YES(?,POLY) * Step 1: TrivialSCCs WORST_CASE(?,POLY) + Considered Problem: Rules: 0. eval_start_start(v_i_0,v_m,v_n) -> eval_start_bb0_in(v_i_0,v_m,v_n) True (1,1) 1. eval_start_bb0_in(v_i_0,v_m,v_n) -> eval_start_0(v_i_0,v_m,v_n) True (?,1) 2. eval_start_0(v_i_0,v_m,v_n) -> eval_start_1(v_i_0,v_m,v_n) True (?,1) 3. eval_start_1(v_i_0,v_m,v_n) -> eval_start_2(v_i_0,v_m,v_n) True (?,1) 4. eval_start_2(v_i_0,v_m,v_n) -> eval_start_3(v_i_0,v_m,v_n) True (?,1) 5. eval_start_3(v_i_0,v_m,v_n) -> eval_start_bb1_in(v_n,v_m,v_n) [-1 + v_m >= 0] (?,1) 6. eval_start_3(v_i_0,v_m,v_n) -> eval_start_bb4_in(v_i_0,v_m,v_n) [0 >= v_m] (?,1) 7. eval_start_bb1_in(v_i_0,v_m,v_n) -> eval_start_bb2_in(v_i_0,v_m,v_n) [-1*v_i_0 + v_n >= 0 && -1 + v_m >= 0 && -1 + v_i_0 >= 0] (?,1) 8. eval_start_bb1_in(v_i_0,v_m,v_n) -> eval_start_bb3_in(v_i_0,v_m,v_n) [-1*v_i_0 + v_n >= 0 && -1 + v_m >= 0 && 0 >= v_i_0] (?,1) 9. eval_start_bb2_in(v_i_0,v_m,v_n) -> eval_start_bb1_in(-1 + v_i_0,v_m,v_n) [-1 + v_n >= 0 (?,1) && -2 + v_m + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1*v_i_0 + v_n >= 0 && -1 + v_m >= 0 && -2 + v_i_0 + v_m >= 0 && -1 + v_i_0 >= 0 && -1 + v_m >= v_i_0] 10. eval_start_bb2_in(v_i_0,v_m,v_n) -> eval_start_bb1_in(v_i_0 + -1*v_m,v_m,v_n) [-1 + v_n >= 0 (?,1) && -2 + v_m + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1*v_i_0 + v_n >= 0 && -1 + v_m >= 0 && -2 + v_i_0 + v_m >= 0 && -1 + v_i_0 >= 0 && v_i_0 >= v_m] 11. eval_start_bb3_in(v_i_0,v_m,v_n) -> eval_start_stop(v_i_0,v_m,v_n) [-1*v_i_0 + v_n >= 0 && -1 + v_m >= 0 && -1 + -1*v_i_0 + v_m >= 0 && -1*v_i_0 >= 0] (?,1) 12. eval_start_bb4_in(v_i_0,v_m,v_n) -> eval_start_8(v_i_0,v_m,v_n) [-1*v_m >= 0] (?,1) 13. eval_start_8(v_i_0,v_m,v_n) -> eval_start_9(v_i_0,v_m,v_n) [-1*v_m >= 0] (?,1) 14. eval_start_9(v_i_0,v_m,v_n) -> eval_start_stop(v_i_0,v_m,v_n) [-1*v_m >= 0] (?,1) Signature: {(eval_start_0,3) ;(eval_start_1,3) ;(eval_start_2,3) ;(eval_start_3,3) ;(eval_start_8,3) ;(eval_start_9,3) ;(eval_start_bb0_in,3) ;(eval_start_bb1_in,3) ;(eval_start_bb2_in,3) ;(eval_start_bb3_in,3) ;(eval_start_bb4_in,3) ;(eval_start_start,3) ;(eval_start_stop,3)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5,6},5->{7,8},6->{12},7->{9,10},8->{11},9->{7,8},10->{7,8},11->{} ,12->{13},13->{14},14->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: AddSinks WORST_CASE(?,POLY) + Considered Problem: Rules: 0. eval_start_start(v_i_0,v_m,v_n) -> eval_start_bb0_in(v_i_0,v_m,v_n) True (1,1) 1. eval_start_bb0_in(v_i_0,v_m,v_n) -> eval_start_0(v_i_0,v_m,v_n) True (1,1) 2. eval_start_0(v_i_0,v_m,v_n) -> eval_start_1(v_i_0,v_m,v_n) True (1,1) 3. eval_start_1(v_i_0,v_m,v_n) -> eval_start_2(v_i_0,v_m,v_n) True (1,1) 4. eval_start_2(v_i_0,v_m,v_n) -> eval_start_3(v_i_0,v_m,v_n) True (1,1) 5. eval_start_3(v_i_0,v_m,v_n) -> eval_start_bb1_in(v_n,v_m,v_n) [-1 + v_m >= 0] (1,1) 6. eval_start_3(v_i_0,v_m,v_n) -> eval_start_bb4_in(v_i_0,v_m,v_n) [0 >= v_m] (1,1) 7. eval_start_bb1_in(v_i_0,v_m,v_n) -> eval_start_bb2_in(v_i_0,v_m,v_n) [-1*v_i_0 + v_n >= 0 && -1 + v_m >= 0 && -1 + v_i_0 >= 0] (?,1) 8. eval_start_bb1_in(v_i_0,v_m,v_n) -> eval_start_bb3_in(v_i_0,v_m,v_n) [-1*v_i_0 + v_n >= 0 && -1 + v_m >= 0 && 0 >= v_i_0] (1,1) 9. eval_start_bb2_in(v_i_0,v_m,v_n) -> eval_start_bb1_in(-1 + v_i_0,v_m,v_n) [-1 + v_n >= 0 (?,1) && -2 + v_m + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1*v_i_0 + v_n >= 0 && -1 + v_m >= 0 && -2 + v_i_0 + v_m >= 0 && -1 + v_i_0 >= 0 && -1 + v_m >= v_i_0] 10. eval_start_bb2_in(v_i_0,v_m,v_n) -> eval_start_bb1_in(v_i_0 + -1*v_m,v_m,v_n) [-1 + v_n >= 0 (?,1) && -2 + v_m + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1*v_i_0 + v_n >= 0 && -1 + v_m >= 0 && -2 + v_i_0 + v_m >= 0 && -1 + v_i_0 >= 0 && v_i_0 >= v_m] 11. eval_start_bb3_in(v_i_0,v_m,v_n) -> eval_start_stop(v_i_0,v_m,v_n) [-1*v_i_0 + v_n >= 0 && -1 + v_m >= 0 && -1 + -1*v_i_0 + v_m >= 0 && -1*v_i_0 >= 0] (1,1) 12. eval_start_bb4_in(v_i_0,v_m,v_n) -> eval_start_8(v_i_0,v_m,v_n) [-1*v_m >= 0] (1,1) 13. eval_start_8(v_i_0,v_m,v_n) -> eval_start_9(v_i_0,v_m,v_n) [-1*v_m >= 0] (1,1) 14. eval_start_9(v_i_0,v_m,v_n) -> eval_start_stop(v_i_0,v_m,v_n) [-1*v_m >= 0] (1,1) Signature: {(eval_start_0,3) ;(eval_start_1,3) ;(eval_start_2,3) ;(eval_start_3,3) ;(eval_start_8,3) ;(eval_start_9,3) ;(eval_start_bb0_in,3) ;(eval_start_bb1_in,3) ;(eval_start_bb2_in,3) ;(eval_start_bb3_in,3) ;(eval_start_bb4_in,3) ;(eval_start_start,3) ;(eval_start_stop,3)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5,6},5->{7,8},6->{12},7->{9,10},8->{11},9->{7,8},10->{7,8},11->{} ,12->{13},13->{14},14->{}] + Applied Processor: AddSinks + Details: () * Step 3: LooptreeTransformer WORST_CASE(?,POLY) + Considered Problem: Rules: 0. eval_start_start(v_i_0,v_m,v_n) -> eval_start_bb0_in(v_i_0,v_m,v_n) True (1,1) 1. eval_start_bb0_in(v_i_0,v_m,v_n) -> eval_start_0(v_i_0,v_m,v_n) True (?,1) 2. eval_start_0(v_i_0,v_m,v_n) -> eval_start_1(v_i_0,v_m,v_n) True (?,1) 3. eval_start_1(v_i_0,v_m,v_n) -> eval_start_2(v_i_0,v_m,v_n) True (?,1) 4. eval_start_2(v_i_0,v_m,v_n) -> eval_start_3(v_i_0,v_m,v_n) True (?,1) 5. eval_start_3(v_i_0,v_m,v_n) -> eval_start_bb1_in(v_n,v_m,v_n) [-1 + v_m >= 0] (?,1) 6. eval_start_3(v_i_0,v_m,v_n) -> eval_start_bb4_in(v_i_0,v_m,v_n) [0 >= v_m] (?,1) 7. eval_start_bb1_in(v_i_0,v_m,v_n) -> eval_start_bb2_in(v_i_0,v_m,v_n) [-1*v_i_0 + v_n >= 0 && -1 + v_m >= 0 && -1 + v_i_0 >= 0] (?,1) 8. eval_start_bb1_in(v_i_0,v_m,v_n) -> eval_start_bb3_in(v_i_0,v_m,v_n) [-1*v_i_0 + v_n >= 0 && -1 + v_m >= 0 && 0 >= v_i_0] (?,1) 9. eval_start_bb2_in(v_i_0,v_m,v_n) -> eval_start_bb1_in(-1 + v_i_0,v_m,v_n) [-1 + v_n >= 0 (?,1) && -2 + v_m + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1*v_i_0 + v_n >= 0 && -1 + v_m >= 0 && -2 + v_i_0 + v_m >= 0 && -1 + v_i_0 >= 0 && -1 + v_m >= v_i_0] 10. eval_start_bb2_in(v_i_0,v_m,v_n) -> eval_start_bb1_in(v_i_0 + -1*v_m,v_m,v_n) [-1 + v_n >= 0 (?,1) && -2 + v_m + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1*v_i_0 + v_n >= 0 && -1 + v_m >= 0 && -2 + v_i_0 + v_m >= 0 && -1 + v_i_0 >= 0 && v_i_0 >= v_m] 11. eval_start_bb3_in(v_i_0,v_m,v_n) -> eval_start_stop(v_i_0,v_m,v_n) [-1*v_i_0 + v_n >= 0 && -1 + v_m >= 0 && -1 + -1*v_i_0 + v_m >= 0 && -1*v_i_0 >= 0] (?,1) 12. eval_start_bb4_in(v_i_0,v_m,v_n) -> eval_start_8(v_i_0,v_m,v_n) [-1*v_m >= 0] (?,1) 13. eval_start_8(v_i_0,v_m,v_n) -> eval_start_9(v_i_0,v_m,v_n) [-1*v_m >= 0] (?,1) 14. eval_start_9(v_i_0,v_m,v_n) -> eval_start_stop(v_i_0,v_m,v_n) [-1*v_m >= 0] (?,1) 15. eval_start_9(v_i_0,v_m,v_n) -> exitus616(v_i_0,v_m,v_n) True (?,1) 16. eval_start_bb3_in(v_i_0,v_m,v_n) -> exitus616(v_i_0,v_m,v_n) True (?,1) Signature: {(eval_start_0,3) ;(eval_start_1,3) ;(eval_start_2,3) ;(eval_start_3,3) ;(eval_start_8,3) ;(eval_start_9,3) ;(eval_start_bb0_in,3) ;(eval_start_bb1_in,3) ;(eval_start_bb2_in,3) ;(eval_start_bb3_in,3) ;(eval_start_bb4_in,3) ;(eval_start_start,3) ;(eval_start_stop,3) ;(exitus616,3)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5,6},5->{7,8},6->{12},7->{9,10},8->{11,16},9->{7,8},10->{7,8},11->{} ,12->{13},13->{14,15},14->{},15->{},16->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16] | `- p:[7,9,10] c: [10] | `- p:[7,9] c: [9] * Step 4: SizeAbstraction WORST_CASE(?,POLY) + Considered Problem: (Rules: 0. eval_start_start(v_i_0,v_m,v_n) -> eval_start_bb0_in(v_i_0,v_m,v_n) True (1,1) 1. eval_start_bb0_in(v_i_0,v_m,v_n) -> eval_start_0(v_i_0,v_m,v_n) True (?,1) 2. eval_start_0(v_i_0,v_m,v_n) -> eval_start_1(v_i_0,v_m,v_n) True (?,1) 3. eval_start_1(v_i_0,v_m,v_n) -> eval_start_2(v_i_0,v_m,v_n) True (?,1) 4. eval_start_2(v_i_0,v_m,v_n) -> eval_start_3(v_i_0,v_m,v_n) True (?,1) 5. eval_start_3(v_i_0,v_m,v_n) -> eval_start_bb1_in(v_n,v_m,v_n) [-1 + v_m >= 0] (?,1) 6. eval_start_3(v_i_0,v_m,v_n) -> eval_start_bb4_in(v_i_0,v_m,v_n) [0 >= v_m] (?,1) 7. eval_start_bb1_in(v_i_0,v_m,v_n) -> eval_start_bb2_in(v_i_0,v_m,v_n) [-1*v_i_0 + v_n >= 0 && -1 + v_m >= 0 && -1 + v_i_0 >= 0] (?,1) 8. eval_start_bb1_in(v_i_0,v_m,v_n) -> eval_start_bb3_in(v_i_0,v_m,v_n) [-1*v_i_0 + v_n >= 0 && -1 + v_m >= 0 && 0 >= v_i_0] (?,1) 9. eval_start_bb2_in(v_i_0,v_m,v_n) -> eval_start_bb1_in(-1 + v_i_0,v_m,v_n) [-1 + v_n >= 0 (?,1) && -2 + v_m + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1*v_i_0 + v_n >= 0 && -1 + v_m >= 0 && -2 + v_i_0 + v_m >= 0 && -1 + v_i_0 >= 0 && -1 + v_m >= v_i_0] 10. eval_start_bb2_in(v_i_0,v_m,v_n) -> eval_start_bb1_in(v_i_0 + -1*v_m,v_m,v_n) [-1 + v_n >= 0 (?,1) && -2 + v_m + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1*v_i_0 + v_n >= 0 && -1 + v_m >= 0 && -2 + v_i_0 + v_m >= 0 && -1 + v_i_0 >= 0 && v_i_0 >= v_m] 11. eval_start_bb3_in(v_i_0,v_m,v_n) -> eval_start_stop(v_i_0,v_m,v_n) [-1*v_i_0 + v_n >= 0 && -1 + v_m >= 0 && -1 + -1*v_i_0 + v_m >= 0 && -1*v_i_0 >= 0] (?,1) 12. eval_start_bb4_in(v_i_0,v_m,v_n) -> eval_start_8(v_i_0,v_m,v_n) [-1*v_m >= 0] (?,1) 13. eval_start_8(v_i_0,v_m,v_n) -> eval_start_9(v_i_0,v_m,v_n) [-1*v_m >= 0] (?,1) 14. eval_start_9(v_i_0,v_m,v_n) -> eval_start_stop(v_i_0,v_m,v_n) [-1*v_m >= 0] (?,1) 15. eval_start_9(v_i_0,v_m,v_n) -> exitus616(v_i_0,v_m,v_n) True (?,1) 16. eval_start_bb3_in(v_i_0,v_m,v_n) -> exitus616(v_i_0,v_m,v_n) True (?,1) Signature: {(eval_start_0,3) ;(eval_start_1,3) ;(eval_start_2,3) ;(eval_start_3,3) ;(eval_start_8,3) ;(eval_start_9,3) ;(eval_start_bb0_in,3) ;(eval_start_bb1_in,3) ;(eval_start_bb2_in,3) ;(eval_start_bb3_in,3) ;(eval_start_bb4_in,3) ;(eval_start_start,3) ;(eval_start_stop,3) ;(exitus616,3)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5,6},5->{7,8},6->{12},7->{9,10},8->{11,16},9->{7,8},10->{7,8},11->{} ,12->{13},13->{14,15},14->{},15->{},16->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16] | `- p:[7,9,10] c: [10] | `- p:[7,9] c: [9]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 5: FlowAbstraction WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [v_i_0,v_m,v_n,0.0,0.0.0] eval_start_start ~> eval_start_bb0_in [v_i_0 <= v_i_0, v_m <= v_m, v_n <= v_n] eval_start_bb0_in ~> eval_start_0 [v_i_0 <= v_i_0, v_m <= v_m, v_n <= v_n] eval_start_0 ~> eval_start_1 [v_i_0 <= v_i_0, v_m <= v_m, v_n <= v_n] eval_start_1 ~> eval_start_2 [v_i_0 <= v_i_0, v_m <= v_m, v_n <= v_n] eval_start_2 ~> eval_start_3 [v_i_0 <= v_i_0, v_m <= v_m, v_n <= v_n] eval_start_3 ~> eval_start_bb1_in [v_i_0 <= v_n, v_m <= v_m, v_n <= v_n] eval_start_3 ~> eval_start_bb4_in [v_i_0 <= v_i_0, v_m <= v_m, v_n <= v_n] eval_start_bb1_in ~> eval_start_bb2_in [v_i_0 <= v_i_0, v_m <= v_m, v_n <= v_n] eval_start_bb1_in ~> eval_start_bb3_in [v_i_0 <= v_i_0, v_m <= v_m, v_n <= v_n] eval_start_bb2_in ~> eval_start_bb1_in [v_i_0 <= v_n, v_m <= v_m, v_n <= v_n] eval_start_bb2_in ~> eval_start_bb1_in [v_i_0 <= v_n, v_m <= v_m, v_n <= v_n] eval_start_bb3_in ~> eval_start_stop [v_i_0 <= v_i_0, v_m <= v_m, v_n <= v_n] eval_start_bb4_in ~> eval_start_8 [v_i_0 <= v_i_0, v_m <= v_m, v_n <= v_n] eval_start_8 ~> eval_start_9 [v_i_0 <= v_i_0, v_m <= v_m, v_n <= v_n] eval_start_9 ~> eval_start_stop [v_i_0 <= v_i_0, v_m <= v_m, v_n <= v_n] eval_start_9 ~> exitus616 [v_i_0 <= v_i_0, v_m <= v_m, v_n <= v_n] eval_start_bb3_in ~> exitus616 [v_i_0 <= v_i_0, v_m <= v_m, v_n <= v_n] + Loop: [0.0 <= v_i_0] eval_start_bb1_in ~> eval_start_bb2_in [v_i_0 <= v_i_0, v_m <= v_m, v_n <= v_n] eval_start_bb2_in ~> eval_start_bb1_in [v_i_0 <= v_n, v_m <= v_m, v_n <= v_n] eval_start_bb2_in ~> eval_start_bb1_in [v_i_0 <= v_n, v_m <= v_m, v_n <= v_n] + Loop: [0.0.0 <= v_i_0] eval_start_bb1_in ~> eval_start_bb2_in [v_i_0 <= v_i_0, v_m <= v_m, v_n <= v_n] eval_start_bb2_in ~> eval_start_bb1_in [v_i_0 <= v_n, v_m <= v_m, v_n <= v_n] + Applied Processor: FlowAbstraction + Details: () * Step 6: LareProcessor WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [tick,huge,K,v_i_0,v_m,v_n,0.0,0.0.0] 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_bb1_in [v_n ~=> v_i_0] eval_start_3 ~> eval_start_bb4_in [] eval_start_bb1_in ~> eval_start_bb2_in [] eval_start_bb1_in ~> eval_start_bb3_in [] eval_start_bb2_in ~> eval_start_bb1_in [v_n ~=> v_i_0] eval_start_bb2_in ~> eval_start_bb1_in [v_n ~=> v_i_0] eval_start_bb3_in ~> eval_start_stop [] eval_start_bb4_in ~> eval_start_8 [] eval_start_8 ~> eval_start_9 [] eval_start_9 ~> eval_start_stop [] eval_start_9 ~> exitus616 [] eval_start_bb3_in ~> exitus616 [] + Loop: [v_i_0 ~=> 0.0] eval_start_bb1_in ~> eval_start_bb2_in [] eval_start_bb2_in ~> eval_start_bb1_in [v_n ~=> v_i_0] eval_start_bb2_in ~> eval_start_bb1_in [v_n ~=> v_i_0] + Loop: [v_i_0 ~=> 0.0.0] eval_start_bb1_in ~> eval_start_bb2_in [] eval_start_bb2_in ~> eval_start_bb1_in [v_n ~=> v_i_0] + Applied Processor: LareProcessor + Details: eval_start_start ~> eval_start_stop [v_n ~=> v_i_0 ,v_n ~=> 0.0 ,v_n ~=> 0.0.0 ,v_n ~+> tick ,tick ~+> tick ,v_n ~*> tick] eval_start_start ~> exitus616 [v_n ~=> v_i_0 ,v_n ~=> 0.0 ,v_n ~=> 0.0.0 ,v_n ~+> tick ,tick ~+> tick ,v_n ~*> tick] + eval_start_bb1_in> [v_i_0 ~=> 0.0 ,v_i_0 ~=> 0.0.0 ,v_n ~=> v_i_0 ,v_n ~=> 0.0.0 ,v_i_0 ~+> tick ,v_n ~+> tick ,tick ~+> tick ,v_i_0 ~*> tick] + eval_start_bb1_in> [v_i_0 ~=> 0.0.0,v_n ~=> v_i_0,v_i_0 ~+> tick,tick ~+> tick] YES(?,POLY)