YES(?,O(n^1)) * Step 1: TrivialSCCs WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_easy2_start(v__0,v_z) -> eval_easy2_bb0_in(v__0,v_z) True (1,1) 1. eval_easy2_bb0_in(v__0,v_z) -> eval_easy2_0(v__0,v_z) True (?,1) 2. eval_easy2_0(v__0,v_z) -> eval_easy2_1(v__0,v_z) True (?,1) 3. eval_easy2_1(v__0,v_z) -> eval_easy2_2(v__0,v_z) True (?,1) 4. eval_easy2_2(v__0,v_z) -> eval_easy2_3(v__0,v_z) True (?,1) 5. eval_easy2_3(v__0,v_z) -> eval_easy2_4(v__0,v_z) True (?,1) 6. eval_easy2_4(v__0,v_z) -> eval_easy2_5(v__0,v_z) True (?,1) 7. eval_easy2_5(v__0,v_z) -> eval_easy2_6(v__0,v_z) True (?,1) 8. eval_easy2_6(v__0,v_z) -> eval_easy2_bb1_in(v_z,v_z) True (?,1) 9. eval_easy2_bb1_in(v__0,v_z) -> eval_easy2_bb2_in(v__0,v_z) [-1*v__0 + v_z >= 0 && -1 + v__0 >= 0] (?,1) 10. eval_easy2_bb1_in(v__0,v_z) -> eval_easy2_bb3_in(v__0,v_z) [-1*v__0 + v_z >= 0 && 0 >= v__0] (?,1) 11. eval_easy2_bb2_in(v__0,v_z) -> eval_easy2_bb1_in(-1 + v__0,v_z) [-1 + v_z >= 0 && -2 + v__0 + v_z >= 0 && -1*v__0 + v_z >= 0 && -1 + v__0 >= 0] (?,1) 12. eval_easy2_bb3_in(v__0,v_z) -> eval_easy2_stop(v__0,v_z) [-1*v__0 + v_z >= 0 && -1*v__0 >= 0] (?,1) Signature: {(eval_easy2_0,2) ;(eval_easy2_1,2) ;(eval_easy2_2,2) ;(eval_easy2_3,2) ;(eval_easy2_4,2) ;(eval_easy2_5,2) ;(eval_easy2_6,2) ;(eval_easy2_bb0_in,2) ;(eval_easy2_bb1_in,2) ;(eval_easy2_bb2_in,2) ;(eval_easy2_bb3_in,2) ;(eval_easy2_start,2) ;(eval_easy2_stop,2)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9,10},9->{11},10->{12},11->{9,10},12->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: AddSinks WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_easy2_start(v__0,v_z) -> eval_easy2_bb0_in(v__0,v_z) True (1,1) 1. eval_easy2_bb0_in(v__0,v_z) -> eval_easy2_0(v__0,v_z) True (1,1) 2. eval_easy2_0(v__0,v_z) -> eval_easy2_1(v__0,v_z) True (1,1) 3. eval_easy2_1(v__0,v_z) -> eval_easy2_2(v__0,v_z) True (1,1) 4. eval_easy2_2(v__0,v_z) -> eval_easy2_3(v__0,v_z) True (1,1) 5. eval_easy2_3(v__0,v_z) -> eval_easy2_4(v__0,v_z) True (1,1) 6. eval_easy2_4(v__0,v_z) -> eval_easy2_5(v__0,v_z) True (1,1) 7. eval_easy2_5(v__0,v_z) -> eval_easy2_6(v__0,v_z) True (1,1) 8. eval_easy2_6(v__0,v_z) -> eval_easy2_bb1_in(v_z,v_z) True (1,1) 9. eval_easy2_bb1_in(v__0,v_z) -> eval_easy2_bb2_in(v__0,v_z) [-1*v__0 + v_z >= 0 && -1 + v__0 >= 0] (?,1) 10. eval_easy2_bb1_in(v__0,v_z) -> eval_easy2_bb3_in(v__0,v_z) [-1*v__0 + v_z >= 0 && 0 >= v__0] (1,1) 11. eval_easy2_bb2_in(v__0,v_z) -> eval_easy2_bb1_in(-1 + v__0,v_z) [-1 + v_z >= 0 && -2 + v__0 + v_z >= 0 && -1*v__0 + v_z >= 0 && -1 + v__0 >= 0] (?,1) 12. eval_easy2_bb3_in(v__0,v_z) -> eval_easy2_stop(v__0,v_z) [-1*v__0 + v_z >= 0 && -1*v__0 >= 0] (1,1) Signature: {(eval_easy2_0,2) ;(eval_easy2_1,2) ;(eval_easy2_2,2) ;(eval_easy2_3,2) ;(eval_easy2_4,2) ;(eval_easy2_5,2) ;(eval_easy2_6,2) ;(eval_easy2_bb0_in,2) ;(eval_easy2_bb1_in,2) ;(eval_easy2_bb2_in,2) ;(eval_easy2_bb3_in,2) ;(eval_easy2_start,2) ;(eval_easy2_stop,2)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9,10},9->{11},10->{12},11->{9,10},12->{}] + Applied Processor: AddSinks + Details: () * Step 3: LooptreeTransformer WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_easy2_start(v__0,v_z) -> eval_easy2_bb0_in(v__0,v_z) True (1,1) 1. eval_easy2_bb0_in(v__0,v_z) -> eval_easy2_0(v__0,v_z) True (?,1) 2. eval_easy2_0(v__0,v_z) -> eval_easy2_1(v__0,v_z) True (?,1) 3. eval_easy2_1(v__0,v_z) -> eval_easy2_2(v__0,v_z) True (?,1) 4. eval_easy2_2(v__0,v_z) -> eval_easy2_3(v__0,v_z) True (?,1) 5. eval_easy2_3(v__0,v_z) -> eval_easy2_4(v__0,v_z) True (?,1) 6. eval_easy2_4(v__0,v_z) -> eval_easy2_5(v__0,v_z) True (?,1) 7. eval_easy2_5(v__0,v_z) -> eval_easy2_6(v__0,v_z) True (?,1) 8. eval_easy2_6(v__0,v_z) -> eval_easy2_bb1_in(v_z,v_z) True (?,1) 9. eval_easy2_bb1_in(v__0,v_z) -> eval_easy2_bb2_in(v__0,v_z) [-1*v__0 + v_z >= 0 && -1 + v__0 >= 0] (?,1) 10. eval_easy2_bb1_in(v__0,v_z) -> eval_easy2_bb3_in(v__0,v_z) [-1*v__0 + v_z >= 0 && 0 >= v__0] (?,1) 11. eval_easy2_bb2_in(v__0,v_z) -> eval_easy2_bb1_in(-1 + v__0,v_z) [-1 + v_z >= 0 && -2 + v__0 + v_z >= 0 && -1*v__0 + v_z >= 0 && -1 + v__0 >= 0] (?,1) 12. eval_easy2_bb3_in(v__0,v_z) -> eval_easy2_stop(v__0,v_z) [-1*v__0 + v_z >= 0 && -1*v__0 >= 0] (?,1) 13. eval_easy2_bb3_in(v__0,v_z) -> exitus616(v__0,v_z) True (?,1) Signature: {(eval_easy2_0,2) ;(eval_easy2_1,2) ;(eval_easy2_2,2) ;(eval_easy2_3,2) ;(eval_easy2_4,2) ;(eval_easy2_5,2) ;(eval_easy2_6,2) ;(eval_easy2_bb0_in,2) ;(eval_easy2_bb1_in,2) ;(eval_easy2_bb2_in,2) ;(eval_easy2_bb3_in,2) ;(eval_easy2_start,2) ;(eval_easy2_stop,2) ;(exitus616,2)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9,10},9->{11},10->{12,13},11->{9,10},12->{} ,13->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13] | `- p:[9,11] c: [11] * Step 4: SizeAbstraction WORST_CASE(?,O(n^1)) + Considered Problem: (Rules: 0. eval_easy2_start(v__0,v_z) -> eval_easy2_bb0_in(v__0,v_z) True (1,1) 1. eval_easy2_bb0_in(v__0,v_z) -> eval_easy2_0(v__0,v_z) True (?,1) 2. eval_easy2_0(v__0,v_z) -> eval_easy2_1(v__0,v_z) True (?,1) 3. eval_easy2_1(v__0,v_z) -> eval_easy2_2(v__0,v_z) True (?,1) 4. eval_easy2_2(v__0,v_z) -> eval_easy2_3(v__0,v_z) True (?,1) 5. eval_easy2_3(v__0,v_z) -> eval_easy2_4(v__0,v_z) True (?,1) 6. eval_easy2_4(v__0,v_z) -> eval_easy2_5(v__0,v_z) True (?,1) 7. eval_easy2_5(v__0,v_z) -> eval_easy2_6(v__0,v_z) True (?,1) 8. eval_easy2_6(v__0,v_z) -> eval_easy2_bb1_in(v_z,v_z) True (?,1) 9. eval_easy2_bb1_in(v__0,v_z) -> eval_easy2_bb2_in(v__0,v_z) [-1*v__0 + v_z >= 0 && -1 + v__0 >= 0] (?,1) 10. eval_easy2_bb1_in(v__0,v_z) -> eval_easy2_bb3_in(v__0,v_z) [-1*v__0 + v_z >= 0 && 0 >= v__0] (?,1) 11. eval_easy2_bb2_in(v__0,v_z) -> eval_easy2_bb1_in(-1 + v__0,v_z) [-1 + v_z >= 0 && -2 + v__0 + v_z >= 0 && -1*v__0 + v_z >= 0 && -1 + v__0 >= 0] (?,1) 12. eval_easy2_bb3_in(v__0,v_z) -> eval_easy2_stop(v__0,v_z) [-1*v__0 + v_z >= 0 && -1*v__0 >= 0] (?,1) 13. eval_easy2_bb3_in(v__0,v_z) -> exitus616(v__0,v_z) True (?,1) Signature: {(eval_easy2_0,2) ;(eval_easy2_1,2) ;(eval_easy2_2,2) ;(eval_easy2_3,2) ;(eval_easy2_4,2) ;(eval_easy2_5,2) ;(eval_easy2_6,2) ;(eval_easy2_bb0_in,2) ;(eval_easy2_bb1_in,2) ;(eval_easy2_bb2_in,2) ;(eval_easy2_bb3_in,2) ;(eval_easy2_start,2) ;(eval_easy2_stop,2) ;(exitus616,2)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9,10},9->{11},10->{12,13},11->{9,10},12->{} ,13->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13] | `- p:[9,11] c: [11]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 5: FlowAbstraction WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [v__0,v_z,0.0] eval_easy2_start ~> eval_easy2_bb0_in [v__0 <= v__0, v_z <= v_z] eval_easy2_bb0_in ~> eval_easy2_0 [v__0 <= v__0, v_z <= v_z] eval_easy2_0 ~> eval_easy2_1 [v__0 <= v__0, v_z <= v_z] eval_easy2_1 ~> eval_easy2_2 [v__0 <= v__0, v_z <= v_z] eval_easy2_2 ~> eval_easy2_3 [v__0 <= v__0, v_z <= v_z] eval_easy2_3 ~> eval_easy2_4 [v__0 <= v__0, v_z <= v_z] eval_easy2_4 ~> eval_easy2_5 [v__0 <= v__0, v_z <= v_z] eval_easy2_5 ~> eval_easy2_6 [v__0 <= v__0, v_z <= v_z] eval_easy2_6 ~> eval_easy2_bb1_in [v__0 <= v_z, v_z <= v_z] eval_easy2_bb1_in ~> eval_easy2_bb2_in [v__0 <= v__0, v_z <= v_z] eval_easy2_bb1_in ~> eval_easy2_bb3_in [v__0 <= v__0, v_z <= v_z] eval_easy2_bb2_in ~> eval_easy2_bb1_in [v__0 <= v_z, v_z <= v_z] eval_easy2_bb3_in ~> eval_easy2_stop [v__0 <= v__0, v_z <= v_z] eval_easy2_bb3_in ~> exitus616 [v__0 <= v__0, v_z <= v_z] + Loop: [0.0 <= v__0] eval_easy2_bb1_in ~> eval_easy2_bb2_in [v__0 <= v__0, v_z <= v_z] eval_easy2_bb2_in ~> eval_easy2_bb1_in [v__0 <= v_z, v_z <= v_z] + Applied Processor: FlowAbstraction + Details: () * Step 6: LareProcessor WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [tick,huge,K,v__0,v_z,0.0] eval_easy2_start ~> eval_easy2_bb0_in [] eval_easy2_bb0_in ~> eval_easy2_0 [] eval_easy2_0 ~> eval_easy2_1 [] eval_easy2_1 ~> eval_easy2_2 [] eval_easy2_2 ~> eval_easy2_3 [] eval_easy2_3 ~> eval_easy2_4 [] eval_easy2_4 ~> eval_easy2_5 [] eval_easy2_5 ~> eval_easy2_6 [] eval_easy2_6 ~> eval_easy2_bb1_in [v_z ~=> v__0] eval_easy2_bb1_in ~> eval_easy2_bb2_in [] eval_easy2_bb1_in ~> eval_easy2_bb3_in [] eval_easy2_bb2_in ~> eval_easy2_bb1_in [v_z ~=> v__0] eval_easy2_bb3_in ~> eval_easy2_stop [] eval_easy2_bb3_in ~> exitus616 [] + Loop: [v__0 ~=> 0.0] eval_easy2_bb1_in ~> eval_easy2_bb2_in [] eval_easy2_bb2_in ~> eval_easy2_bb1_in [v_z ~=> v__0] + Applied Processor: LareProcessor + Details: eval_easy2_start ~> eval_easy2_stop [v_z ~=> v__0,v_z ~=> 0.0,v_z ~+> tick,tick ~+> tick] eval_easy2_start ~> exitus616 [v_z ~=> v__0,v_z ~=> 0.0,v_z ~+> tick,tick ~+> tick] + eval_easy2_bb1_in> [v__0 ~=> 0.0,v_z ~=> v__0,v__0 ~+> tick,tick ~+> tick] YES(?,O(n^1))