YES
* Step 1: TrivialSCCs YES
    + Considered Problem:
        Rules:
          0.  eval_abc_start(v_a,v_b,v_i_0)  -> eval_abc_bb0_in(v_a,v_b,v_i_0)     True                                                              (1,1)
          1.  eval_abc_bb0_in(v_a,v_b,v_i_0) -> eval_abc_0(v_a,v_b,v_i_0)          True                                                              (?,1)
          2.  eval_abc_0(v_a,v_b,v_i_0)      -> eval_abc_1(v_a,v_b,v_i_0)          True                                                              (?,1)
          3.  eval_abc_1(v_a,v_b,v_i_0)      -> eval_abc_2(v_a,v_b,v_i_0)          True                                                              (?,1)
          4.  eval_abc_2(v_a,v_b,v_i_0)      -> eval_abc_3(v_a,v_b,v_i_0)          True                                                              (?,1)
          5.  eval_abc_3(v_a,v_b,v_i_0)      -> eval_abc_4(v_a,v_b,v_i_0)          True                                                              (?,1)
          6.  eval_abc_4(v_a,v_b,v_i_0)      -> eval_abc_bb1_in(v_a,v_b,v_a)       True                                                              (?,1)
          7.  eval_abc_bb1_in(v_a,v_b,v_i_0) -> eval_abc_bb2_in(v_a,v_b,v_i_0)     [-1*v_a + v_i_0 >= 0 && v_b >= v_i_0]                             (?,1)
          8.  eval_abc_bb1_in(v_a,v_b,v_i_0) -> eval_abc_bb3_in(v_a,v_b,v_i_0)     [-1*v_a + v_i_0 >= 0 && -1 + v_i_0 >= v_b]                        (?,1)
          9.  eval_abc_bb2_in(v_a,v_b,v_i_0) -> eval_abc_bb1_in(v_a,v_b,1 + v_i_0) [v_b + -1*v_i_0 >= 0 && -1*v_a + v_i_0 >= 0 && -1*v_a + v_b >= 0] (?,1)
          10. eval_abc_bb3_in(v_a,v_b,v_i_0) -> eval_abc_stop(v_a,v_b,v_i_0)       [-1 + -1*v_b + v_i_0 >= 0 && -1*v_a + v_i_0 >= 0]                 (?,1)
        Signature:
          {(eval_abc_0,3)
          ;(eval_abc_1,3)
          ;(eval_abc_2,3)
          ;(eval_abc_3,3)
          ;(eval_abc_4,3)
          ;(eval_abc_bb0_in,3)
          ;(eval_abc_bb1_in,3)
          ;(eval_abc_bb2_in,3)
          ;(eval_abc_bb3_in,3)
          ;(eval_abc_start,3)
          ;(eval_abc_stop,3)}
        Flow Graph:
          [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7,8},7->{9},8->{10},9->{7,8},10->{}]
        
    + Applied Processor:
        TrivialSCCs
    + Details:
        All trivial SCCs of the transition graph admit timebound 1.
* Step 2: Looptree YES
    + Considered Problem:
        Rules:
          0.  eval_abc_start(v_a,v_b,v_i_0)  -> eval_abc_bb0_in(v_a,v_b,v_i_0)     True                                                              (1,1)
          1.  eval_abc_bb0_in(v_a,v_b,v_i_0) -> eval_abc_0(v_a,v_b,v_i_0)          True                                                              (1,1)
          2.  eval_abc_0(v_a,v_b,v_i_0)      -> eval_abc_1(v_a,v_b,v_i_0)          True                                                              (1,1)
          3.  eval_abc_1(v_a,v_b,v_i_0)      -> eval_abc_2(v_a,v_b,v_i_0)          True                                                              (1,1)
          4.  eval_abc_2(v_a,v_b,v_i_0)      -> eval_abc_3(v_a,v_b,v_i_0)          True                                                              (1,1)
          5.  eval_abc_3(v_a,v_b,v_i_0)      -> eval_abc_4(v_a,v_b,v_i_0)          True                                                              (1,1)
          6.  eval_abc_4(v_a,v_b,v_i_0)      -> eval_abc_bb1_in(v_a,v_b,v_a)       True                                                              (1,1)
          7.  eval_abc_bb1_in(v_a,v_b,v_i_0) -> eval_abc_bb2_in(v_a,v_b,v_i_0)     [-1*v_a + v_i_0 >= 0 && v_b >= v_i_0]                             (?,1)
          8.  eval_abc_bb1_in(v_a,v_b,v_i_0) -> eval_abc_bb3_in(v_a,v_b,v_i_0)     [-1*v_a + v_i_0 >= 0 && -1 + v_i_0 >= v_b]                        (1,1)
          9.  eval_abc_bb2_in(v_a,v_b,v_i_0) -> eval_abc_bb1_in(v_a,v_b,1 + v_i_0) [v_b + -1*v_i_0 >= 0 && -1*v_a + v_i_0 >= 0 && -1*v_a + v_b >= 0] (?,1)
          10. eval_abc_bb3_in(v_a,v_b,v_i_0) -> eval_abc_stop(v_a,v_b,v_i_0)       [-1 + -1*v_b + v_i_0 >= 0 && -1*v_a + v_i_0 >= 0]                 (1,1)
        Signature:
          {(eval_abc_0,3)
          ;(eval_abc_1,3)
          ;(eval_abc_2,3)
          ;(eval_abc_3,3)
          ;(eval_abc_4,3)
          ;(eval_abc_bb0_in,3)
          ;(eval_abc_bb1_in,3)
          ;(eval_abc_bb2_in,3)
          ;(eval_abc_bb3_in,3)
          ;(eval_abc_start,3)
          ;(eval_abc_stop,3)}
        Flow Graph:
          [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7,8},7->{9},8->{10},9->{7,8},10->{}]
        
    + Applied Processor:
        Looptree
    + Details:
        We construct a looptree:
          P: [0,1,2,3,4,5,6,7,8,9,10]
          |
          `- p:[7,9] c: [9]

YES