YES
* Step 1: FromIts YES
    + Considered Problem:
        Rules:
          0.  eval_start_start(v_m,v_n,v_x_0,v_y_0)  -> eval_start_bb0_in(v_m,v_n,v_x_0,v_y_0)         True                (1,1)
          1.  eval_start_bb0_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_0(v_m,v_n,v_x_0,v_y_0)              True                (?,1)
          2.  eval_start_0(v_m,v_n,v_x_0,v_y_0)      -> eval_start_1(v_m,v_n,v_x_0,v_y_0)              True                (?,1)
          3.  eval_start_1(v_m,v_n,v_x_0,v_y_0)      -> eval_start_2(v_m,v_n,v_x_0,v_y_0)              True                (?,1)
          4.  eval_start_2(v_m,v_n,v_x_0,v_y_0)      -> eval_start_3(v_m,v_n,v_x_0,v_y_0)              True                (?,1)
          5.  eval_start_3(v_m,v_n,v_x_0,v_y_0)      -> eval_start_4(v_m,v_n,v_x_0,v_y_0)              True                (?,1)
          6.  eval_start_4(v_m,v_n,v_x_0,v_y_0)      -> eval_start_5(v_m,v_n,v_x_0,v_y_0)              True                (?,1)
          7.  eval_start_5(v_m,v_n,v_x_0,v_y_0)      -> eval_start_6(v_m,v_n,v_x_0,v_y_0)              True                (?,1)
          8.  eval_start_6(v_m,v_n,v_x_0,v_y_0)      -> eval_start_7(v_m,v_n,v_x_0,v_y_0)              True                (?,1)
          9.  eval_start_7(v_m,v_n,v_x_0,v_y_0)      -> eval_start_8(v_m,v_n,v_x_0,v_y_0)              True                (?,1)
          10. eval_start_8(v_m,v_n,v_x_0,v_y_0)      -> eval_start_bb1_in(v_m,v_n,0,0)                 True                (?,1)
          11. eval_start_bb1_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb2_in(v_m,v_n,v_x_0,v_y_0)         [-1 + v_n >= v_x_0] (?,1)
          12. eval_start_bb1_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb3_in(v_m,v_n,v_x_0,v_y_0)         [v_x_0 >= v_n]      (?,1)
          13. eval_start_bb2_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_m,v_n,1 + v_x_0,1 + v_y_0) True                (?,1)
          14. eval_start_bb3_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb4_in(v_m,v_n,v_x_0,v_y_0)         [-1 + v_m >= v_y_0] (?,1)
          15. eval_start_bb3_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb5_in(v_m,v_n,v_x_0,v_y_0)         [v_y_0 >= v_m]      (?,1)
          16. eval_start_bb4_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_m,v_n,1 + v_x_0,1 + v_y_0) True                (?,1)
          17. eval_start_bb5_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_stop(v_m,v_n,v_x_0,v_y_0)           True                (?,1)
        Signature:
          {(eval_start_0,4)
          ;(eval_start_1,4)
          ;(eval_start_2,4)
          ;(eval_start_3,4)
          ;(eval_start_4,4)
          ;(eval_start_5,4)
          ;(eval_start_6,4)
          ;(eval_start_7,4)
          ;(eval_start_8,4)
          ;(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},6->{7},7->{8},8->{9},9->{10},10->{11,12},11->{13},12->{14,15}
          ,13->{11,12},14->{16},15->{17},16->{11,12},17->{}]
        
    + Applied Processor:
        FromIts
    + Details:
        ()
* Step 2: Decompose YES
    + Considered Problem:
        Rules:
          eval_start_start(v_m,v_n,v_x_0,v_y_0)   -> eval_start_bb0_in(v_m,v_n,v_x_0,v_y_0)           True
          eval_start_bb0_in(v_m,v_n,v_x_0,v_y_0)  -> eval_start_0(v_m,v_n,v_x_0,v_y_0)                True
          eval_start_0(v_m,v_n,v_x_0,v_y_0)       -> eval_start_1(v_m,v_n,v_x_0,v_y_0)                True
          eval_start_1(v_m,v_n,v_x_0,v_y_0)       -> eval_start_2(v_m,v_n,v_x_0,v_y_0)                True
          eval_start_2(v_m,v_n,v_x_0,v_y_0)       -> eval_start_3(v_m,v_n,v_x_0,v_y_0)                True
          eval_start_3(v_m,v_n,v_x_0,v_y_0)       -> eval_start_4(v_m,v_n,v_x_0,v_y_0)                True
          eval_start_4(v_m,v_n,v_x_0,v_y_0)       -> eval_start_5(v_m,v_n,v_x_0,v_y_0)                True
          eval_start_5(v_m,v_n,v_x_0,v_y_0)       -> eval_start_6(v_m,v_n,v_x_0,v_y_0)                True
          eval_start_6(v_m,v_n,v_x_0,v_y_0)       -> eval_start_7(v_m,v_n,v_x_0,v_y_0)                True
          eval_start_7(v_m,v_n,v_x_0,v_y_0)       -> eval_start_8(v_m,v_n,v_x_0,v_y_0)                True
          eval_start_8(v_m,v_n,v_x_0,v_y_0)       -> eval_start_bb1_in(v_m,v_n,0,0)                   True
          eval_start_bb1_in(v_m,v_n,v_x_0,v_y_0)  -> eval_start_bb2_in(v_m,v_n,v_x_0,v_y_0)          
          [-1 + v_n >= v_x_0]
          eval_start_bb1_in(v_m,v_n,v_x_0,v_y_0)  -> eval_start_bb3_in(v_m,v_n,v_x_0,v_y_0)           [v_x_0 >= v_n]
          eval_start_bb2_in(v_m,v_n,v_x_0,v_y_0)  -> eval_start_bb1_in(v_m,v_n,1 + v_x_0,1 + v_y_0)   True
          eval_start_bb3_in(v_m,v_n,v_x_0,v_y_0)  -> eval_start_bb4_in(v_m,v_n,v_x_0,v_y_0)          
          [-1 + v_m >= v_y_0]
          eval_start_bb3_in(v_m,v_n,v_x_0,v_y_0)  -> eval_start_bb5_in(v_m,v_n,v_x_0,v_y_0)           [v_y_0 >= v_m]
          eval_start_bb4_in(v_m,v_n,v_x_0,v_y_0)  -> eval_start_bb1_in(v_m,v_n,1 + v_x_0,1 + v_y_0)   True
          eval_start_bb5_in(v_m,v_n,v_x_0,v_y_0)  -> eval_start_stop(v_m,v_n,v_x_0,v_y_0)             True
        Signature:
          {(eval_start_0,4)
          ;(eval_start_1,4)
          ;(eval_start_2,4)
          ;(eval_start_3,4)
          ;(eval_start_4,4)
          ;(eval_start_5,4)
          ;(eval_start_6,4)
          ;(eval_start_7,4)
          ;(eval_start_8,4)
          ;(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)}
        Rule Graph:
          [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9},9->{10},10->{11,12},11->{13},12->{14,15}
          ,13->{11,12},14->{16},15->{17},16->{11,12},17->{}]
    + Applied Processor:
        Decompose NoGreedy
    + Details:
        We construct a looptree:
          P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17]
          |
          `- p:[11,13,16,14,12] c: [11,13]
             |
             `- p:[12,16,14] c: [12,14,16]
* Step 3: CloseWith YES
    + Considered Problem:
        (Rules:
          eval_start_start(v_m,v_n,v_x_0,v_y_0)   -> eval_start_bb0_in(v_m,v_n,v_x_0,v_y_0)           True
          eval_start_bb0_in(v_m,v_n,v_x_0,v_y_0)  -> eval_start_0(v_m,v_n,v_x_0,v_y_0)                True
          eval_start_0(v_m,v_n,v_x_0,v_y_0)       -> eval_start_1(v_m,v_n,v_x_0,v_y_0)                True
          eval_start_1(v_m,v_n,v_x_0,v_y_0)       -> eval_start_2(v_m,v_n,v_x_0,v_y_0)                True
          eval_start_2(v_m,v_n,v_x_0,v_y_0)       -> eval_start_3(v_m,v_n,v_x_0,v_y_0)                True
          eval_start_3(v_m,v_n,v_x_0,v_y_0)       -> eval_start_4(v_m,v_n,v_x_0,v_y_0)                True
          eval_start_4(v_m,v_n,v_x_0,v_y_0)       -> eval_start_5(v_m,v_n,v_x_0,v_y_0)                True
          eval_start_5(v_m,v_n,v_x_0,v_y_0)       -> eval_start_6(v_m,v_n,v_x_0,v_y_0)                True
          eval_start_6(v_m,v_n,v_x_0,v_y_0)       -> eval_start_7(v_m,v_n,v_x_0,v_y_0)                True
          eval_start_7(v_m,v_n,v_x_0,v_y_0)       -> eval_start_8(v_m,v_n,v_x_0,v_y_0)                True
          eval_start_8(v_m,v_n,v_x_0,v_y_0)       -> eval_start_bb1_in(v_m,v_n,0,0)                   True
          eval_start_bb1_in(v_m,v_n,v_x_0,v_y_0)  -> eval_start_bb2_in(v_m,v_n,v_x_0,v_y_0)          
          [-1 + v_n >= v_x_0]
          eval_start_bb1_in(v_m,v_n,v_x_0,v_y_0)  -> eval_start_bb3_in(v_m,v_n,v_x_0,v_y_0)           [v_x_0 >= v_n]
          eval_start_bb2_in(v_m,v_n,v_x_0,v_y_0)  -> eval_start_bb1_in(v_m,v_n,1 + v_x_0,1 + v_y_0)   True
          eval_start_bb3_in(v_m,v_n,v_x_0,v_y_0)  -> eval_start_bb4_in(v_m,v_n,v_x_0,v_y_0)          
          [-1 + v_m >= v_y_0]
          eval_start_bb3_in(v_m,v_n,v_x_0,v_y_0)  -> eval_start_bb5_in(v_m,v_n,v_x_0,v_y_0)           [v_y_0 >= v_m]
          eval_start_bb4_in(v_m,v_n,v_x_0,v_y_0)  -> eval_start_bb1_in(v_m,v_n,1 + v_x_0,1 + v_y_0)   True
          eval_start_bb5_in(v_m,v_n,v_x_0,v_y_0)  -> eval_start_stop(v_m,v_n,v_x_0,v_y_0)             True
        Signature:
          {(eval_start_0,4)
          ;(eval_start_1,4)
          ;(eval_start_2,4)
          ;(eval_start_3,4)
          ;(eval_start_4,4)
          ;(eval_start_5,4)
          ;(eval_start_6,4)
          ;(eval_start_7,4)
          ;(eval_start_8,4)
          ;(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)}
        Rule Graph:
          [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9},9->{10},10->{11,12},11->{13},12->{14,15}
          ,13->{11,12},14->{16},15->{17},16->{11,12},17->{}]
        ,We construct a looptree:
          P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17]
          |
          `- p:[11,13,16,14,12] c: [11,13]
             |
             `- p:[12,16,14] c: [12,14,16])
    + Applied Processor:
        CloseWith True
    + Details:
        ()

YES