YES(?,O(1))
* Step 1: TrivialSCCs WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0.  eval_relation1_start(v_x,v_y)  -> eval_relation1_bb0_in(v_x,v_y) True (1,1)
          1.  eval_relation1_bb0_in(v_x,v_y) -> eval_relation1_0(v_x,v_y)      True (?,1)
          2.  eval_relation1_0(v_x,v_y)      -> eval_relation1_1(v_x,v_y)      True (?,1)
          3.  eval_relation1_1(v_x,v_y)      -> eval_relation1_2(v_x,v_y)      True (?,1)
          4.  eval_relation1_2(v_x,v_y)      -> eval_relation1_3(v_x,v_y)      True (?,1)
          5.  eval_relation1_3(v_x,v_y)      -> eval_relation1_4(v_x,v_y)      True (?,1)
          6.  eval_relation1_4(v_x,v_y)      -> eval_relation1_5(v_x,v_y)      True (?,1)
          7.  eval_relation1_5(v_x,v_y)      -> eval_relation1_bb1_in(v_x,v_y) True (?,1)
          8.  eval_relation1_bb1_in(v_x,v_y) -> eval_relation1_6(v_x,v_y)      True (?,1)
          9.  eval_relation1_6(v_x,v_y)      -> eval_relation1_7(v_x,v_y)      True (?,1)
          10. eval_relation1_7(v_x,v_y)      -> eval_relation1_bb2_in(v_x,v_y) True (?,1)
          11. eval_relation1_bb2_in(v_x,v_y) -> eval_relation1_stop(v_x,v_y)   True (?,1)
        Signature:
          {(eval_relation1_0,2)
          ;(eval_relation1_1,2)
          ;(eval_relation1_2,2)
          ;(eval_relation1_3,2)
          ;(eval_relation1_4,2)
          ;(eval_relation1_5,2)
          ;(eval_relation1_6,2)
          ;(eval_relation1_7,2)
          ;(eval_relation1_bb0_in,2)
          ;(eval_relation1_bb1_in,2)
          ;(eval_relation1_bb2_in,2)
          ;(eval_relation1_start,2)
          ;(eval_relation1_stop,2)}
        Flow Graph:
          [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9},9->{10},10->{11},11->{}]
        
    + Applied Processor:
        TrivialSCCs
    + Details:
        All trivial SCCs of the transition graph admit timebound 1.
* Step 2: UnsatRules WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0.  eval_relation1_start(v_x,v_y)  -> eval_relation1_bb0_in(v_x,v_y) True (1,1)
          1.  eval_relation1_bb0_in(v_x,v_y) -> eval_relation1_0(v_x,v_y)      True (1,1)
          2.  eval_relation1_0(v_x,v_y)      -> eval_relation1_1(v_x,v_y)      True (1,1)
          3.  eval_relation1_1(v_x,v_y)      -> eval_relation1_2(v_x,v_y)      True (1,1)
          4.  eval_relation1_2(v_x,v_y)      -> eval_relation1_3(v_x,v_y)      True (1,1)
          5.  eval_relation1_3(v_x,v_y)      -> eval_relation1_4(v_x,v_y)      True (1,1)
          6.  eval_relation1_4(v_x,v_y)      -> eval_relation1_5(v_x,v_y)      True (1,1)
          7.  eval_relation1_5(v_x,v_y)      -> eval_relation1_bb1_in(v_x,v_y) True (1,1)
          8.  eval_relation1_bb1_in(v_x,v_y) -> eval_relation1_6(v_x,v_y)      True (1,1)
          9.  eval_relation1_6(v_x,v_y)      -> eval_relation1_7(v_x,v_y)      True (1,1)
          10. eval_relation1_7(v_x,v_y)      -> eval_relation1_bb2_in(v_x,v_y) True (1,1)
          11. eval_relation1_bb2_in(v_x,v_y) -> eval_relation1_stop(v_x,v_y)   True (1,1)
        Signature:
          {(eval_relation1_0,2)
          ;(eval_relation1_1,2)
          ;(eval_relation1_2,2)
          ;(eval_relation1_3,2)
          ;(eval_relation1_4,2)
          ;(eval_relation1_5,2)
          ;(eval_relation1_6,2)
          ;(eval_relation1_7,2)
          ;(eval_relation1_bb0_in,2)
          ;(eval_relation1_bb1_in,2)
          ;(eval_relation1_bb2_in,2)
          ;(eval_relation1_start,2)
          ;(eval_relation1_stop,2)}
        Flow Graph:
          [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9},9->{10},10->{11},11->{}]
        
    + Applied Processor:
        UnsatRules
    + Details:
        The problem is already solved.

YES(?,O(1))