YES(?,O(n^1)) * Step 1: UnsatPaths WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_start_start(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb0_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) True (1,1) 1. eval_start_bb0_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_0(v_1,v_3,v_n,v_x_0,v_x_0_sink) True (?,1) 2. eval_start_0(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_1(v_1,v_3,v_n,v_x_0,v_x_0_sink) True (?,1) 3. eval_start_1(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_2(v_1,v_3,v_n,v_x_0,v_x_0_sink) True (?,1) 4. eval_start_2(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_3(v_1,v_3,v_n,v_x_0,v_x_0_sink) True (?,1) 5. eval_start_3(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb1_in(v_1,v_3,v_n,0,v_x_0_sink) True (?,1) 6. eval_start_bb1_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_x_0) [v_x_0 >= 0 && -1 + v_n >= v_x_0] (?,1) 7. eval_start_bb1_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb4_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) [v_x_0 >= 0 && v_x_0 >= v_n] (?,1) 8. eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb3_in(1 + v_x_0_sink,v_3,v_n,v_x_0,v_x_0_sink) [-1 + v_n + -1*v_x_0_sink >= 0 (?,1) && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -1 + v_n + v_x_0_sink >= 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 + v_n >= 1 + v_x_0_sink] 9. eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb1_in(v_1,v_3,v_n,1 + v_x_0_sink,v_x_0_sink) [-1 + v_n + -1*v_x_0_sink >= 0 (?,1) && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -1 + v_n + v_x_0_sink >= 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 + v_x_0_sink >= v_n] 10. eval_start_bb3_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_6(v_1,v_3,v_n,v_x_0,v_x_0_sink) [-2 + v_n + -1*v_x_0_sink >= 0 (?,1) && -1 + v_1 + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -2 + v_n + v_x_0_sink >= 0 && -1 + v_1 + v_x_0_sink >= 0 && 1 + -1*v_1 + v_x_0_sink >= 0 && -2 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -2 + v_n + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && -2 + v_n >= 0 && -3 + v_1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1 + v_1 >= 0] 11. eval_start_6(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_7(v_1,nondef_0,v_n,v_x_0,v_x_0_sink) [-2 + v_n + -1*v_x_0_sink >= 0 (?,1) && -1 + v_1 + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -2 + v_n + v_x_0_sink >= 0 && -1 + v_1 + v_x_0_sink >= 0 && 1 + -1*v_1 + v_x_0_sink >= 0 && -2 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -2 + v_n + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && -2 + v_n >= 0 && -3 + v_1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1 + v_1 >= 0] 12. eval_start_7(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb1_in(v_1,v_3,v_n,v_1,v_x_0_sink) [-2 + v_n + -1*v_x_0_sink >= 0 (?,1) && -1 + v_1 + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -2 + v_n + v_x_0_sink >= 0 && -1 + v_1 + v_x_0_sink >= 0 && 1 + -1*v_1 + v_x_0_sink >= 0 && -2 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -2 + v_n + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && -2 + v_n >= 0 && -3 + v_1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1 + v_1 >= 0 && -1 + v_3 >= 0] 13. eval_start_7(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_1) [-2 + v_n + -1*v_x_0_sink >= 0 (?,1) && -1 + v_1 + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -2 + v_n + v_x_0_sink >= 0 && -1 + v_1 + v_x_0_sink >= 0 && 1 + -1*v_1 + v_x_0_sink >= 0 && -2 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -2 + v_n + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && -2 + v_n >= 0 && -3 + v_1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1 + v_1 >= 0 && 0 >= v_3] 14. eval_start_bb4_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_stop(v_1,v_3,v_n,v_x_0,v_x_0_sink) [v_x_0 >= 0 && -1*v_n + v_x_0 >= 0] (?,1) Signature: {(eval_start_0,5) ;(eval_start_1,5) ;(eval_start_2,5) ;(eval_start_3,5) ;(eval_start_6,5) ;(eval_start_7,5) ;(eval_start_bb0_in,5) ;(eval_start_bb1_in,5) ;(eval_start_bb2_in,5) ;(eval_start_bb3_in,5) ;(eval_start_bb4_in,5) ;(eval_start_start,5) ;(eval_start_stop,5)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6,7},6->{8,9},7->{14},8->{10},9->{6,7},10->{11},11->{12,13},12->{6 ,7},13->{8,9},14->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(9,6),(12,7)] * Step 2: FromIts WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_start_start(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb0_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) True (1,1) 1. eval_start_bb0_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_0(v_1,v_3,v_n,v_x_0,v_x_0_sink) True (?,1) 2. eval_start_0(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_1(v_1,v_3,v_n,v_x_0,v_x_0_sink) True (?,1) 3. eval_start_1(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_2(v_1,v_3,v_n,v_x_0,v_x_0_sink) True (?,1) 4. eval_start_2(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_3(v_1,v_3,v_n,v_x_0,v_x_0_sink) True (?,1) 5. eval_start_3(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb1_in(v_1,v_3,v_n,0,v_x_0_sink) True (?,1) 6. eval_start_bb1_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_x_0) [v_x_0 >= 0 && -1 + v_n >= v_x_0] (?,1) 7. eval_start_bb1_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb4_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) [v_x_0 >= 0 && v_x_0 >= v_n] (?,1) 8. eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb3_in(1 + v_x_0_sink,v_3,v_n,v_x_0,v_x_0_sink) [-1 + v_n + -1*v_x_0_sink >= 0 (?,1) && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -1 + v_n + v_x_0_sink >= 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 + v_n >= 1 + v_x_0_sink] 9. eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb1_in(v_1,v_3,v_n,1 + v_x_0_sink,v_x_0_sink) [-1 + v_n + -1*v_x_0_sink >= 0 (?,1) && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -1 + v_n + v_x_0_sink >= 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 + v_x_0_sink >= v_n] 10. eval_start_bb3_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_6(v_1,v_3,v_n,v_x_0,v_x_0_sink) [-2 + v_n + -1*v_x_0_sink >= 0 (?,1) && -1 + v_1 + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -2 + v_n + v_x_0_sink >= 0 && -1 + v_1 + v_x_0_sink >= 0 && 1 + -1*v_1 + v_x_0_sink >= 0 && -2 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -2 + v_n + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && -2 + v_n >= 0 && -3 + v_1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1 + v_1 >= 0] 11. eval_start_6(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_7(v_1,nondef_0,v_n,v_x_0,v_x_0_sink) [-2 + v_n + -1*v_x_0_sink >= 0 (?,1) && -1 + v_1 + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -2 + v_n + v_x_0_sink >= 0 && -1 + v_1 + v_x_0_sink >= 0 && 1 + -1*v_1 + v_x_0_sink >= 0 && -2 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -2 + v_n + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && -2 + v_n >= 0 && -3 + v_1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1 + v_1 >= 0] 12. eval_start_7(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb1_in(v_1,v_3,v_n,v_1,v_x_0_sink) [-2 + v_n + -1*v_x_0_sink >= 0 (?,1) && -1 + v_1 + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -2 + v_n + v_x_0_sink >= 0 && -1 + v_1 + v_x_0_sink >= 0 && 1 + -1*v_1 + v_x_0_sink >= 0 && -2 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -2 + v_n + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && -2 + v_n >= 0 && -3 + v_1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1 + v_1 >= 0 && -1 + v_3 >= 0] 13. eval_start_7(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_1) [-2 + v_n + -1*v_x_0_sink >= 0 (?,1) && -1 + v_1 + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -2 + v_n + v_x_0_sink >= 0 && -1 + v_1 + v_x_0_sink >= 0 && 1 + -1*v_1 + v_x_0_sink >= 0 && -2 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -2 + v_n + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && -2 + v_n >= 0 && -3 + v_1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1 + v_1 >= 0 && 0 >= v_3] 14. eval_start_bb4_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_stop(v_1,v_3,v_n,v_x_0,v_x_0_sink) [v_x_0 >= 0 && -1*v_n + v_x_0 >= 0] (?,1) Signature: {(eval_start_0,5) ;(eval_start_1,5) ;(eval_start_2,5) ;(eval_start_3,5) ;(eval_start_6,5) ;(eval_start_7,5) ;(eval_start_bb0_in,5) ;(eval_start_bb1_in,5) ;(eval_start_bb2_in,5) ;(eval_start_bb3_in,5) ;(eval_start_bb4_in,5) ;(eval_start_start,5) ;(eval_start_stop,5)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6,7},6->{8,9},7->{14},8->{10},9->{7},10->{11},11->{12,13},12->{6} ,13->{8,9},14->{}] + Applied Processor: FromIts + Details: () * Step 3: AddSinks WORST_CASE(?,O(n^1)) + Considered Problem: Rules: eval_start_start(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb0_in(v_1,v_3,v_n,v_x_0 ,v_x_0_sink) True eval_start_bb0_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_0(v_1,v_3,v_n,v_x_0 ,v_x_0_sink) True eval_start_0(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_1(v_1,v_3,v_n,v_x_0 ,v_x_0_sink) True eval_start_1(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_2(v_1,v_3,v_n,v_x_0 ,v_x_0_sink) True eval_start_2(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_3(v_1,v_3,v_n,v_x_0 ,v_x_0_sink) True eval_start_3(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb1_in(v_1,v_3,v_n,0 ,v_x_0_sink) True eval_start_bb1_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb2_in(v_1,v_3,v_n,v_x_0 ,v_x_0) [v_x_0 >= 0 && -1 + v_n >= v_x_0] eval_start_bb1_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb4_in(v_1,v_3,v_n,v_x_0 ,v_x_0_sink) [v_x_0 >= 0 && v_x_0 >= v_n] eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb3_in(1 + v_x_0_sink,v_3,v_n,v_x_0 ,v_x_0_sink) [-1 + v_n + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -1 + v_n + v_x_0_sink >= 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 + v_n >= 1 + v_x_0_sink] eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb1_in(v_1,v_3,v_n,1 + v_x_0_sink ,v_x_0_sink) [-1 + v_n + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -1 + v_n + v_x_0_sink >= 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 + v_x_0_sink >= v_n] eval_start_bb3_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_6(v_1,v_3,v_n,v_x_0 ,v_x_0_sink) [-2 + v_n + -1*v_x_0_sink >= 0 && -1 + v_1 + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -2 + v_n + v_x_0_sink >= 0 && -1 + v_1 + v_x_0_sink >= 0 && 1 + -1*v_1 + v_x_0_sink >= 0 && -2 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -2 + v_n + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && -2 + v_n >= 0 && -3 + v_1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1 + v_1 >= 0] eval_start_6(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_7(v_1,nondef_0,v_n,v_x_0 ,v_x_0_sink) [-2 + v_n + -1*v_x_0_sink >= 0 && -1 + v_1 + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -2 + v_n + v_x_0_sink >= 0 && -1 + v_1 + v_x_0_sink >= 0 && 1 + -1*v_1 + v_x_0_sink >= 0 && -2 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -2 + v_n + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && -2 + v_n >= 0 && -3 + v_1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1 + v_1 >= 0] eval_start_7(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb1_in(v_1,v_3,v_n,v_1 ,v_x_0_sink) [-2 + v_n + -1*v_x_0_sink >= 0 && -1 + v_1 + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -2 + v_n + v_x_0_sink >= 0 && -1 + v_1 + v_x_0_sink >= 0 && 1 + -1*v_1 + v_x_0_sink >= 0 && -2 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -2 + v_n + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && -2 + v_n >= 0 && -3 + v_1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1 + v_1 >= 0 && -1 + v_3 >= 0] eval_start_7(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb2_in(v_1,v_3,v_n,v_x_0 ,v_1) [-2 + v_n + -1*v_x_0_sink >= 0 && -1 + v_1 + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -2 + v_n + v_x_0_sink >= 0 && -1 + v_1 + v_x_0_sink >= 0 && 1 + -1*v_1 + v_x_0_sink >= 0 && -2 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -2 + v_n + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && -2 + v_n >= 0 && -3 + v_1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1 + v_1 >= 0 && 0 >= v_3] eval_start_bb4_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_stop(v_1,v_3,v_n,v_x_0 ,v_x_0_sink) [v_x_0 >= 0 && -1*v_n + v_x_0 >= 0] Signature: {(eval_start_0,5) ;(eval_start_1,5) ;(eval_start_2,5) ;(eval_start_3,5) ;(eval_start_6,5) ;(eval_start_7,5) ;(eval_start_bb0_in,5) ;(eval_start_bb1_in,5) ;(eval_start_bb2_in,5) ;(eval_start_bb3_in,5) ;(eval_start_bb4_in,5) ;(eval_start_start,5) ;(eval_start_stop,5)} Rule Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6,7},6->{8,9},7->{14},8->{10},9->{7},10->{11},11->{12,13},12->{6} ,13->{8,9},14->{}] + Applied Processor: AddSinks + Details: () * Step 4: Decompose WORST_CASE(?,O(n^1)) + Considered Problem: Rules: eval_start_start(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb0_in(v_1,v_3,v_n,v_x_0 ,v_x_0_sink) True eval_start_bb0_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_0(v_1,v_3,v_n,v_x_0 ,v_x_0_sink) True eval_start_0(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_1(v_1,v_3,v_n,v_x_0 ,v_x_0_sink) True eval_start_1(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_2(v_1,v_3,v_n,v_x_0 ,v_x_0_sink) True eval_start_2(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_3(v_1,v_3,v_n,v_x_0 ,v_x_0_sink) True eval_start_3(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb1_in(v_1,v_3,v_n,0 ,v_x_0_sink) True eval_start_bb1_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb2_in(v_1,v_3,v_n,v_x_0 ,v_x_0) [v_x_0 >= 0 && -1 + v_n >= v_x_0] eval_start_bb1_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb4_in(v_1,v_3,v_n,v_x_0 ,v_x_0_sink) [v_x_0 >= 0 && v_x_0 >= v_n] eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb3_in(1 + v_x_0_sink,v_3,v_n,v_x_0 ,v_x_0_sink) [-1 + v_n + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -1 + v_n + v_x_0_sink >= 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 + v_n >= 1 + v_x_0_sink] eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb1_in(v_1,v_3,v_n,1 + v_x_0_sink ,v_x_0_sink) [-1 + v_n + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -1 + v_n + v_x_0_sink >= 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 + v_x_0_sink >= v_n] eval_start_bb3_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_6(v_1,v_3,v_n,v_x_0 ,v_x_0_sink) [-2 + v_n + -1*v_x_0_sink >= 0 && -1 + v_1 + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -2 + v_n + v_x_0_sink >= 0 && -1 + v_1 + v_x_0_sink >= 0 && 1 + -1*v_1 + v_x_0_sink >= 0 && -2 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -2 + v_n + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && -2 + v_n >= 0 && -3 + v_1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1 + v_1 >= 0] eval_start_6(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_7(v_1,nondef_0,v_n,v_x_0 ,v_x_0_sink) [-2 + v_n + -1*v_x_0_sink >= 0 && -1 + v_1 + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -2 + v_n + v_x_0_sink >= 0 && -1 + v_1 + v_x_0_sink >= 0 && 1 + -1*v_1 + v_x_0_sink >= 0 && -2 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -2 + v_n + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && -2 + v_n >= 0 && -3 + v_1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1 + v_1 >= 0] eval_start_7(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb1_in(v_1,v_3,v_n,v_1 ,v_x_0_sink) [-2 + v_n + -1*v_x_0_sink >= 0 && -1 + v_1 + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -2 + v_n + v_x_0_sink >= 0 && -1 + v_1 + v_x_0_sink >= 0 && 1 + -1*v_1 + v_x_0_sink >= 0 && -2 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -2 + v_n + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && -2 + v_n >= 0 && -3 + v_1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1 + v_1 >= 0 && -1 + v_3 >= 0] eval_start_7(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb2_in(v_1,v_3,v_n,v_x_0 ,v_1) [-2 + v_n + -1*v_x_0_sink >= 0 && -1 + v_1 + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -2 + v_n + v_x_0_sink >= 0 && -1 + v_1 + v_x_0_sink >= 0 && 1 + -1*v_1 + v_x_0_sink >= 0 && -2 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -2 + v_n + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && -2 + v_n >= 0 && -3 + v_1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1 + v_1 >= 0 && 0 >= v_3] eval_start_bb4_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_stop(v_1,v_3,v_n,v_x_0 ,v_x_0_sink) [v_x_0 >= 0 && -1*v_n + v_x_0 >= 0] eval_start_stop(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> exitus616(v_1,v_3,v_n,v_x_0 ,v_x_0_sink) True Signature: {(eval_start_0,5) ;(eval_start_1,5) ;(eval_start_2,5) ;(eval_start_3,5) ;(eval_start_6,5) ;(eval_start_7,5) ;(eval_start_bb0_in,5) ;(eval_start_bb1_in,5) ;(eval_start_bb2_in,5) ;(eval_start_bb3_in,5) ;(eval_start_bb4_in,5) ;(eval_start_start,5) ;(eval_start_stop,5) ;(exitus616,5)} Rule Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6,7},6->{8,9},7->{14},8->{10},9->{7},10->{11},11->{12,13},12->{6} ,13->{8,9},14->{15}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15] | `- p:[6,12,11,10,8,13] c: [6,8,10,11,12,13] * Step 5: AbstractSize WORST_CASE(?,O(n^1)) + Considered Problem: (Rules: eval_start_start(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb0_in(v_1,v_3,v_n,v_x_0 ,v_x_0_sink) True eval_start_bb0_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_0(v_1,v_3,v_n,v_x_0 ,v_x_0_sink) True eval_start_0(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_1(v_1,v_3,v_n,v_x_0 ,v_x_0_sink) True eval_start_1(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_2(v_1,v_3,v_n,v_x_0 ,v_x_0_sink) True eval_start_2(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_3(v_1,v_3,v_n,v_x_0 ,v_x_0_sink) True eval_start_3(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb1_in(v_1,v_3,v_n,0 ,v_x_0_sink) True eval_start_bb1_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb2_in(v_1,v_3,v_n,v_x_0 ,v_x_0) [v_x_0 >= 0 && -1 + v_n >= v_x_0] eval_start_bb1_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb4_in(v_1,v_3,v_n,v_x_0 ,v_x_0_sink) [v_x_0 >= 0 && v_x_0 >= v_n] eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb3_in(1 + v_x_0_sink,v_3,v_n,v_x_0 ,v_x_0_sink) [-1 + v_n + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -1 + v_n + v_x_0_sink >= 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 + v_n >= 1 + v_x_0_sink] eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb1_in(v_1,v_3,v_n,1 + v_x_0_sink ,v_x_0_sink) [-1 + v_n + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -1 + v_n + v_x_0_sink >= 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 + v_x_0_sink >= v_n] eval_start_bb3_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_6(v_1,v_3,v_n,v_x_0 ,v_x_0_sink) [-2 + v_n + -1*v_x_0_sink >= 0 && -1 + v_1 + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -2 + v_n + v_x_0_sink >= 0 && -1 + v_1 + v_x_0_sink >= 0 && 1 + -1*v_1 + v_x_0_sink >= 0 && -2 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -2 + v_n + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && -2 + v_n >= 0 && -3 + v_1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1 + v_1 >= 0] eval_start_6(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_7(v_1,nondef_0,v_n,v_x_0 ,v_x_0_sink) [-2 + v_n + -1*v_x_0_sink >= 0 && -1 + v_1 + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -2 + v_n + v_x_0_sink >= 0 && -1 + v_1 + v_x_0_sink >= 0 && 1 + -1*v_1 + v_x_0_sink >= 0 && -2 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -2 + v_n + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && -2 + v_n >= 0 && -3 + v_1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1 + v_1 >= 0] eval_start_7(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb1_in(v_1,v_3,v_n,v_1 ,v_x_0_sink) [-2 + v_n + -1*v_x_0_sink >= 0 && -1 + v_1 + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -2 + v_n + v_x_0_sink >= 0 && -1 + v_1 + v_x_0_sink >= 0 && 1 + -1*v_1 + v_x_0_sink >= 0 && -2 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -2 + v_n + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && -2 + v_n >= 0 && -3 + v_1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1 + v_1 >= 0 && -1 + v_3 >= 0] eval_start_7(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb2_in(v_1,v_3,v_n,v_x_0 ,v_1) [-2 + v_n + -1*v_x_0_sink >= 0 && -1 + v_1 + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -2 + v_n + v_x_0_sink >= 0 && -1 + v_1 + v_x_0_sink >= 0 && 1 + -1*v_1 + v_x_0_sink >= 0 && -2 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -2 + v_n + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && -2 + v_n >= 0 && -3 + v_1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1 + v_1 >= 0 && 0 >= v_3] eval_start_bb4_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_stop(v_1,v_3,v_n,v_x_0 ,v_x_0_sink) [v_x_0 >= 0 && -1*v_n + v_x_0 >= 0] eval_start_stop(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> exitus616(v_1,v_3,v_n,v_x_0 ,v_x_0_sink) True Signature: {(eval_start_0,5) ;(eval_start_1,5) ;(eval_start_2,5) ;(eval_start_3,5) ;(eval_start_6,5) ;(eval_start_7,5) ;(eval_start_bb0_in,5) ;(eval_start_bb1_in,5) ;(eval_start_bb2_in,5) ;(eval_start_bb3_in,5) ;(eval_start_bb4_in,5) ;(eval_start_start,5) ;(eval_start_stop,5) ;(exitus616,5)} Rule Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6,7},6->{8,9},7->{14},8->{10},9->{7},10->{11},11->{12,13},12->{6} ,13->{8,9},14->{15}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15] | `- p:[6,12,11,10,8,13] c: [6,8,10,11,12,13]) + Applied Processor: AbstractSize Minimize + Details: () * Step 6: AbstractFlow WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [v_1,v_3,v_n,v_x_0,v_x_0_sink,0.0] eval_start_start ~> eval_start_bb0_in [v_1 <= v_1, v_3 <= v_3, v_n <= v_n, v_x_0 <= v_x_0, v_x_0_sink <= v_x_0_sink] eval_start_bb0_in ~> eval_start_0 [v_1 <= v_1, v_3 <= v_3, v_n <= v_n, v_x_0 <= v_x_0, v_x_0_sink <= v_x_0_sink] eval_start_0 ~> eval_start_1 [v_1 <= v_1, v_3 <= v_3, v_n <= v_n, v_x_0 <= v_x_0, v_x_0_sink <= v_x_0_sink] eval_start_1 ~> eval_start_2 [v_1 <= v_1, v_3 <= v_3, v_n <= v_n, v_x_0 <= v_x_0, v_x_0_sink <= v_x_0_sink] eval_start_2 ~> eval_start_3 [v_1 <= v_1, v_3 <= v_3, v_n <= v_n, v_x_0 <= v_x_0, v_x_0_sink <= v_x_0_sink] eval_start_3 ~> eval_start_bb1_in [v_1 <= v_1, v_3 <= v_3, v_n <= v_n, v_x_0 <= 0*K, v_x_0_sink <= v_x_0_sink] eval_start_bb1_in ~> eval_start_bb2_in [v_1 <= v_1, v_3 <= v_3, v_n <= v_n, v_x_0 <= v_x_0, v_x_0_sink <= v_x_0] eval_start_bb1_in ~> eval_start_bb4_in [v_1 <= v_1, v_3 <= v_3, v_n <= v_n, v_x_0 <= v_x_0, v_x_0_sink <= v_x_0_sink] eval_start_bb2_in ~> eval_start_bb3_in [v_1 <= v_n, v_3 <= v_3, v_n <= v_n, v_x_0 <= v_x_0, v_x_0_sink <= v_x_0_sink] eval_start_bb2_in ~> eval_start_bb1_in [v_1 <= v_1, v_3 <= v_3, v_n <= v_n, v_x_0 <= v_n, v_x_0_sink <= v_x_0_sink] eval_start_bb3_in ~> eval_start_6 [v_1 <= v_1, v_3 <= v_3, v_n <= v_n, v_x_0 <= v_x_0, v_x_0_sink <= v_x_0_sink] eval_start_6 ~> eval_start_7 [v_1 <= v_1, v_3 <= unknown, v_n <= v_n, v_x_0 <= v_x_0, v_x_0_sink <= v_x_0_sink] eval_start_7 ~> eval_start_bb1_in [v_1 <= v_1, v_3 <= v_3, v_n <= v_n, v_x_0 <= v_1, v_x_0_sink <= v_x_0_sink] eval_start_7 ~> eval_start_bb2_in [v_1 <= v_1, v_3 <= v_3, v_n <= v_n, v_x_0 <= v_x_0, v_x_0_sink <= v_1] eval_start_bb4_in ~> eval_start_stop [v_1 <= v_1, v_3 <= v_3, v_n <= v_n, v_x_0 <= v_x_0, v_x_0_sink <= v_x_0_sink] eval_start_stop ~> exitus616 [v_1 <= v_1, v_3 <= v_3, v_n <= v_n, v_x_0 <= v_x_0, v_x_0_sink <= v_x_0_sink] + Loop: [0.0 <= 2*K + v_n + v_x_0] eval_start_bb1_in ~> eval_start_bb2_in [v_1 <= v_1, v_3 <= v_3, v_n <= v_n, v_x_0 <= v_x_0, v_x_0_sink <= v_x_0] eval_start_7 ~> eval_start_bb1_in [v_1 <= v_1, v_3 <= v_3, v_n <= v_n, v_x_0 <= v_1, v_x_0_sink <= v_x_0_sink] eval_start_6 ~> eval_start_7 [v_1 <= v_1, v_3 <= unknown, v_n <= v_n, v_x_0 <= v_x_0, v_x_0_sink <= v_x_0_sink] eval_start_bb3_in ~> eval_start_6 [v_1 <= v_1, v_3 <= v_3, v_n <= v_n, v_x_0 <= v_x_0, v_x_0_sink <= v_x_0_sink] eval_start_bb2_in ~> eval_start_bb3_in [v_1 <= v_n, v_3 <= v_3, v_n <= v_n, v_x_0 <= v_x_0, v_x_0_sink <= v_x_0_sink] eval_start_7 ~> eval_start_bb2_in [v_1 <= v_1, v_3 <= v_3, v_n <= v_n, v_x_0 <= v_x_0, v_x_0_sink <= v_1] + Applied Processor: AbstractFlow + Details: () * Step 7: Lare WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [tick,huge,K,v_1,v_3,v_n,v_x_0,v_x_0_sink,0.0] eval_start_start ~> eval_start_bb0_in [] eval_start_bb0_in ~> eval_start_0 [] eval_start_0 ~> eval_start_1 [] eval_start_1 ~> eval_start_2 [] eval_start_2 ~> eval_start_3 [] eval_start_3 ~> eval_start_bb1_in [K ~=> v_x_0] eval_start_bb1_in ~> eval_start_bb2_in [v_x_0 ~=> v_x_0_sink] eval_start_bb1_in ~> eval_start_bb4_in [] eval_start_bb2_in ~> eval_start_bb3_in [v_n ~=> v_1] eval_start_bb2_in ~> eval_start_bb1_in [v_n ~=> v_x_0] eval_start_bb3_in ~> eval_start_6 [] eval_start_6 ~> eval_start_7 [huge ~=> v_3] eval_start_7 ~> eval_start_bb1_in [v_1 ~=> v_x_0] eval_start_7 ~> eval_start_bb2_in [v_1 ~=> v_x_0_sink] eval_start_bb4_in ~> eval_start_stop [] eval_start_stop ~> exitus616 [] + Loop: [v_n ~+> 0.0,v_x_0 ~+> 0.0,K ~*> 0.0] eval_start_bb1_in ~> eval_start_bb2_in [v_x_0 ~=> v_x_0_sink] eval_start_7 ~> eval_start_bb1_in [v_1 ~=> v_x_0] eval_start_6 ~> eval_start_7 [huge ~=> v_3] eval_start_bb3_in ~> eval_start_6 [] eval_start_bb2_in ~> eval_start_bb3_in [v_n ~=> v_1] eval_start_7 ~> eval_start_bb2_in [v_1 ~=> v_x_0_sink] + Applied Processor: Lare + Details: eval_start_start ~> exitus616 [v_n ~=> v_1 ,v_n ~=> v_x_0 ,v_n ~=> v_x_0_sink ,K ~=> v_x_0 ,K ~=> v_x_0_sink ,huge ~=> v_3 ,v_n ~+> 0.0 ,v_n ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> tick ,K ~*> 0.0 ,K ~*> tick] + eval_start_bb2_in> [v_n ~=> v_1 ,v_n ~=> v_x_0 ,v_n ~=> v_x_0_sink ,v_x_0 ~=> v_x_0_sink ,huge ~=> v_3 ,v_n ~+> 0.0 ,v_n ~+> tick ,v_x_0 ~+> 0.0 ,v_x_0 ~+> tick ,tick ~+> tick ,K ~*> 0.0 ,K ~*> tick] eval_start_bb1_in> [v_n ~=> v_1 ,v_n ~=> v_x_0 ,v_n ~=> v_x_0_sink ,v_x_0 ~=> v_x_0_sink ,huge ~=> v_3 ,v_n ~+> 0.0 ,v_n ~+> tick ,v_x_0 ~+> 0.0 ,v_x_0 ~+> tick ,tick ~+> tick ,K ~*> 0.0 ,K ~*> tick] YES(?,O(n^1))