YES(?,O(1)) * Step 1: TrivialSCCs WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. eval_nd_loop_start(v_0,v_x_0) -> eval_nd_loop_bb0_in(v_0,v_x_0) True (1,1) 1. eval_nd_loop_bb0_in(v_0,v_x_0) -> eval_nd_loop_0(v_0,v_x_0) True (?,1) 2. eval_nd_loop_0(v_0,v_x_0) -> eval_nd_loop_1(v_0,v_x_0) True (?,1) 3. eval_nd_loop_1(v_0,v_x_0) -> eval_nd_loop_2(v_0,v_x_0) True (?,1) 4. eval_nd_loop_2(v_0,v_x_0) -> eval_nd_loop_3(v_0,v_x_0) True (?,1) 5. eval_nd_loop_3(v_0,v_x_0) -> eval_nd_loop_bb1_in(v_0,0) True (?,1) 6. eval_nd_loop_bb1_in(v_0,v_x_0) -> eval_nd_loop_4(v_0,v_x_0) True (?,1) 7. eval_nd_loop_4(v_0,v_x_0) -> eval_nd_loop_5(nondef_0,v_x_0) True (?,1) 8. eval_nd_loop_5(v_0,v_x_0) -> eval_nd_loop_bb1_in(v_0,v_0) [2 >= v_0 + -1*v_x_0 && v_0 + -1*v_x_0 >= 1 && 9 >= v_0] (?,1) 9. eval_nd_loop_5(v_0,v_x_0) -> eval_nd_loop_bb2_in(v_0,v_x_0) [-1 + v_0 + -1*v_x_0 >= 2] (?,1) 10. eval_nd_loop_5(v_0,v_x_0) -> eval_nd_loop_bb2_in(v_0,v_x_0) [0 >= v_0 + -1*v_x_0] (?,1) 11. eval_nd_loop_5(v_0,v_x_0) -> eval_nd_loop_bb2_in(v_0,v_x_0) [v_0 >= 10] (?,1) 12. eval_nd_loop_bb2_in(v_0,v_x_0) -> eval_nd_loop_stop(v_0,v_x_0) True (?,1) Signature: {(eval_nd_loop_0,2) ;(eval_nd_loop_1,2) ;(eval_nd_loop_2,2) ;(eval_nd_loop_3,2) ;(eval_nd_loop_4,2) ;(eval_nd_loop_5,2) ;(eval_nd_loop_bb0_in,2) ;(eval_nd_loop_bb1_in,2) ;(eval_nd_loop_bb2_in,2) ;(eval_nd_loop_start,2) ;(eval_nd_loop_stop,2)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8,9,10,11},8->{6},9->{12},10->{12},11->{12},12->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: AddSinks WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. eval_nd_loop_start(v_0,v_x_0) -> eval_nd_loop_bb0_in(v_0,v_x_0) True (1,1) 1. eval_nd_loop_bb0_in(v_0,v_x_0) -> eval_nd_loop_0(v_0,v_x_0) True (1,1) 2. eval_nd_loop_0(v_0,v_x_0) -> eval_nd_loop_1(v_0,v_x_0) True (1,1) 3. eval_nd_loop_1(v_0,v_x_0) -> eval_nd_loop_2(v_0,v_x_0) True (1,1) 4. eval_nd_loop_2(v_0,v_x_0) -> eval_nd_loop_3(v_0,v_x_0) True (1,1) 5. eval_nd_loop_3(v_0,v_x_0) -> eval_nd_loop_bb1_in(v_0,0) True (1,1) 6. eval_nd_loop_bb1_in(v_0,v_x_0) -> eval_nd_loop_4(v_0,v_x_0) True (?,1) 7. eval_nd_loop_4(v_0,v_x_0) -> eval_nd_loop_5(nondef_0,v_x_0) True (?,1) 8. eval_nd_loop_5(v_0,v_x_0) -> eval_nd_loop_bb1_in(v_0,v_0) [2 >= v_0 + -1*v_x_0 && v_0 + -1*v_x_0 >= 1 && 9 >= v_0] (?,1) 9. eval_nd_loop_5(v_0,v_x_0) -> eval_nd_loop_bb2_in(v_0,v_x_0) [-1 + v_0 + -1*v_x_0 >= 2] (1,1) 10. eval_nd_loop_5(v_0,v_x_0) -> eval_nd_loop_bb2_in(v_0,v_x_0) [0 >= v_0 + -1*v_x_0] (1,1) 11. eval_nd_loop_5(v_0,v_x_0) -> eval_nd_loop_bb2_in(v_0,v_x_0) [v_0 >= 10] (1,1) 12. eval_nd_loop_bb2_in(v_0,v_x_0) -> eval_nd_loop_stop(v_0,v_x_0) True (1,1) Signature: {(eval_nd_loop_0,2) ;(eval_nd_loop_1,2) ;(eval_nd_loop_2,2) ;(eval_nd_loop_3,2) ;(eval_nd_loop_4,2) ;(eval_nd_loop_5,2) ;(eval_nd_loop_bb0_in,2) ;(eval_nd_loop_bb1_in,2) ;(eval_nd_loop_bb2_in,2) ;(eval_nd_loop_start,2) ;(eval_nd_loop_stop,2)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8,9,10,11},8->{6},9->{12},10->{12},11->{12},12->{}] + Applied Processor: AddSinks + Details: () * Step 3: LooptreeTransformer WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. eval_nd_loop_start(v_0,v_x_0) -> eval_nd_loop_bb0_in(v_0,v_x_0) True (1,1) 1. eval_nd_loop_bb0_in(v_0,v_x_0) -> eval_nd_loop_0(v_0,v_x_0) True (?,1) 2. eval_nd_loop_0(v_0,v_x_0) -> eval_nd_loop_1(v_0,v_x_0) True (?,1) 3. eval_nd_loop_1(v_0,v_x_0) -> eval_nd_loop_2(v_0,v_x_0) True (?,1) 4. eval_nd_loop_2(v_0,v_x_0) -> eval_nd_loop_3(v_0,v_x_0) True (?,1) 5. eval_nd_loop_3(v_0,v_x_0) -> eval_nd_loop_bb1_in(v_0,0) True (?,1) 6. eval_nd_loop_bb1_in(v_0,v_x_0) -> eval_nd_loop_4(v_0,v_x_0) True (?,1) 7. eval_nd_loop_4(v_0,v_x_0) -> eval_nd_loop_5(nondef_0,v_x_0) True (?,1) 8. eval_nd_loop_5(v_0,v_x_0) -> eval_nd_loop_bb1_in(v_0,v_0) [2 >= v_0 + -1*v_x_0 && v_0 + -1*v_x_0 >= 1 && 9 >= v_0] (?,1) 9. eval_nd_loop_5(v_0,v_x_0) -> eval_nd_loop_bb2_in(v_0,v_x_0) [-1 + v_0 + -1*v_x_0 >= 2] (?,1) 10. eval_nd_loop_5(v_0,v_x_0) -> eval_nd_loop_bb2_in(v_0,v_x_0) [0 >= v_0 + -1*v_x_0] (?,1) 11. eval_nd_loop_5(v_0,v_x_0) -> eval_nd_loop_bb2_in(v_0,v_x_0) [v_0 >= 10] (?,1) 12. eval_nd_loop_bb2_in(v_0,v_x_0) -> eval_nd_loop_stop(v_0,v_x_0) True (?,1) 13. eval_nd_loop_bb2_in(v_0,v_x_0) -> exitus616(v_0,v_x_0) True (?,1) Signature: {(eval_nd_loop_0,2) ;(eval_nd_loop_1,2) ;(eval_nd_loop_2,2) ;(eval_nd_loop_3,2) ;(eval_nd_loop_4,2) ;(eval_nd_loop_5,2) ;(eval_nd_loop_bb0_in,2) ;(eval_nd_loop_bb1_in,2) ;(eval_nd_loop_bb2_in,2) ;(eval_nd_loop_start,2) ;(eval_nd_loop_stop,2) ;(exitus616,2)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8,9,10,11},8->{6},9->{12,13},10->{12,13},11->{12,13} ,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:[6,8,7] c: [8] * Step 4: SizeAbstraction WORST_CASE(?,O(1)) + Considered Problem: (Rules: 0. eval_nd_loop_start(v_0,v_x_0) -> eval_nd_loop_bb0_in(v_0,v_x_0) True (1,1) 1. eval_nd_loop_bb0_in(v_0,v_x_0) -> eval_nd_loop_0(v_0,v_x_0) True (?,1) 2. eval_nd_loop_0(v_0,v_x_0) -> eval_nd_loop_1(v_0,v_x_0) True (?,1) 3. eval_nd_loop_1(v_0,v_x_0) -> eval_nd_loop_2(v_0,v_x_0) True (?,1) 4. eval_nd_loop_2(v_0,v_x_0) -> eval_nd_loop_3(v_0,v_x_0) True (?,1) 5. eval_nd_loop_3(v_0,v_x_0) -> eval_nd_loop_bb1_in(v_0,0) True (?,1) 6. eval_nd_loop_bb1_in(v_0,v_x_0) -> eval_nd_loop_4(v_0,v_x_0) True (?,1) 7. eval_nd_loop_4(v_0,v_x_0) -> eval_nd_loop_5(nondef_0,v_x_0) True (?,1) 8. eval_nd_loop_5(v_0,v_x_0) -> eval_nd_loop_bb1_in(v_0,v_0) [2 >= v_0 + -1*v_x_0 && v_0 + -1*v_x_0 >= 1 && 9 >= v_0] (?,1) 9. eval_nd_loop_5(v_0,v_x_0) -> eval_nd_loop_bb2_in(v_0,v_x_0) [-1 + v_0 + -1*v_x_0 >= 2] (?,1) 10. eval_nd_loop_5(v_0,v_x_0) -> eval_nd_loop_bb2_in(v_0,v_x_0) [0 >= v_0 + -1*v_x_0] (?,1) 11. eval_nd_loop_5(v_0,v_x_0) -> eval_nd_loop_bb2_in(v_0,v_x_0) [v_0 >= 10] (?,1) 12. eval_nd_loop_bb2_in(v_0,v_x_0) -> eval_nd_loop_stop(v_0,v_x_0) True (?,1) 13. eval_nd_loop_bb2_in(v_0,v_x_0) -> exitus616(v_0,v_x_0) True (?,1) Signature: {(eval_nd_loop_0,2) ;(eval_nd_loop_1,2) ;(eval_nd_loop_2,2) ;(eval_nd_loop_3,2) ;(eval_nd_loop_4,2) ;(eval_nd_loop_5,2) ;(eval_nd_loop_bb0_in,2) ;(eval_nd_loop_bb1_in,2) ;(eval_nd_loop_bb2_in,2) ;(eval_nd_loop_start,2) ;(eval_nd_loop_stop,2) ;(exitus616,2)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8,9,10,11},8->{6},9->{12,13},10->{12,13},11->{12,13} ,12->{},13->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13] | `- p:[6,8,7] c: [8]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 5: FlowAbstraction WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [v_0,v_x_0,0.0] eval_nd_loop_start ~> eval_nd_loop_bb0_in [v_0 <= v_0, v_x_0 <= v_x_0] eval_nd_loop_bb0_in ~> eval_nd_loop_0 [v_0 <= v_0, v_x_0 <= v_x_0] eval_nd_loop_0 ~> eval_nd_loop_1 [v_0 <= v_0, v_x_0 <= v_x_0] eval_nd_loop_1 ~> eval_nd_loop_2 [v_0 <= v_0, v_x_0 <= v_x_0] eval_nd_loop_2 ~> eval_nd_loop_3 [v_0 <= v_0, v_x_0 <= v_x_0] eval_nd_loop_3 ~> eval_nd_loop_bb1_in [v_0 <= v_0, v_x_0 <= 0*K] eval_nd_loop_bb1_in ~> eval_nd_loop_4 [v_0 <= v_0, v_x_0 <= v_x_0] eval_nd_loop_4 ~> eval_nd_loop_5 [v_0 <= unknown, v_x_0 <= v_x_0] eval_nd_loop_5 ~> eval_nd_loop_bb1_in [v_0 <= v_0, v_x_0 <= v_0] eval_nd_loop_5 ~> eval_nd_loop_bb2_in [v_0 <= v_0, v_x_0 <= v_x_0] eval_nd_loop_5 ~> eval_nd_loop_bb2_in [v_0 <= v_0, v_x_0 <= v_x_0] eval_nd_loop_5 ~> eval_nd_loop_bb2_in [v_0 <= v_0, v_x_0 <= v_x_0] eval_nd_loop_bb2_in ~> eval_nd_loop_stop [v_0 <= v_0, v_x_0 <= v_x_0] eval_nd_loop_bb2_in ~> exitus616 [v_0 <= v_0, v_x_0 <= v_x_0] + Loop: [0.0 <= 9*K + v_x_0] eval_nd_loop_bb1_in ~> eval_nd_loop_4 [v_0 <= v_0, v_x_0 <= v_x_0] eval_nd_loop_5 ~> eval_nd_loop_bb1_in [v_0 <= v_0, v_x_0 <= v_0] eval_nd_loop_4 ~> eval_nd_loop_5 [v_0 <= unknown, v_x_0 <= v_x_0] + Applied Processor: FlowAbstraction + Details: () * Step 6: LareProcessor WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [tick,huge,K,v_0,v_x_0,0.0] eval_nd_loop_start ~> eval_nd_loop_bb0_in [] eval_nd_loop_bb0_in ~> eval_nd_loop_0 [] eval_nd_loop_0 ~> eval_nd_loop_1 [] eval_nd_loop_1 ~> eval_nd_loop_2 [] eval_nd_loop_2 ~> eval_nd_loop_3 [] eval_nd_loop_3 ~> eval_nd_loop_bb1_in [K ~=> v_x_0] eval_nd_loop_bb1_in ~> eval_nd_loop_4 [] eval_nd_loop_4 ~> eval_nd_loop_5 [huge ~=> v_0] eval_nd_loop_5 ~> eval_nd_loop_bb1_in [v_0 ~=> v_x_0] eval_nd_loop_5 ~> eval_nd_loop_bb2_in [] eval_nd_loop_5 ~> eval_nd_loop_bb2_in [] eval_nd_loop_5 ~> eval_nd_loop_bb2_in [] eval_nd_loop_bb2_in ~> eval_nd_loop_stop [] eval_nd_loop_bb2_in ~> exitus616 [] + Loop: [v_x_0 ~+> 0.0,K ~*> 0.0] eval_nd_loop_bb1_in ~> eval_nd_loop_4 [] eval_nd_loop_5 ~> eval_nd_loop_bb1_in [v_0 ~=> v_x_0] eval_nd_loop_4 ~> eval_nd_loop_5 [huge ~=> v_0] + Applied Processor: LareProcessor + Details: eval_nd_loop_start ~> eval_nd_loop_stop [K ~=> v_x_0 ,huge ~=> v_0 ,huge ~=> v_x_0 ,tick ~+> tick ,K ~+> 0.0 ,K ~+> tick ,K ~*> 0.0 ,K ~*> tick] eval_nd_loop_start ~> exitus616 [K ~=> v_x_0 ,huge ~=> v_0 ,huge ~=> v_x_0 ,tick ~+> tick ,K ~+> 0.0 ,K ~+> tick ,K ~*> 0.0 ,K ~*> tick] + eval_nd_loop_5> [huge ~=> v_0 ,huge ~=> v_x_0 ,v_x_0 ~+> 0.0 ,v_x_0 ~+> tick ,tick ~+> tick ,K ~*> 0.0 ,K ~*> tick] YES(?,O(1))