YES
* Step 1: FromIts YES
    + Considered Problem:
        Rules:
          0.  eval_while2_start(v_3,v_N,v_i_0,v_j_0)  -> eval_while2_bb0_in(v_3,v_N,v_i_0,v_j_0)      True              (1,1)
          1.  eval_while2_bb0_in(v_3,v_N,v_i_0,v_j_0) -> eval_while2_0(v_3,v_N,v_i_0,v_j_0)           True              (?,1)
          2.  eval_while2_0(v_3,v_N,v_i_0,v_j_0)      -> eval_while2_1(v_3,v_N,v_i_0,v_j_0)           True              (?,1)
          3.  eval_while2_1(v_3,v_N,v_i_0,v_j_0)      -> eval_while2_2(v_3,v_N,v_i_0,v_j_0)           True              (?,1)
          4.  eval_while2_2(v_3,v_N,v_i_0,v_j_0)      -> eval_while2_3(v_3,v_N,v_i_0,v_j_0)           True              (?,1)
          5.  eval_while2_3(v_3,v_N,v_i_0,v_j_0)      -> eval_while2_4(v_3,v_N,v_i_0,v_j_0)           True              (?,1)
          6.  eval_while2_4(v_3,v_N,v_i_0,v_j_0)      -> eval_while2_bb1_in(v_3,v_N,v_N,v_j_0)        True              (?,1)
          7.  eval_while2_bb1_in(v_3,v_N,v_i_0,v_j_0) -> eval_while2_bb2_in(v_3,v_N,v_i_0,v_N)        [-1 + v_i_0 >= 0] (?,1)
          8.  eval_while2_bb1_in(v_3,v_N,v_i_0,v_j_0) -> eval_while2_bb5_in(v_3,v_N,v_i_0,v_j_0)      [0 >= v_i_0]      (?,1)
          9.  eval_while2_bb2_in(v_3,v_N,v_i_0,v_j_0) -> eval_while2_bb3_in(v_3,v_N,v_i_0,v_j_0)      [-1 + v_j_0 >= 0] (?,1)
          10. eval_while2_bb2_in(v_3,v_N,v_i_0,v_j_0) -> eval_while2_bb4_in(v_3,v_N,v_i_0,v_j_0)      [0 >= v_j_0]      (?,1)
          11. eval_while2_bb3_in(v_3,v_N,v_i_0,v_j_0) -> eval_while2_bb2_in(v_3,v_N,v_i_0,-1 + v_j_0) True              (?,1)
          12. eval_while2_bb4_in(v_3,v_N,v_i_0,v_j_0) -> eval_while2_8(-1 + v_i_0,v_N,v_i_0,v_j_0)    True              (?,1)
          13. eval_while2_8(v_3,v_N,v_i_0,v_j_0)      -> eval_while2_9(v_3,v_N,v_i_0,v_j_0)           True              (?,1)
          14. eval_while2_9(v_3,v_N,v_i_0,v_j_0)      -> eval_while2_bb1_in(v_3,v_N,v_3,v_j_0)        True              (?,1)
          15. eval_while2_bb5_in(v_3,v_N,v_i_0,v_j_0) -> eval_while2_stop(v_3,v_N,v_i_0,v_j_0)        True              (?,1)
        Signature:
          {(eval_while2_0,4)
          ;(eval_while2_1,4)
          ;(eval_while2_2,4)
          ;(eval_while2_3,4)
          ;(eval_while2_4,4)
          ;(eval_while2_8,4)
          ;(eval_while2_9,4)
          ;(eval_while2_bb0_in,4)
          ;(eval_while2_bb1_in,4)
          ;(eval_while2_bb2_in,4)
          ;(eval_while2_bb3_in,4)
          ;(eval_while2_bb4_in,4)
          ;(eval_while2_bb5_in,4)
          ;(eval_while2_start,4)
          ;(eval_while2_stop,4)}
        Flow Graph:
          [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7,8},7->{9,10},8->{15},9->{11},10->{12},11->{9,10},12->{13}
          ,13->{14},14->{7,8},15->{}]
        
    + Applied Processor:
        FromIts
    + Details:
        ()
* Step 2: Decompose YES
    + Considered Problem:
        Rules:
          eval_while2_start(v_3,v_N,v_i_0,v_j_0)   -> eval_while2_bb0_in(v_3,v_N,v_i_0,v_j_0)        True
          eval_while2_bb0_in(v_3,v_N,v_i_0,v_j_0)  -> eval_while2_0(v_3,v_N,v_i_0,v_j_0)             True
          eval_while2_0(v_3,v_N,v_i_0,v_j_0)       -> eval_while2_1(v_3,v_N,v_i_0,v_j_0)             True
          eval_while2_1(v_3,v_N,v_i_0,v_j_0)       -> eval_while2_2(v_3,v_N,v_i_0,v_j_0)             True
          eval_while2_2(v_3,v_N,v_i_0,v_j_0)       -> eval_while2_3(v_3,v_N,v_i_0,v_j_0)             True
          eval_while2_3(v_3,v_N,v_i_0,v_j_0)       -> eval_while2_4(v_3,v_N,v_i_0,v_j_0)             True
          eval_while2_4(v_3,v_N,v_i_0,v_j_0)       -> eval_while2_bb1_in(v_3,v_N,v_N,v_j_0)          True
          eval_while2_bb1_in(v_3,v_N,v_i_0,v_j_0)  -> eval_while2_bb2_in(v_3,v_N,v_i_0,v_N)          [-1 + v_i_0 >= 0]
          eval_while2_bb1_in(v_3,v_N,v_i_0,v_j_0)  -> eval_while2_bb5_in(v_3,v_N,v_i_0,v_j_0)        [0 >= v_i_0]
          eval_while2_bb2_in(v_3,v_N,v_i_0,v_j_0)  -> eval_while2_bb3_in(v_3,v_N,v_i_0,v_j_0)        [-1 + v_j_0 >= 0]
          eval_while2_bb2_in(v_3,v_N,v_i_0,v_j_0)  -> eval_while2_bb4_in(v_3,v_N,v_i_0,v_j_0)        [0 >= v_j_0]
          eval_while2_bb3_in(v_3,v_N,v_i_0,v_j_0)  -> eval_while2_bb2_in(v_3,v_N,v_i_0,-1 + v_j_0)   True
          eval_while2_bb4_in(v_3,v_N,v_i_0,v_j_0)  -> eval_while2_8(-1 + v_i_0,v_N,v_i_0,v_j_0)      True
          eval_while2_8(v_3,v_N,v_i_0,v_j_0)       -> eval_while2_9(v_3,v_N,v_i_0,v_j_0)             True
          eval_while2_9(v_3,v_N,v_i_0,v_j_0)       -> eval_while2_bb1_in(v_3,v_N,v_3,v_j_0)          True
          eval_while2_bb5_in(v_3,v_N,v_i_0,v_j_0)  -> eval_while2_stop(v_3,v_N,v_i_0,v_j_0)          True
        Signature:
          {(eval_while2_0,4)
          ;(eval_while2_1,4)
          ;(eval_while2_2,4)
          ;(eval_while2_3,4)
          ;(eval_while2_4,4)
          ;(eval_while2_8,4)
          ;(eval_while2_9,4)
          ;(eval_while2_bb0_in,4)
          ;(eval_while2_bb1_in,4)
          ;(eval_while2_bb2_in,4)
          ;(eval_while2_bb3_in,4)
          ;(eval_while2_bb4_in,4)
          ;(eval_while2_bb5_in,4)
          ;(eval_while2_start,4)
          ;(eval_while2_stop,4)}
        Rule Graph:
          [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7,8},7->{9,10},8->{15},9->{11},10->{12},11->{9,10},12->{13}
          ,13->{14},14->{7,8},15->{}]
    + 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]
          |
          `- p:[7,14,13,12,10,11,9] c: [7,10,12,13,14]
             |
             `- p:[9,11] c: [9,11]
* Step 3: CloseWith YES
    + Considered Problem:
        (Rules:
          eval_while2_start(v_3,v_N,v_i_0,v_j_0)   -> eval_while2_bb0_in(v_3,v_N,v_i_0,v_j_0)        True
          eval_while2_bb0_in(v_3,v_N,v_i_0,v_j_0)  -> eval_while2_0(v_3,v_N,v_i_0,v_j_0)             True
          eval_while2_0(v_3,v_N,v_i_0,v_j_0)       -> eval_while2_1(v_3,v_N,v_i_0,v_j_0)             True
          eval_while2_1(v_3,v_N,v_i_0,v_j_0)       -> eval_while2_2(v_3,v_N,v_i_0,v_j_0)             True
          eval_while2_2(v_3,v_N,v_i_0,v_j_0)       -> eval_while2_3(v_3,v_N,v_i_0,v_j_0)             True
          eval_while2_3(v_3,v_N,v_i_0,v_j_0)       -> eval_while2_4(v_3,v_N,v_i_0,v_j_0)             True
          eval_while2_4(v_3,v_N,v_i_0,v_j_0)       -> eval_while2_bb1_in(v_3,v_N,v_N,v_j_0)          True
          eval_while2_bb1_in(v_3,v_N,v_i_0,v_j_0)  -> eval_while2_bb2_in(v_3,v_N,v_i_0,v_N)          [-1 + v_i_0 >= 0]
          eval_while2_bb1_in(v_3,v_N,v_i_0,v_j_0)  -> eval_while2_bb5_in(v_3,v_N,v_i_0,v_j_0)        [0 >= v_i_0]
          eval_while2_bb2_in(v_3,v_N,v_i_0,v_j_0)  -> eval_while2_bb3_in(v_3,v_N,v_i_0,v_j_0)        [-1 + v_j_0 >= 0]
          eval_while2_bb2_in(v_3,v_N,v_i_0,v_j_0)  -> eval_while2_bb4_in(v_3,v_N,v_i_0,v_j_0)        [0 >= v_j_0]
          eval_while2_bb3_in(v_3,v_N,v_i_0,v_j_0)  -> eval_while2_bb2_in(v_3,v_N,v_i_0,-1 + v_j_0)   True
          eval_while2_bb4_in(v_3,v_N,v_i_0,v_j_0)  -> eval_while2_8(-1 + v_i_0,v_N,v_i_0,v_j_0)      True
          eval_while2_8(v_3,v_N,v_i_0,v_j_0)       -> eval_while2_9(v_3,v_N,v_i_0,v_j_0)             True
          eval_while2_9(v_3,v_N,v_i_0,v_j_0)       -> eval_while2_bb1_in(v_3,v_N,v_3,v_j_0)          True
          eval_while2_bb5_in(v_3,v_N,v_i_0,v_j_0)  -> eval_while2_stop(v_3,v_N,v_i_0,v_j_0)          True
        Signature:
          {(eval_while2_0,4)
          ;(eval_while2_1,4)
          ;(eval_while2_2,4)
          ;(eval_while2_3,4)
          ;(eval_while2_4,4)
          ;(eval_while2_8,4)
          ;(eval_while2_9,4)
          ;(eval_while2_bb0_in,4)
          ;(eval_while2_bb1_in,4)
          ;(eval_while2_bb2_in,4)
          ;(eval_while2_bb3_in,4)
          ;(eval_while2_bb4_in,4)
          ;(eval_while2_bb5_in,4)
          ;(eval_while2_start,4)
          ;(eval_while2_stop,4)}
        Rule Graph:
          [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7,8},7->{9,10},8->{15},9->{11},10->{12},11->{9,10},12->{13}
          ,13->{14},14->{7,8},15->{}]
        ,We construct a looptree:
          P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]
          |
          `- p:[7,14,13,12,10,11,9] c: [7,10,12,13,14]
             |
             `- p:[9,11] c: [9,11])
    + Applied Processor:
        CloseWith True
    + Details:
        ()

YES