processor:
        TrivialSCCs
    + Details:
        All trivial SCCs of the transition graph admit timebound 1.
* Step 5: PolyRank WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          1. f3(A,B,C) -> f7(0,D,C)         [A = 0]                (1,1)
          2. f4(A,B,C) -> f7(0,D,C)         [A = 0]                (1,1)
          3. f6(A,B,C) -> f4(A,B,1)         [A >= 1]               (1,1)
          4. f3(A,B,C) -> f4(-1 + -1*A,B,1) [0 >= 1 + A && 0 >= C] (?,1)
          9. f4(A,B,C) -> f3(1 + -1*A,B,0)  [A >= 1 && C = 1]      (?,1)
        Signature:
          {(f0,3);(f3,3);(f4,3);(f5,3);(f6,3);(f7,3)}
        Flow Graph:
          [1->{},2->{},3->{9},4->{2,9},9->{1,4}]
        
    + Applied Processor:
        PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
    + Details:
        We apply a polynomial interpretation of shape linear:
          p(f3) = -1*x1
          p(f4) = x1   
          p(f6) = x1   
          p(f7) = 0    
        
        Following rules are strictly oriented:
        [A >= 1 && C = 1] ==>                 
                f4(A,B,C)   = A               
                            > -1 + A          
                            = f3(1 + -1*A,B,0)
        
        
        Following rules are weakly oriented:
                       [A = 0] ==>                  
                     f3(A,B,C)   = -1*A             
                                >= 0                
                                 = f7(0,D,C)        
        
                       [A = 0] ==>                  
                     f4(A,B,C)   = A                
                                >= 0                
                                 = f7(0,D,C)        
        
                      [A >= 1] ==>                  
                     f6(A,B,C)   = A                
                                >= A                
                                 = f4(A,B,1)        
        
        [0 >= 1 + A && 0 >= C] ==>                  
                     f3(A,B,C)   = -1*A             
                                >= -1 + -1*A        
                                 = f4(-1 + -1*A,B,1)
        
        
* Step 6: KnowledgePropagation WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          1. f3(A,B,C) -> f7(0,D,C)         [A = 0]                (1,1)
          2. f4(A,B,C) -> f7(0,D,C)         [A = 0]                (1,1)
          3. f6(A,B,C) -> f4(A,B,1)         [A >= 1]               (1,1)
          4. f3(A,B,C) -> f4(-1 + -1*A,B,1) [0 >= 1 + A && 0 >= C] (?,1)
          9. f4(A,B,C) -> f3(1 + -1*A,B,0)  [A >= 1 && C = 1]      (A,1)
        Signature:
          {(f0,3);(f3,3);(f4,3);(f5,3);(f6,3);(f7,3)}
        Flow Graph:
          [1->{},2->{},3->{9},4->{2,9},9->{1,4}]
        
    + Applied Processor:
        KnowledgePropagation
    + Details:
        We propagate bounds from predecessors.
* Step 7: PolyRank WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          1. f3(A,B,C) -> f7(0,D,C)         [A = 0]                (1,1)
          2. f4(A,B,C) -> f7(0,D,C)         [A = 0]                (1,1)
          3. f6(A,B,C) -> f4(A,B,1)         [A >= 1]               (1,1)
          4. f3(A,B,C) -> f4(-1 + -1*A,B,1) [0 >= 1 + A && 0 >= C] (A,1)
          9. f4(A,B,C) -> f3(1 + -1*A,B,0)  [A >= 1 && C = 1]      (A,1)
        Signature:
          {(f0,3);(f3,3);(f4,3);(f5,3);(f6,3);(f7,3)}
        Flow Graph:
          [1->{},2->{},3->{9},4->{2,9},9->{1,4}]
        
    + Applied Processor:
        PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
    + Details:
        The problem is already solved.

YES(?,O(n^1))