YES(?,O(n^1)) * Step 1: FromIts WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_start_start(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb0_in(v__0,v__01,v_1,v_x,v_y) True (1,1) 1. eval_start_bb0_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_0(v__0,v__01,v_1,v_x,v_y) True (?,1) 2. eval_start_0(v__0,v__01,v_1,v_x,v_y) -> eval_start_1(v__0,v__01,v_1,v_x,v_y) True (?,1) 3. eval_start_1(v__0,v__01,v_1,v_x,v_y) -> eval_start_2(v__0,v__01,v_1,v_x,v_y) True (?,1) 4. eval_start_2(v__0,v__01,v_1,v_x,v_y) -> eval_start_3(v__0,v__01,v_1,v_x,v_y) True (?,1) 5. eval_start_3(v__0,v__01,v_1,v_x,v_y) -> eval_start_4(v__0,v__01,v_1,v_x,v_y) True (?,1) 6. eval_start_4(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb1_in(v_x,v_y,v_1,v_x,v_y) True (?,1) 7. eval_start_bb1_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb2_in(v__0,v__01,v_1,v_x,v_y) [v__01 + -1*v_y >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 >= v__01] (?,1) 8. eval_start_bb1_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb3_in(v__0,v__01,v_1,v_x,v_y) [v__01 + -1*v_y >= 0 && -1*v__0 + v_x >= 0 && v__01 >= v__0] (?,1) 9. eval_start_bb2_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_5(v__0,v__01,v_1,v_x,v_y) [-1 + v_x + -1*v_y >= 0 (?,1) && v__01 + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + -1*v__01 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 + -1*v__01 >= 0] 10. eval_start_5(v__0,v__01,v_1,v_x,v_y) -> eval_start_6(v__0,v__01,nondef_0,v_x,v_y) [-1 + v_x + -1*v_y >= 0 (?,1) && v__01 + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + -1*v__01 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 + -1*v__01 >= 0] 11. eval_start_6(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb1_in(v__0,1 + v__01,v_1,v_x,v_y) [-1 + v_x + -1*v_y >= 0 (?,1) && v__01 + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + -1*v__01 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 + -1*v__01 >= 0 && -1 + v_1 >= 0] 12. eval_start_6(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb1_in(-1 + v__0,v__01,v_1,v_x,v_y) [-1 + v_x + -1*v_y >= 0 (?,1) && v__01 + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + -1*v__01 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 + -1*v__01 >= 0 && 0 >= v_1] 13. eval_start_bb3_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_stop(v__0,v__01,v_1,v_x,v_y) [v__01 + -1*v_y >= 0 && -1*v__0 + v_x >= 0 && -1*v__0 + v__01 >= 0] (?,1) Signature: {(eval_start_0,5) ;(eval_start_1,5) ;(eval_start_2,5) ;(eval_start_3,5) ;(eval_start_4,5) ;(eval_start_5,5) ;(eval_start_6,5) ;(eval_start_bb0_in,5) ;(eval_start_bb1_in,5) ;(eval_start_bb2_in,5) ;(eval_start_bb3_in,5) ;(eval_start_start,5) ;(eval_start_stop,5)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7,8},7->{9},8->{13},9->{10},10->{11,12},11->{7,8},12->{7,8} ,13->{}] + Applied Processor: FromIts + Details: () * Step 2: AddSinks WORST_CASE(?,O(n^1)) + Considered Problem: Rules: eval_start_start(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb0_in(v__0,v__01,v_1,v_x,v_y) True eval_start_bb0_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_0(v__0,v__01,v_1,v_x,v_y) True eval_start_0(v__0,v__01,v_1,v_x,v_y) -> eval_start_1(v__0,v__01,v_1,v_x,v_y) True eval_start_1(v__0,v__01,v_1,v_x,v_y) -> eval_start_2(v__0,v__01,v_1,v_x,v_y) True eval_start_2(v__0,v__01,v_1,v_x,v_y) -> eval_start_3(v__0,v__01,v_1,v_x,v_y) True eval_start_3(v__0,v__01,v_1,v_x,v_y) -> eval_start_4(v__0,v__01,v_1,v_x,v_y) True eval_start_4(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb1_in(v_x,v_y,v_1,v_x,v_y) True eval_start_bb1_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb2_in(v__0,v__01,v_1,v_x,v_y) [v__01 + -1*v_y >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 >= v__01] eval_start_bb1_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb3_in(v__0,v__01,v_1,v_x,v_y) [v__01 + -1*v_y >= 0 && -1*v__0 + v_x >= 0 && v__01 >= v__0] eval_start_bb2_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_5(v__0,v__01,v_1,v_x,v_y) [-1 + v_x + -1*v_y >= 0 && v__01 + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + -1*v__01 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 + -1*v__01 >= 0] eval_start_5(v__0,v__01,v_1,v_x,v_y) -> eval_start_6(v__0,v__01,nondef_0,v_x,v_y) [-1 + v_x + -1*v_y >= 0 && v__01 + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + -1*v__01 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 + -1*v__01 >= 0] eval_start_6(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb1_in(v__0,1 + v__01,v_1,v_x,v_y) [-1 + v_x + -1*v_y >= 0 && v__01 + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + -1*v__01 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 + -1*v__01 >= 0 && -1 + v_1 >= 0] eval_start_6(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb1_in(-1 + v__0,v__01,v_1,v_x,v_y) [-1 + v_x + -1*v_y >= 0 && v__01 + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + -1*v__01 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 + -1*v__01 >= 0 && 0 >= v_1] eval_start_bb3_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_stop(v__0,v__01,v_1,v_x,v_y) [v__01 + -1*v_y >= 0 && -1*v__0 + v_x >= 0 && -1*v__0 + v__01 >= 0] Signature: {(eval_start_0,5) ;(eval_start_1,5) ;(eval_start_2,5) ;(eval_start_3,5) ;(eval_start_4,5) ;(eval_start_5,5) ;(eval_start_6,5) ;(eval_start_bb0_in,5) ;(eval_start_bb1_in,5) ;(eval_start_bb2_in,5) ;(eval_start_bb3_in,5) ;(eval_start_start,5) ;(eval_start_stop,5)} Rule Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7,8},7->{9},8->{13},9->{10},10->{11,12},11->{7,8},12->{7,8} ,13->{}] + Applied Processor: AddSinks + Details: () * Step 3: Decompose WORST_CASE(?,O(n^1)) + Considered Problem: Rules: eval_start_start(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb0_in(v__0,v__01,v_1,v_x,v_y) True eval_start_bb0_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_0(v__0,v__01,v_1,v_x,v_y) True eval_start_0(v__0,v__01,v_1,v_x,v_y) -> eval_start_1(v__0,v__01,v_1,v_x,v_y) True eval_start_1(v__0,v__01,v_1,v_x,v_y) -> eval_start_2(v__0,v__01,v_1,v_x,v_y) True eval_start_2(v__0,v__01,v_1,v_x,v_y) -> eval_start_3(v__0,v__01,v_1,v_x,v_y) True eval_start_3(v__0,v__01,v_1,v_x,v_y) -> eval_start_4(v__0,v__01,v_1,v_x,v_y) True eval_start_4(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb1_in(v_x,v_y,v_1,v_x,v_y) True eval_start_bb1_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb2_in(v__0,v__01,v_1,v_x,v_y) [v__01 + -1*v_y >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 >= v__01] eval_start_bb1_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb3_in(v__0,v__01,v_1,v_x,v_y) [v__01 + -1*v_y >= 0 && -1*v__0 + v_x >= 0 && v__01 >= v__0] eval_start_bb2_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_5(v__0,v__01,v_1,v_x,v_y) [-1 + v_x + -1*v_y >= 0 && v__01 + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + -1*v__01 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 + -1*v__01 >= 0] eval_start_5(v__0,v__01,v_1,v_x,v_y) -> eval_start_6(v__0,v__01,nondef_0,v_x,v_y) [-1 + v_x + -1*v_y >= 0 && v__01 + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + -1*v__01 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 + -1*v__01 >= 0] eval_start_6(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb1_in(v__0,1 + v__01,v_1,v_x,v_y) [-1 + v_x + -1*v_y >= 0 && v__01 + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + -1*v__01 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 + -1*v__01 >= 0 && -1 + v_1 >= 0] eval_start_6(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb1_in(-1 + v__0,v__01,v_1,v_x,v_y) [-1 + v_x + -1*v_y >= 0 && v__01 + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + -1*v__01 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 + -1*v__01 >= 0 && 0 >= v_1] eval_start_bb3_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_stop(v__0,v__01,v_1,v_x,v_y) [v__01 + -1*v_y >= 0 && -1*v__0 + v_x >= 0 && -1*v__0 + v__01 >= 0] eval_start_stop(v__0,v__01,v_1,v_x,v_y) -> exitus616(v__0,v__01,v_1,v_x,v_y) True Signature: {(eval_start_0,5) ;(eval_start_1,5) ;(eval_start_2,5) ;(eval_start_3,5) ;(eval_start_4,5) ;(eval_start_5,5) ;(eval_start_6,5) ;(eval_start_bb0_in,5) ;(eval_start_bb1_in,5) ;(eval_start_bb2_in,5) ;(eval_start_bb3_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},6->{7,8},7->{9},8->{13},9->{10},10->{11,12},11->{7,8},12->{7,8} ,13->{14}] + 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] | `- p:[7,11,10,9,12] c: [7,9,10,11,12] * Step 4: AbstractSize WORST_CASE(?,O(n^1)) + Considered Problem: (Rules: eval_start_start(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb0_in(v__0,v__01,v_1,v_x,v_y) True eval_start_bb0_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_0(v__0,v__01,v_1,v_x,v_y) True eval_start_0(v__0,v__01,v_1,v_x,v_y) -> eval_start_1(v__0,v__01,v_1,v_x,v_y) True eval_start_1(v__0,v__01,v_1,v_x,v_y) -> eval_start_2(v__0,v__01,v_1,v_x,v_y) True eval_start_2(v__0,v__01,v_1,v_x,v_y) -> eval_start_3(v__0,v__01,v_1,v_x,v_y) True eval_start_3(v__0,v__01,v_1,v_x,v_y) -> eval_start_4(v__0,v__01,v_1,v_x,v_y) True eval_start_4(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb1_in(v_x,v_y,v_1,v_x,v_y) True eval_start_bb1_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb2_in(v__0,v__01,v_1,v_x,v_y) [v__01 + -1*v_y >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 >= v__01] eval_start_bb1_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb3_in(v__0,v__01,v_1,v_x,v_y) [v__01 + -1*v_y >= 0 && -1*v__0 + v_x >= 0 && v__01 >= v__0] eval_start_bb2_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_5(v__0,v__01,v_1,v_x,v_y) [-1 + v_x + -1*v_y >= 0 && v__01 + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + -1*v__01 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 + -1*v__01 >= 0] eval_start_5(v__0,v__01,v_1,v_x,v_y) -> eval_start_6(v__0,v__01,nondef_0,v_x,v_y) [-1 + v_x + -1*v_y >= 0 && v__01 + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + -1*v__01 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 + -1*v__01 >= 0] eval_start_6(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb1_in(v__0,1 + v__01,v_1,v_x,v_y) [-1 + v_x + -1*v_y >= 0 && v__01 + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + -1*v__01 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 + -1*v__01 >= 0 && -1 + v_1 >= 0] eval_start_6(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb1_in(-1 + v__0,v__01,v_1,v_x,v_y) [-1 + v_x + -1*v_y >= 0 && v__01 + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + -1*v__01 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 + -1*v__01 >= 0 && 0 >= v_1] eval_start_bb3_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_stop(v__0,v__01,v_1,v_x,v_y) [v__01 + -1*v_y >= 0 && -1*v__0 + v_x >= 0 && -1*v__0 + v__01 >= 0] eval_start_stop(v__0,v__01,v_1,v_x,v_y) -> exitus616(v__0,v__01,v_1,v_x,v_y) True Signature: {(eval_start_0,5) ;(eval_start_1,5) ;(eval_start_2,5) ;(eval_start_3,5) ;(eval_start_4,5) ;(eval_start_5,5) ;(eval_start_6,5) ;(eval_start_bb0_in,5) ;(eval_start_bb1_in,5) ;(eval_start_bb2_in,5) ;(eval_start_bb3_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},6->{7,8},7->{9},8->{13},9->{10},10->{11,12},11->{7,8},12->{7,8} ,13->{14}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14] | `- p:[7,11,10,9,12] c: [7,9,10,11,12]) + Applied Processor: AbstractSize Minimize + Details: () * Step 5: AbstractFlow WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [v__0,v__01,v_1,v_x,v_y,0.0] eval_start_start ~> eval_start_bb0_in [v__0 <= v__0, v__01 <= v__01, v_1 <= v_1, v_x <= v_x, v_y <= v_y] eval_start_bb0_in ~> eval_start_0 [v__0 <= v__0, v__01 <= v__01, v_1 <= v_1, v_x <= v_x, v_y <= v_y] eval_start_0 ~> eval_start_1 [v__0 <= v__0, v__01 <= v__01, v_1 <= v_1, v_x <= v_x, v_y <= v_y] eval_start_1 ~> eval_start_2 [v__0 <= v__0, v__01 <= v__01, v_1 <= v_1, v_x <= v_x, v_y <= v_y] eval_start_2 ~> eval_start_3 [v__0 <= v__0, v__01 <= v__01, v_1 <= v_1, v_x <= v_x, v_y <= v_y] eval_start_3 ~> eval_start_4 [v__0 <= v__0, v__01 <= v__01, v_1 <= v_1, v_x <= v_x, v_y <= v_y] eval_start_4 ~> eval_start_bb1_in [v__0 <= v_x, v__01 <= v_y, v_1 <= v_1, v_x <= v_x, v_y <= v_y] eval_start_bb1_in ~> eval_start_bb2_in [v__0 <= v__0, v__01 <= v__01, v_1 <= v_1, v_x <= v_x, v_y <= v_y] eval_start_bb1_in ~> eval_start_bb3_in [v__0 <= v__0, v__01 <= v__01, v_1 <= v_1, v_x <= v_x, v_y <= v_y] eval_start_bb2_in ~> eval_start_5 [v__0 <= v__0, v__01 <= v__01, v_1 <= v_1, v_x <= v_x, v_y <= v_y] eval_start_5 ~> eval_start_6 [v__0 <= v__0, v__01 <= v__01, v_1 <= unknown, v_x <= v_x, v_y <= v_y] eval_start_6 ~> eval_start_bb1_in [v__0 <= v__0, v__01 <= v_x + v_y, v_1 <= v_1, v_x <= v_x, v_y <= v_y] eval_start_6 ~> eval_start_bb1_in [v__0 <= v_x + v_y, v__01 <= v__01, v_1 <= v_1, v_x <= v_x, v_y <= v_y] eval_start_bb3_in ~> eval_start_stop [v__0 <= v__0, v__01 <= v__01, v_1 <= v_1, v_x <= v_x, v_y <= v_y] eval_start_stop ~> exitus616 [v__0 <= v__0, v__01 <= v__01, v_1 <= v_1, v_x <= v_x, v_y <= v_y] + Loop: [0.0 <= K + v__0 + v__01] eval_start_bb1_in ~> eval_start_bb2_in [v__0 <= v__0, v__01 <= v__01, v_1 <= v_1, v_x <= v_x, v_y <= v_y] eval_start_6 ~> eval_start_bb1_in [v__0 <= v__0, v__01 <= v_x + v_y, v_1 <= v_1, v_x <= v_x, v_y <= v_y] eval_start_5 ~> eval_start_6 [v__0 <= v__0, v__01 <= v__01, v_1 <= unknown, v_x <= v_x, v_y <= v_y] eval_start_bb2_in ~> eval_start_5 [v__0 <= v__0, v__01 <= v__01, v_1 <= v_1, v_x <= v_x, v_y <= v_y] eval_start_6 ~> eval_start_bb1_in [v__0 <= v_x + v_y, v__01 <= v__01, v_1 <= v_1, v_x <= v_x, v_y <= v_y] + Applied Processor: AbstractFlow + Details: () * Step 6: Lare WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [tick,huge,K,v__0,v__01,v_1,v_x,v_y,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_4 [] eval_start_4 ~> eval_start_bb1_in [v_x ~=> v__0,v_y ~=> v__01] eval_start_bb1_in ~> eval_start_bb2_in [] eval_start_bb1_in ~> eval_start_bb3_in [] eval_start_bb2_in ~> eval_start_5 [] eval_start_5 ~> eval_start_6 [huge ~=> v_1] eval_start_6 ~> eval_start_bb1_in [v_x ~+> v__01,v_y ~+> v__01] eval_start_6 ~> eval_start_bb1_in [v_x ~+> v__0,v_y ~+> v__0] eval_start_bb3_in ~> eval_start_stop [] eval_start_stop ~> exitus616 [] + Loop: [v__0 ~+> 0.0,v__01 ~+> 0.0,K ~+> 0.0] eval_start_bb1_in ~> eval_start_bb2_in [] eval_start_6 ~> eval_start_bb1_in [v_x ~+> v__01,v_y ~+> v__01] eval_start_5 ~> eval_start_6 [huge ~=> v_1] eval_start_bb2_in ~> eval_start_5 [] eval_start_6 ~> eval_start_bb1_in [v_x ~+> v__0,v_y ~+> v__0] + Applied Processor: Lare + Details: eval_start_start ~> exitus616 [v_x ~=> v__0 ,v_y ~=> v__01 ,huge ~=> v_1 ,v_x ~+> v__0 ,v_x ~+> v__01 ,v_x ~+> 0.0 ,v_x ~+> tick ,v_y ~+> v__0 ,v_y ~+> v__01 ,v_y ~+> 0.0 ,v_y ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> tick] + eval_start_bb1_in> [huge ~=> v_1 ,v__0 ~+> 0.0 ,v__0 ~+> tick ,v__01 ~+> 0.0 ,v__01 ~+> tick ,v_x ~+> v__0 ,v_x ~+> v__01 ,v_y ~+> v__0 ,v_y ~+> v__01 ,tick ~+> tick ,K ~+> 0.0 ,K ~+> tick] YES(?,O(n^1))