YES(?,O(n^1)) * Step 1: FromIts WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_start_start(v_n,v_x_0) -> eval_start_bb0_in(v_n,v_x_0) True (1,1) 1. eval_start_bb0_in(v_n,v_x_0) -> eval_start_0(v_n,v_x_0) True (?,1) 2. eval_start_0(v_n,v_x_0) -> eval_start_1(v_n,v_x_0) True (?,1) 3. eval_start_1(v_n,v_x_0) -> eval_start_2(v_n,v_x_0) True (?,1) 4. eval_start_2(v_n,v_x_0) -> eval_start_3(v_n,v_x_0) True (?,1) 5. eval_start_3(v_n,v_x_0) -> eval_start_4(v_n,v_x_0) True (?,1) 6. eval_start_4(v_n,v_x_0) -> eval_start_bb1_in(v_n,0) True (?,1) 7. eval_start_bb1_in(v_n,v_x_0) -> eval_start_bb2_in(v_n,v_x_0) [v_x_0 >= 0 && -1 + v_n >= v_x_0] (?,1) 8. eval_start_bb1_in(v_n,v_x_0) -> eval_start_bb3_in(v_n,v_x_0) [v_x_0 >= 0 && v_x_0 >= v_n] (?,1) 9. eval_start_bb2_in(v_n,v_x_0) -> eval_start_5(v_n,v_x_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) 10. eval_start_5(v_n,v_x_0) -> eval_start_6(v_n,v_x_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) 11. eval_start_6(v_n,v_x_0) -> eval_start_bb1_in(v_n,1 + v_x_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) 12. eval_start_bb3_in(v_n,v_x_0) -> eval_start_stop(v_n,v_x_0) [v_x_0 >= 0 && -1*v_n + v_x_0 >= 0] (?,1) Signature: {(eval_start_0,2) ;(eval_start_1,2) ;(eval_start_2,2) ;(eval_start_3,2) ;(eval_start_4,2) ;(eval_start_5,2) ;(eval_start_6,2) ;(eval_start_bb0_in,2) ;(eval_start_bb1_in,2) ;(eval_start_bb2_in,2) ;(eval_start_bb3_in,2) ;(eval_start_start,2) ;(eval_start_stop,2)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7,8},7->{9},8->{12},9->{10},10->{11},11->{7,8},12->{}] + Applied Processor: FromIts + Details: () * Step 2: AddSinks WORST_CASE(?,O(n^1)) + Considered Problem: Rules: eval_start_start(v_n,v_x_0) -> eval_start_bb0_in(v_n,v_x_0) True eval_start_bb0_in(v_n,v_x_0) -> eval_start_0(v_n,v_x_0) True eval_start_0(v_n,v_x_0) -> eval_start_1(v_n,v_x_0) True eval_start_1(v_n,v_x_0) -> eval_start_2(v_n,v_x_0) True eval_start_2(v_n,v_x_0) -> eval_start_3(v_n,v_x_0) True eval_start_3(v_n,v_x_0) -> eval_start_4(v_n,v_x_0) True eval_start_4(v_n,v_x_0) -> eval_start_bb1_in(v_n,0) True eval_start_bb1_in(v_n,v_x_0) -> eval_start_bb2_in(v_n,v_x_0) [v_x_0 >= 0 && -1 + v_n >= v_x_0] eval_start_bb1_in(v_n,v_x_0) -> eval_start_bb3_in(v_n,v_x_0) [v_x_0 >= 0 && v_x_0 >= v_n] eval_start_bb2_in(v_n,v_x_0) -> eval_start_5(v_n,v_x_0) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] eval_start_5(v_n,v_x_0) -> eval_start_6(v_n,v_x_0) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] eval_start_6(v_n,v_x_0) -> eval_start_bb1_in(v_n,1 + v_x_0) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] eval_start_bb3_in(v_n,v_x_0) -> eval_start_stop(v_n,v_x_0) [v_x_0 >= 0 && -1*v_n + v_x_0 >= 0] Signature: {(eval_start_0,2) ;(eval_start_1,2) ;(eval_start_2,2) ;(eval_start_3,2) ;(eval_start_4,2) ;(eval_start_5,2) ;(eval_start_6,2) ;(eval_start_bb0_in,2) ;(eval_start_bb1_in,2) ;(eval_start_bb2_in,2) ;(eval_start_bb3_in,2) ;(eval_start_start,2) ;(eval_start_stop,2)} Rule Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7,8},7->{9},8->{12},9->{10},10->{11},11->{7,8},12->{}] + Applied Processor: AddSinks + Details: () * Step 3: Decompose WORST_CASE(?,O(n^1)) + Considered Problem: Rules: eval_start_start(v_n,v_x_0) -> eval_start_bb0_in(v_n,v_x_0) True eval_start_bb0_in(v_n,v_x_0) -> eval_start_0(v_n,v_x_0) True eval_start_0(v_n,v_x_0) -> eval_start_1(v_n,v_x_0) True eval_start_1(v_n,v_x_0) -> eval_start_2(v_n,v_x_0) True eval_start_2(v_n,v_x_0) -> eval_start_3(v_n,v_x_0) True eval_start_3(v_n,v_x_0) -> eval_start_4(v_n,v_x_0) True eval_start_4(v_n,v_x_0) -> eval_start_bb1_in(v_n,0) True eval_start_bb1_in(v_n,v_x_0) -> eval_start_bb2_in(v_n,v_x_0) [v_x_0 >= 0 && -1 + v_n >= v_x_0] eval_start_bb1_in(v_n,v_x_0) -> eval_start_bb3_in(v_n,v_x_0) [v_x_0 >= 0 && v_x_0 >= v_n] eval_start_bb2_in(v_n,v_x_0) -> eval_start_5(v_n,v_x_0) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] eval_start_5(v_n,v_x_0) -> eval_start_6(v_n,v_x_0) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] eval_start_6(v_n,v_x_0) -> eval_start_bb1_in(v_n,1 + v_x_0) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] eval_start_bb3_in(v_n,v_x_0) -> eval_start_stop(v_n,v_x_0) [v_x_0 >= 0 && -1*v_n + v_x_0 >= 0] eval_start_stop(v_n,v_x_0) -> exitus616(v_n,v_x_0) True Signature: {(eval_start_0,2) ;(eval_start_1,2) ;(eval_start_2,2) ;(eval_start_3,2) ;(eval_start_4,2) ;(eval_start_5,2) ;(eval_start_6,2) ;(eval_start_bb0_in,2) ;(eval_start_bb1_in,2) ;(eval_start_bb2_in,2) ;(eval_start_bb3_in,2) ;(eval_start_start,2) ;(eval_start_stop,2) ;(exitus616,2)} Rule Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7,8},7->{9},8->{12},9->{10},10->{11},11->{7,8},12->{13}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13] | `- p:[7,11,10,9] c: [7,9,10,11] * Step 4: AbstractSize WORST_CASE(?,O(n^1)) + Considered Problem: (Rules: eval_start_start(v_n,v_x_0) -> eval_start_bb0_in(v_n,v_x_0) True eval_start_bb0_in(v_n,v_x_0) -> eval_start_0(v_n,v_x_0) True eval_start_0(v_n,v_x_0) -> eval_start_1(v_n,v_x_0) True eval_start_1(v_n,v_x_0) -> eval_start_2(v_n,v_x_0) True eval_start_2(v_n,v_x_0) -> eval_start_3(v_n,v_x_0) True eval_start_3(v_n,v_x_0) -> eval_start_4(v_n,v_x_0) True eval_start_4(v_n,v_x_0) -> eval_start_bb1_in(v_n,0) True eval_start_bb1_in(v_n,v_x_0) -> eval_start_bb2_in(v_n,v_x_0) [v_x_0 >= 0 && -1 + v_n >= v_x_0] eval_start_bb1_in(v_n,v_x_0) -> eval_start_bb3_in(v_n,v_x_0) [v_x_0 >= 0 && v_x_0 >= v_n] eval_start_bb2_in(v_n,v_x_0) -> eval_start_5(v_n,v_x_0) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] eval_start_5(v_n,v_x_0) -> eval_start_6(v_n,v_x_0) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] eval_start_6(v_n,v_x_0) -> eval_start_bb1_in(v_n,1 + v_x_0) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] eval_start_bb3_in(v_n,v_x_0) -> eval_start_stop(v_n,v_x_0) [v_x_0 >= 0 && -1*v_n + v_x_0 >= 0] eval_start_stop(v_n,v_x_0) -> exitus616(v_n,v_x_0) True Signature: {(eval_start_0,2) ;(eval_start_1,2) ;(eval_start_2,2) ;(eval_start_3,2) ;(eval_start_4,2) ;(eval_start_5,2) ;(eval_start_6,2) ;(eval_start_bb0_in,2) ;(eval_start_bb1_in,2) ;(eval_start_bb2_in,2) ;(eval_start_bb3_in,2) ;(eval_start_start,2) ;(eval_start_stop,2) ;(exitus616,2)} Rule Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7,8},7->{9},8->{12},9->{10},10->{11},11->{7,8},12->{13}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13] | `- p:[7,11,10,9] c: [7,9,10,11]) + Applied Processor: AbstractSize Minimize + Details: () * Step 5: AbstractFlow WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [v_n,v_x_0,0.0] eval_start_start ~> eval_start_bb0_in [v_n <= v_n, v_x_0 <= v_x_0] eval_start_bb0_in ~> eval_start_0 [v_n <= v_n, v_x_0 <= v_x_0] eval_start_0 ~> eval_start_1 [v_n <= v_n, v_x_0 <= v_x_0] eval_start_1 ~> eval_start_2 [v_n <= v_n, v_x_0 <= v_x_0] eval_start_2 ~> eval_start_3 [v_n <= v_n, v_x_0 <= v_x_0] eval_start_3 ~> eval_start_4 [v_n <= v_n, v_x_0 <= v_x_0] eval_start_4 ~> eval_start_bb1_in [v_n <= v_n, v_x_0 <= 0*K] eval_start_bb1_in ~> eval_start_bb2_in [v_n <= v_n, v_x_0 <= v_x_0] eval_start_bb1_in ~> eval_start_bb3_in [v_n <= v_n, v_x_0 <= v_x_0] eval_start_bb2_in ~> eval_start_5 [v_n <= v_n, v_x_0 <= v_x_0] eval_start_5 ~> eval_start_6 [v_n <= v_n, v_x_0 <= v_x_0] eval_start_6 ~> eval_start_bb1_in [v_n <= v_n, v_x_0 <= v_n] eval_start_bb3_in ~> eval_start_stop [v_n <= v_n, v_x_0 <= v_x_0] eval_start_stop ~> exitus616 [v_n <= v_n, v_x_0 <= v_x_0] + Loop: [0.0 <= K + v_n + v_x_0] eval_start_bb1_in ~> eval_start_bb2_in [v_n <= v_n, v_x_0 <= v_x_0] eval_start_6 ~> eval_start_bb1_in [v_n <= v_n, v_x_0 <= v_n] eval_start_5 ~> eval_start_6 [v_n <= v_n, v_x_0 <= v_x_0] eval_start_bb2_in ~> eval_start_5 [v_n <= v_n, v_x_0 <= v_x_0] + Applied Processor: AbstractFlow + Details: () * Step 6: Lare WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [tick,huge,K,v_n,v_x_0,0.0] 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 [K ~=> v_x_0] 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 [] eval_start_6 ~> eval_start_bb1_in [v_n ~=> v_x_0] eval_start_bb3_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 [] eval_start_6 ~> eval_start_bb1_in [v_n ~=> v_x_0] eval_start_5 ~> eval_start_6 [] eval_start_bb2_in ~> eval_start_5 [] + Applied Processor: Lare + Details: eval_start_start ~> exitus616 [v_n ~=> v_x_0 ,K ~=> v_x_0 ,v_n ~+> 0.0 ,v_n ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> tick ,K ~*> 0.0 ,K ~*> tick] + eval_start_bb1_in> [v_n ~=> v_x_0 ,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))