YES
* Step 1: TrivialSCCs YES
    + Considered Problem:
        Rules:
          0.  eval_start_start(v__0,v__1,v_y,v_z)  -> eval_start_bb0_in(v__0,v__1,v_y,v_z)      True                                                                                  (1,1)
          1.  eval_start_bb0_in(v__0,v__1,v_y,v_z) -> eval_start_0(v__0,v__1,v_y,v_z)           True                                                                                  (?,1)
          2.  eval_start_0(v__0,v__1,v_y,v_z)      -> eval_start_1(v__0,v__1,v_y,v_z)           True                                                                                  (?,1)
          3.  eval_start_1(v__0,v__1,v_y,v_z)      -> eval_start_2(v__0,v__1,v_y,v_z)           True                                                                                  (?,1)
          4.  eval_start_2(v__0,v__1,v_y,v_z)      -> eval_start_3(v__0,v__1,v_y,v_z)           True                                                                                  (?,1)
          5.  eval_start_3(v__0,v__1,v_y,v_z)      -> eval_start_bb1_in(v_y,v__1,v_y,v_z)       True                                                                                  (?,1)
          6.  eval_start_bb1_in(v__0,v__1,v_y,v_z) -> eval_start_bb2_in(v__0,v__1,v_y,v_z)      [v__0 + -1*v_y >= 0 && -1 + v_z >= v__0]                                              (?,1)
          7.  eval_start_bb1_in(v__0,v__1,v_y,v_z) -> eval_start_bb3_in(v__0,v__0,v_y,v_z)      [v__0 + -1*v_y >= 0 && v__0 >= v_z]                                                   (?,1)
          8.  eval_start_bb2_in(v__0,v__1,v_y,v_z) -> eval_start_bb1_in(1 + v__0,v__1,v_y,v_z)  [-1 + -1*v_y + v_z >= 0 && -1 + -1*v__0 + v_z >= 0 && v__0 + -1*v_y >= 0]             (?,1)
          9.  eval_start_bb3_in(v__0,v__1,v_y,v_z) -> eval_start_bb4_in(v__0,v__1,v_y,v_z)      [v__0 + -1*v_z >= 0 && v__0 + -1*v_y >= 0 && v__0 + -1*v__1 >= 0 && -1 + v__1 >= 2]   (?,1)
          10. eval_start_bb3_in(v__0,v__1,v_y,v_z) -> eval_start_bb5_in(v__0,v__1,v_y,v_z)      [v__0 + -1*v_z >= 0 && v__0 + -1*v_y >= 0 && v__0 + -1*v__1 >= 0 && 2 >= v__1]        (?,1)
          11. eval_start_bb4_in(v__0,v__1,v_y,v_z) -> eval_start_bb3_in(v__0,-3 + v__1,v_y,v_z) [v__0 + -1*v_z >= 0                                                                   (?,1)
                                                                                                 && v__0 + -1*v_y >= 0                                                                     
                                                                                                 && v__0 + -1*v__1 >= 0                                                                    
                                                                                                 && -3 + v__1 >= 0                                                                         
                                                                                                 && -6 + v__0 + v__1 >= 0                                                                  
                                                                                                 && -3 + v__0 >= 0]                                                                        
          12. eval_start_bb5_in(v__0,v__1,v_y,v_z) -> eval_start_stop(v__0,v__1,v_y,v_z)        [v__0 + -1*v_z >= 0 && v__0 + -1*v_y >= 0 && 2 + -1*v__1 >= 0 && v__0 + -1*v__1 >= 0] (?,1)
        Signature:
          {(eval_start_0,4)
          ;(eval_start_1,4)
          ;(eval_start_2,4)
          ;(eval_start_3,4)
          ;(eval_start_bb0_in,4)
          ;(eval_start_bb1_in,4)
          ;(eval_start_bb2_in,4)
          ;(eval_start_bb3_in,4)
          ;(eval_start_bb4_in,4)
          ;(eval_start_bb5_in,4)
          ;(eval_start_start,4)
          ;(eval_start_stop,4)}
        Flow Graph:
          [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6,7},6->{8},7->{9,10},8->{6,7},9->{11},10->{12},11->{9,10},12->{}]
        
    + Applied Processor:
        TrivialSCCs
    + Details:
        All trivial SCCs of the transition graph admit timebound 1.
* Step 2: Looptree YES
    + Considered Problem:
        Rules:
          0.  eval_start_start(v__0,v__1,v_y,v_z)  -> eval_start_bb0_in(v__0,v__1,v_y,v_z)      True                                                                                  (1,1)
          1.  eval_start_bb0_in(v__0,v__1,v_y,v_z) -> eval_start_0(v__0,v__1,v_y,v_z)           True                                                                                  (1,1)
          2.  eval_start_0(v__0,v__1,v_y,v_z)      -> eval_start_1(v__0,v__1,v_y,v_z)           True                                                                                  (1,1)
          3.  eval_start_1(v__0,v__1,v_y,v_z)      -> eval_start_2(v__0,v__1,v_y,v_z)           True                                                                                  (1,1)
          4.  eval_start_2(v__0,v__1,v_y,v_z)      -> eval_start_3(v__0,v__1,v_y,v_z)           True                                                                                  (1,1)
          5.  eval_start_3(v__0,v__1,v_y,v_z)      -> eval_start_bb1_in(v_y,v__1,v_y,v_z)       True                                                                                  (1,1)
          6.  eval_start_bb1_in(v__0,v__1,v_y,v_z) -> eval_start_bb2_in(v__0,v__1,v_y,v_z)      [v__0 + -1*v_y >= 0 && -1 + v_z >= v__0]                                              (?,1)
          7.  eval_start_bb1_in(v__0,v__1,v_y,v_z) -> eval_start_bb3_in(v__0,v__0,v_y,v_z)      [v__0 + -1*v_y >= 0 && v__0 >= v_z]                                                   (1,1)
          8.  eval_start_bb2_in(v__0,v__1,v_y,v_z) -> eval_start_bb1_in(1 + v__0,v__1,v_y,v_z)  [-1 + -1*v_y + v_z >= 0 && -1 + -1*v__0 + v_z >= 0 && v__0 + -1*v_y >= 0]             (?,1)
          9.  eval_start_bb3_in(v__0,v__1,v_y,v_z) -> eval_start_bb4_in(v__0,v__1,v_y,v_z)      [v__0 + -1*v_z >= 0 && v__0 + -1*v_y >= 0 && v__0 + -1*v__1 >= 0 && -1 + v__1 >= 2]   (?,1)
          10. eval_start_bb3_in(v__0,v__1,v_y,v_z) -> eval_start_bb5_in(v__0,v__1,v_y,v_z)      [v__0 + -1*v_z >= 0 && v__0 + -1*v_y >= 0 && v__0 + -1*v__1 >= 0 && 2 >= v__1]        (1,1)
          11. eval_start_bb4_in(v__0,v__1,v_y,v_z) -> eval_start_bb3_in(v__0,-3 + v__1,v_y,v_z) [v__0 + -1*v_z >= 0                                                                   (?,1)
                                                                                                 && v__0 + -1*v_y >= 0                                                                     
                                                                                                 && v__0 + -1*v__1 >= 0                                                                    
                                                                                                 && -3 + v__1 >= 0                                                                         
                                                                                                 && -6 + v__0 + v__1 >= 0                                                                  
                                                                                                 && -3 + v__0 >= 0]                                                                        
          12. eval_start_bb5_in(v__0,v__1,v_y,v_z) -> eval_start_stop(v__0,v__1,v_y,v_z)        [v__0 + -1*v_z >= 0 && v__0 + -1*v_y >= 0 && 2 + -1*v__1 >= 0 && v__0 + -1*v__1 >= 0] (1,1)
        Signature:
          {(eval_start_0,4)
          ;(eval_start_1,4)
          ;(eval_start_2,4)
          ;(eval_start_3,4)
          ;(eval_start_bb0_in,4)
          ;(eval_start_bb1_in,4)
          ;(eval_start_bb2_in,4)
          ;(eval_start_bb3_in,4)
          ;(eval_start_bb4_in,4)
          ;(eval_start_bb5_in,4)
          ;(eval_start_start,4)
          ;(eval_start_stop,4)}
        Flow Graph:
          [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6,7},6->{8},7->{9,10},8->{6,7},9->{11},10->{12},11->{9,10},12->{}]
        
    + Applied Processor:
        Looptree
    + Details:
        We construct a looptree:
          P: [0,1,2,3,4,5,6,7,8,9,10,11,12]
          |
          +- p:[6,8] c: [8]
          |
          `- p:[9,11] c: [11]

YES