YES
* Step 1: TrivialSCCs YES
    + Considered Problem:
        Rules:
          0.  eval_speedSingleSingle_start(v_n,v_x_0)  -> eval_speedSingleSingle_bb0_in(v_n,v_x_0)     True                                                                               (1,1)
          1.  eval_speedSingleSingle_bb0_in(v_n,v_x_0) -> eval_speedSingleSingle_0(v_n,v_x_0)          True                                                                               (?,1)
          2.  eval_speedSingleSingle_0(v_n,v_x_0)      -> eval_speedSingleSingle_1(v_n,v_x_0)          True                                                                               (?,1)
          3.  eval_speedSingleSingle_1(v_n,v_x_0)      -> eval_speedSingleSingle_2(v_n,v_x_0)          True                                                                               (?,1)
          4.  eval_speedSingleSingle_2(v_n,v_x_0)      -> eval_speedSingleSingle_3(v_n,v_x_0)          True                                                                               (?,1)
          5.  eval_speedSingleSingle_3(v_n,v_x_0)      -> eval_speedSingleSingle_4(v_n,v_x_0)          True                                                                               (?,1)
          6.  eval_speedSingleSingle_4(v_n,v_x_0)      -> eval_speedSingleSingle_bb1_in(v_n,0)         True                                                                               (?,1)
          7.  eval_speedSingleSingle_bb1_in(v_n,v_x_0) -> eval_speedSingleSingle_bb2_in(v_n,v_x_0)     [v_x_0 >= 0 && -1 + v_n >= v_x_0]                                                  (?,1)
          8.  eval_speedSingleSingle_bb1_in(v_n,v_x_0) -> eval_speedSingleSingle_bb3_in(v_n,v_x_0)     [v_x_0 >= 0 && v_x_0 >= v_n]                                                       (?,1)
          9.  eval_speedSingleSingle_bb2_in(v_n,v_x_0) -> eval_speedSingleSingle_5(v_n,v_x_0)          [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] (?,1)
          10. eval_speedSingleSingle_5(v_n,v_x_0)      -> eval_speedSingleSingle_6(v_n,v_x_0)          [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] (?,1)
          11. eval_speedSingleSingle_6(v_n,v_x_0)      -> eval_speedSingleSingle_bb1_in(v_n,1 + v_x_0) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] (?,1)
          12. eval_speedSingleSingle_bb3_in(v_n,v_x_0) -> eval_speedSingleSingle_stop(v_n,v_x_0)       [v_x_0 >= 0 && -1*v_n + v_x_0 >= 0]                                                (?,1)
        Signature:
          {(eval_speedSingleSingle_0,2)
          ;(eval_speedSingleSingle_1,2)
          ;(eval_speedSingleSingle_2,2)
          ;(eval_speedSingleSingle_3,2)
          ;(eval_speedSingleSingle_4,2)
          ;(eval_speedSingleSingle_5,2)
          ;(eval_speedSingleSingle_6,2)
          ;(eval_speedSingleSingle_bb0_in,2)
          ;(eval_speedSingleSingle_bb1_in,2)
          ;(eval_speedSingleSingle_bb2_in,2)
          ;(eval_speedSingleSingle_bb3_in,2)
          ;(eval_speedSingleSingle_start,2)
          ;(eval_speedSingleSingle_stop,2)}
        Flow Graph:
          [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7,8},7->{9},8->{12},9->{10},10->{11},11->{7,8},12->{}]
        
    + Applied Processor:
        TrivialSCCs
    + Details:
        All trivial SCCs of the transition graph admit timebound 1.
* Step 2: Looptree YES
    + Considered Problem:
        Rules:
          0.  eval_speedSingleSingle_start(v_n,v_x_0)  -> eval_speedSingleSingle_bb0_in(v_n,v_x_0)     True                                                                               (1,1)
          1.  eval_speedSingleSingle_bb0_in(v_n,v_x_0) -> eval_speedSingleSingle_0(v_n,v_x_0)          True                                                                               (1,1)
          2.  eval_speedSingleSingle_0(v_n,v_x_0)      -> eval_speedSingleSingle_1(v_n,v_x_0)          True                                                                               (1,1)
          3.  eval_speedSingleSingle_1(v_n,v_x_0)      -> eval_speedSingleSingle_2(v_n,v_x_0)          True                                                                               (1,1)
          4.  eval_speedSingleSingle_2(v_n,v_x_0)      -> eval_speedSingleSingle_3(v_n,v_x_0)          True                                                                               (1,1)
          5.  eval_speedSingleSingle_3(v_n,v_x_0)      -> eval_speedSingleSingle_4(v_n,v_x_0)          True                                                                               (1,1)
          6.  eval_speedSingleSingle_4(v_n,v_x_0)      -> eval_speedSingleSingle_bb1_in(v_n,0)         True                                                                               (1,1)
          7.  eval_speedSingleSingle_bb1_in(v_n,v_x_0) -> eval_speedSingleSingle_bb2_in(v_n,v_x_0)     [v_x_0 >= 0 && -1 + v_n >= v_x_0]                                                  (?,1)
          8.  eval_speedSingleSingle_bb1_in(v_n,v_x_0) -> eval_speedSingleSingle_bb3_in(v_n,v_x_0)     [v_x_0 >= 0 && v_x_0 >= v_n]                                                       (1,1)
          9.  eval_speedSingleSingle_bb2_in(v_n,v_x_0) -> eval_speedSingleSingle_5(v_n,v_x_0)          [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] (?,1)
          10. eval_speedSingleSingle_5(v_n,v_x_0)      -> eval_speedSingleSingle_6(v_n,v_x_0)          [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] (?,1)
          11. eval_speedSingleSingle_6(v_n,v_x_0)      -> eval_speedSingleSingle_bb1_in(v_n,1 + v_x_0) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] (?,1)
          12. eval_speedSingleSingle_bb3_in(v_n,v_x_0) -> eval_speedSingleSingle_stop(v_n,v_x_0)       [v_x_0 >= 0 && -1*v_n + v_x_0 >= 0]                                                (1,1)
        Signature:
          {(eval_speedSingleSingle_0,2)
          ;(eval_speedSingleSingle_1,2)
          ;(eval_speedSingleSingle_2,2)
          ;(eval_speedSingleSingle_3,2)
          ;(eval_speedSingleSingle_4,2)
          ;(eval_speedSingleSingle_5,2)
          ;(eval_speedSingleSingle_6,2)
          ;(eval_speedSingleSingle_bb0_in,2)
          ;(eval_speedSingleSingle_bb1_in,2)
          ;(eval_speedSingleSingle_bb2_in,2)
          ;(eval_speedSingleSingle_bb3_in,2)
          ;(eval_speedSingleSingle_start,2)
          ;(eval_speedSingleSingle_stop,2)}
        Flow Graph:
          [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7,8},7->{9},8->{12},9->{10},10->{11},11->{7,8},12->{}]
        
    + Applied Processor:
        Looptree
    + Details:
        We construct a looptree:
          P: [0,1,2,3,4,5,6,7,8,9,10,11,12]
          |
          `- p:[7,11,10,9] c: [11]

YES