YES(?,PRIMREC) * Step 1: TrivialSCCs MAYBE + Considered Problem: Rules: 0. eval_start_start(v_n,v_x_0,v_y_0) -> eval_start_bb0_in(v_n,v_x_0,v_y_0) True (1,1) 1. eval_start_bb0_in(v_n,v_x_0,v_y_0) -> eval_start_0(v_n,v_x_0,v_y_0) True (?,1) 2. eval_start_0(v_n,v_x_0,v_y_0) -> eval_start_1(v_n,v_x_0,v_y_0) True (?,1) 3. eval_start_1(v_n,v_x_0,v_y_0) -> eval_start_2(v_n,v_x_0,v_y_0) True (?,1) 4. eval_start_2(v_n,v_x_0,v_y_0) -> eval_start_3(v_n,v_x_0,v_y_0) True (?,1) 5. eval_start_3(v_n,v_x_0,v_y_0) -> eval_start_4(v_n,v_x_0,v_y_0) True (?,1) 6. eval_start_4(v_n,v_x_0,v_y_0) -> eval_start_5(v_n,v_x_0,v_y_0) True (?,1) 7. eval_start_5(v_n,v_x_0,v_y_0) -> eval_start_6(v_n,v_x_0,v_y_0) True (?,1) 8. eval_start_6(v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_n,0,0) True (?,1) 9. eval_start_bb1_in(v_n,v_x_0,v_y_0) -> eval_start_bb2_in(v_n,v_x_0,v_y_0) [-1 + v_n >= v_x_0] (?,1) 10. eval_start_bb1_in(v_n,v_x_0,v_y_0) -> eval_start_bb3_in(v_n,v_x_0,v_y_0) [v_x_0 >= v_n] (?,1) 11. eval_start_bb2_in(v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_n,1 + v_x_0,1 + v_y_0) True (?,1) 12. eval_start_bb3_in(v_n,v_x_0,v_y_0) -> eval_start_bb4_in(v_n,v_x_0,v_y_0) [-1 + v_y_0 >= 0] (?,1) 13. eval_start_bb3_in(v_n,v_x_0,v_y_0) -> eval_start_bb5_in(v_n,v_x_0,v_y_0) [0 >= v_y_0] (?,1) 14. eval_start_bb4_in(v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_n,v_x_0,-1 + v_y_0) True (?,1) 15. eval_start_bb5_in(v_n,v_x_0,v_y_0) -> eval_start_stop(v_n,v_x_0,v_y_0) True (?,1) Signature: {(eval_start_0,3) ;(eval_start_1,3) ;(eval_start_2,3) ;(eval_start_3,3) ;(eval_start_4,3) ;(eval_start_5,3) ;(eval_start_6,3) ;(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_bb5_in,3) ;(eval_start_start,3) ;(eval_start_stop,3)} 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->{14} ,13->{15},14->{9,10},15->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: AddSinks MAYBE + Considered Problem: Rules: 0. eval_start_start(v_n,v_x_0,v_y_0) -> eval_start_bb0_in(v_n,v_x_0,v_y_0) True (1,1) 1. eval_start_bb0_in(v_n,v_x_0,v_y_0) -> eval_start_0(v_n,v_x_0,v_y_0) True (1,1) 2. eval_start_0(v_n,v_x_0,v_y_0) -> eval_start_1(v_n,v_x_0,v_y_0) True (1,1) 3. eval_start_1(v_n,v_x_0,v_y_0) -> eval_start_2(v_n,v_x_0,v_y_0) True (1,1) 4. eval_start_2(v_n,v_x_0,v_y_0) -> eval_start_3(v_n,v_x_0,v_y_0) True (1,1) 5. eval_start_3(v_n,v_x_0,v_y_0) -> eval_start_4(v_n,v_x_0,v_y_0) True (1,1) 6. eval_start_4(v_n,v_x_0,v_y_0) -> eval_start_5(v_n,v_x_0,v_y_0) True (1,1) 7. eval_start_5(v_n,v_x_0,v_y_0) -> eval_start_6(v_n,v_x_0,v_y_0) True (1,1) 8. eval_start_6(v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_n,0,0) True (1,1) 9. eval_start_bb1_in(v_n,v_x_0,v_y_0) -> eval_start_bb2_in(v_n,v_x_0,v_y_0) [-1 + v_n >= v_x_0] (?,1) 10. eval_start_bb1_in(v_n,v_x_0,v_y_0) -> eval_start_bb3_in(v_n,v_x_0,v_y_0) [v_x_0 >= v_n] (?,1) 11. eval_start_bb2_in(v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_n,1 + v_x_0,1 + v_y_0) True (?,1) 12. eval_start_bb3_in(v_n,v_x_0,v_y_0) -> eval_start_bb4_in(v_n,v_x_0,v_y_0) [-1 + v_y_0 >= 0] (?,1) 13. eval_start_bb3_in(v_n,v_x_0,v_y_0) -> eval_start_bb5_in(v_n,v_x_0,v_y_0) [0 >= v_y_0] (1,1) 14. eval_start_bb4_in(v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_n,v_x_0,-1 + v_y_0) True (?,1) 15. eval_start_bb5_in(v_n,v_x_0,v_y_0) -> eval_start_stop(v_n,v_x_0,v_y_0) True (1,1) Signature: {(eval_start_0,3) ;(eval_start_1,3) ;(eval_start_2,3) ;(eval_start_3,3) ;(eval_start_4,3) ;(eval_start_5,3) ;(eval_start_6,3) ;(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_bb5_in,3) ;(eval_start_start,3) ;(eval_start_stop,3)} 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->{14} ,13->{15},14->{9,10},15->{}] + Applied Processor: AddSinks + Details: () * Step 3: LooptreeTransformer MAYBE + Considered Problem: Rules: 0. eval_start_start(v_n,v_x_0,v_y_0) -> eval_start_bb0_in(v_n,v_x_0,v_y_0) True (1,1) 1. eval_start_bb0_in(v_n,v_x_0,v_y_0) -> eval_start_0(v_n,v_x_0,v_y_0) True (?,1) 2. eval_start_0(v_n,v_x_0,v_y_0) -> eval_start_1(v_n,v_x_0,v_y_0) True (?,1) 3. eval_start_1(v_n,v_x_0,v_y_0) -> eval_start_2(v_n,v_x_0,v_y_0) True (?,1) 4. eval_start_2(v_n,v_x_0,v_y_0) -> eval_start_3(v_n,v_x_0,v_y_0) True (?,1) 5. eval_start_3(v_n,v_x_0,v_y_0) -> eval_start_4(v_n,v_x_0,v_y_0) True (?,1) 6. eval_start_4(v_n,v_x_0,v_y_0) -> eval_start_5(v_n,v_x_0,v_y_0) True (?,1) 7. eval_start_5(v_n,v_x_0,v_y_0) -> eval_start_6(v_n,v_x_0,v_y_0) True (?,1) 8. eval_start_6(v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_n,0,0) True (?,1) 9. eval_start_bb1_in(v_n,v_x_0,v_y_0) -> eval_start_bb2_in(v_n,v_x_0,v_y_0) [-1 + v_n >= v_x_0] (?,1) 10. eval_start_bb1_in(v_n,v_x_0,v_y_0) -> eval_start_bb3_in(v_n,v_x_0,v_y_0) [v_x_0 >= v_n] (?,1) 11. eval_start_bb2_in(v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_n,1 + v_x_0,1 + v_y_0) True (?,1) 12. eval_start_bb3_in(v_n,v_x_0,v_y_0) -> eval_start_bb4_in(v_n,v_x_0,v_y_0) [-1 + v_y_0 >= 0] (?,1) 13. eval_start_bb3_in(v_n,v_x_0,v_y_0) -> eval_start_bb5_in(v_n,v_x_0,v_y_0) [0 >= v_y_0] (?,1) 14. eval_start_bb4_in(v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_n,v_x_0,-1 + v_y_0) True (?,1) 15. eval_start_bb5_in(v_n,v_x_0,v_y_0) -> eval_start_stop(v_n,v_x_0,v_y_0) True (?,1) 16. eval_start_bb5_in(v_n,v_x_0,v_y_0) -> exitus616(v_n,v_x_0,v_y_0) True (?,1) Signature: {(eval_start_0,3) ;(eval_start_1,3) ;(eval_start_2,3) ;(eval_start_3,3) ;(eval_start_4,3) ;(eval_start_5,3) ;(eval_start_6,3) ;(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_bb5_in,3) ;(eval_start_start,3) ;(eval_start_stop,3) ;(exitus616,3)} 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->{14} ,13->{15,16},14->{9,10},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:[9,11,14,12,10] c: [9] | `- p:[10,14,12] c: [12] * Step 4: SizeAbstraction MAYBE + Considered Problem: (Rules: 0. eval_start_start(v_n,v_x_0,v_y_0) -> eval_start_bb0_in(v_n,v_x_0,v_y_0) True (1,1) 1. eval_start_bb0_in(v_n,v_x_0,v_y_0) -> eval_start_0(v_n,v_x_0,v_y_0) True (?,1) 2. eval_start_0(v_n,v_x_0,v_y_0) -> eval_start_1(v_n,v_x_0,v_y_0) True (?,1) 3. eval_start_1(v_n,v_x_0,v_y_0) -> eval_start_2(v_n,v_x_0,v_y_0) True (?,1) 4. eval_start_2(v_n,v_x_0,v_y_0) -> eval_start_3(v_n,v_x_0,v_y_0) True (?,1) 5. eval_start_3(v_n,v_x_0,v_y_0) -> eval_start_4(v_n,v_x_0,v_y_0) True (?,1) 6. eval_start_4(v_n,v_x_0,v_y_0) -> eval_start_5(v_n,v_x_0,v_y_0) True (?,1) 7. eval_start_5(v_n,v_x_0,v_y_0) -> eval_start_6(v_n,v_x_0,v_y_0) True (?,1) 8. eval_start_6(v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_n,0,0) True (?,1) 9. eval_start_bb1_in(v_n,v_x_0,v_y_0) -> eval_start_bb2_in(v_n,v_x_0,v_y_0) [-1 + v_n >= v_x_0] (?,1) 10. eval_start_bb1_in(v_n,v_x_0,v_y_0) -> eval_start_bb3_in(v_n,v_x_0,v_y_0) [v_x_0 >= v_n] (?,1) 11. eval_start_bb2_in(v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_n,1 + v_x_0,1 + v_y_0) True (?,1) 12. eval_start_bb3_in(v_n,v_x_0,v_y_0) -> eval_start_bb4_in(v_n,v_x_0,v_y_0) [-1 + v_y_0 >= 0] (?,1) 13. eval_start_bb3_in(v_n,v_x_0,v_y_0) -> eval_start_bb5_in(v_n,v_x_0,v_y_0) [0 >= v_y_0] (?,1) 14. eval_start_bb4_in(v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_n,v_x_0,-1 + v_y_0) True (?,1) 15. eval_start_bb5_in(v_n,v_x_0,v_y_0) -> eval_start_stop(v_n,v_x_0,v_y_0) True (?,1) 16. eval_start_bb5_in(v_n,v_x_0,v_y_0) -> exitus616(v_n,v_x_0,v_y_0) True (?,1) Signature: {(eval_start_0,3) ;(eval_start_1,3) ;(eval_start_2,3) ;(eval_start_3,3) ;(eval_start_4,3) ;(eval_start_5,3) ;(eval_start_6,3) ;(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_bb5_in,3) ;(eval_start_start,3) ;(eval_start_stop,3) ;(exitus616,3)} 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->{14} ,13->{15,16},14->{9,10},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:[9,11,14,12,10] c: [9] | `- p:[10,14,12] c: [12]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 5: FlowAbstraction MAYBE + Considered Problem: Program: Domain: [v_n,v_x_0,v_y_0,0.0,0.0.0] eval_start_start ~> eval_start_bb0_in [v_n <= v_n, v_x_0 <= v_x_0, v_y_0 <= v_y_0] eval_start_bb0_in ~> eval_start_0 [v_n <= v_n, v_x_0 <= v_x_0, v_y_0 <= v_y_0] eval_start_0 ~> eval_start_1 [v_n <= v_n, v_x_0 <= v_x_0, v_y_0 <= v_y_0] eval_start_1 ~> eval_start_2 [v_n <= v_n, v_x_0 <= v_x_0, v_y_0 <= v_y_0] eval_start_2 ~> eval_start_3 [v_n <= v_n, v_x_0 <= v_x_0, v_y_0 <= v_y_0] eval_start_3 ~> eval_start_4 [v_n <= v_n, v_x_0 <= v_x_0, v_y_0 <= v_y_0] eval_start_4 ~> eval_start_5 [v_n <= v_n, v_x_0 <= v_x_0, v_y_0 <= v_y_0] eval_start_5 ~> eval_start_6 [v_n <= v_n, v_x_0 <= v_x_0, v_y_0 <= v_y_0] eval_start_6 ~> eval_start_bb1_in [v_n <= v_n, v_x_0 <= 0*K, v_y_0 <= 0*K] eval_start_bb1_in ~> eval_start_bb2_in [v_n <= v_n, v_x_0 <= v_x_0, v_y_0 <= v_y_0] eval_start_bb1_in ~> eval_start_bb3_in [v_n <= v_n, v_x_0 <= v_x_0, v_y_0 <= v_y_0] eval_start_bb2_in ~> eval_start_bb1_in [v_n <= v_n, v_x_0 <= K + v_x_0, v_y_0 <= K + v_y_0] eval_start_bb3_in ~> eval_start_bb4_in [v_n <= v_n, v_x_0 <= v_x_0, v_y_0 <= v_y_0] eval_start_bb3_in ~> eval_start_bb5_in [v_n <= v_n, v_x_0 <= v_x_0, v_y_0 <= v_y_0] eval_start_bb4_in ~> eval_start_bb1_in [v_n <= v_n, v_x_0 <= v_x_0, v_y_0 <= K + v_y_0] eval_start_bb5_in ~> eval_start_stop [v_n <= v_n, v_x_0 <= v_x_0, v_y_0 <= v_y_0] eval_start_bb5_in ~> exitus616 [v_n <= v_n, v_x_0 <= v_x_0, v_y_0 <= v_y_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, v_y_0 <= v_y_0] eval_start_bb2_in ~> eval_start_bb1_in [v_n <= v_n, v_x_0 <= K + v_x_0, v_y_0 <= K + v_y_0] eval_start_bb4_in ~> eval_start_bb1_in [v_n <= v_n, v_x_0 <= v_x_0, v_y_0 <= K + v_y_0] eval_start_bb3_in ~> eval_start_bb4_in [v_n <= v_n, v_x_0 <= v_x_0, v_y_0 <= v_y_0] eval_start_bb1_in ~> eval_start_bb3_in [v_n <= v_n, v_x_0 <= v_x_0, v_y_0 <= v_y_0] + Loop: [0.0.0 <= 2*K + v_y_0] eval_start_bb1_in ~> eval_start_bb3_in [v_n <= v_n, v_x_0 <= v_x_0, v_y_0 <= v_y_0] eval_start_bb4_in ~> eval_start_bb1_in [v_n <= v_n, v_x_0 <= v_x_0, v_y_0 <= K + v_y_0] eval_start_bb3_in ~> eval_start_bb4_in [v_n <= v_n, v_x_0 <= v_x_0, v_y_0 <= v_y_0] + Applied Processor: FlowAbstraction + Details: () * Step 6: LareProcessor MAYBE + Considered Problem: Program: Domain: [tick,huge,K,v_n,v_x_0,v_y_0,0.0,0.0.0] 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_4 [] eval_start_4 ~> eval_start_5 [] eval_start_5 ~> eval_start_6 [] eval_start_6 ~> eval_start_bb1_in [K ~=> v_x_0,K ~=> v_y_0] 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_x_0 ~+> v_x_0,v_y_0 ~+> v_y_0,K ~+> v_x_0,K ~+> v_y_0] eval_start_bb3_in ~> eval_start_bb4_in [] eval_start_bb3_in ~> eval_start_bb5_in [] eval_start_bb4_in ~> eval_start_bb1_in [v_y_0 ~+> v_y_0,K ~+> v_y_0] eval_start_bb5_in ~> eval_start_stop [] eval_start_bb5_in ~> exitus616 [] + Loop: [v_n ~+> 0.0,v_x_0 ~+> 0.0,K ~+> 0.0] eval_start_bb1_in ~> eval_start_bb2_in [] eval_start_bb2_in ~> eval_start_bb1_in [v_x_0 ~+> v_x_0,v_y_0 ~+> v_y_0,K ~+> v_x_0,K ~+> v_y_0] eval_start_bb4_in ~> eval_start_bb1_in [v_y_0 ~+> v_y_0,K ~+> v_y_0] eval_start_bb3_in ~> eval_start_bb4_in [] eval_start_bb1_in ~> eval_start_bb3_in [] + Loop: [v_y_0 ~+> 0.0.0,K ~*> 0.0.0] eval_start_bb1_in ~> eval_start_bb3_in [] eval_start_bb4_in ~> eval_start_bb1_in [v_y_0 ~+> v_y_0,K ~+> v_y_0] eval_start_bb3_in ~> eval_start_bb4_in [] + Applied Processor: LareProcessor + Details: eval_start_start ~> exitus616 [K ~=> v_x_0 ,K ~=> v_y_0 ,v_n ~+> 0.0 ,v_n ~+> tick ,tick ~+> tick ,K ~+> v_x_0 ,K ~+> v_y_0 ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,v_n ~*> v_x_0 ,v_n ~*> v_y_0 ,v_n ~*> 0.0.0 ,v_n ~*> tick ,K ~*> v_x_0 ,K ~*> v_y_0 ,K ~*> 0.0 ,K ~*> 0.0.0 ,K ~*> tick ,v_n ~^> v_y_0 ,v_n ~^> 0.0.0 ,v_n ~^> tick ,K ~^> v_y_0 ,K ~^> 0.0.0 ,K ~^> tick] eval_start_start ~> eval_start_stop [K ~=> v_x_0 ,K ~=> v_y_0 ,v_n ~+> 0.0 ,v_n ~+> tick ,tick ~+> tick ,K ~+> v_x_0 ,K ~+> v_y_0 ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,v_n ~*> v_x_0 ,v_n ~*> v_y_0 ,v_n ~*> 0.0.0 ,v_n ~*> tick ,K ~*> v_x_0 ,K ~*> v_y_0 ,K ~*> 0.0 ,K ~*> 0.0.0 ,K ~*> tick ,v_n ~^> v_y_0 ,v_n ~^> 0.0.0 ,v_n ~^> tick ,K ~^> v_y_0 ,K ~^> 0.0.0 ,K ~^> tick] + eval_start_bb3_in> [v_n ~+> 0.0 ,v_n ~+> tick ,v_x_0 ~+> v_x_0 ,v_x_0 ~+> 0.0 ,v_x_0 ~+> tick ,v_y_0 ~+> v_y_0 ,v_y_0 ~+> 0.0.0 ,v_y_0 ~+> tick ,tick ~+> tick ,K ~+> v_x_0 ,K ~+> v_y_0 ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,v_n ~*> v_x_0 ,v_n ~*> v_y_0 ,v_n ~*> 0.0.0 ,v_n ~*> tick ,v_x_0 ~*> v_x_0 ,v_x_0 ~*> v_y_0 ,v_x_0 ~*> 0.0.0 ,v_x_0 ~*> tick ,v_y_0 ~*> v_y_0 ,v_y_0 ~*> 0.0.0 ,v_y_0 ~*> tick ,K ~*> v_x_0 ,K ~*> v_y_0 ,K ~*> 0.0.0 ,K ~*> tick ,v_n ~^> v_y_0 ,v_n ~^> 0.0.0 ,v_n ~^> tick ,v_x_0 ~^> v_y_0 ,v_x_0 ~^> 0.0.0 ,v_x_0 ~^> tick ,K ~^> v_y_0 ,K ~^> 0.0.0 ,K ~^> tick] + eval_start_bb3_in> [v_y_0 ~+> v_y_0 ,v_y_0 ~+> 0.0.0 ,v_y_0 ~+> tick ,tick ~+> tick ,K ~+> v_y_0 ,v_y_0 ~*> v_y_0 ,K ~*> v_y_0 ,K ~*> 0.0.0 ,K ~*> tick] eval_start_bb1_in> [v_y_0 ~+> v_y_0 ,v_y_0 ~+> 0.0.0 ,v_y_0 ~+> tick ,tick ~+> tick ,K ~+> v_y_0 ,v_y_0 ~*> v_y_0 ,K ~*> v_y_0 ,K ~*> 0.0.0 ,K ~*> tick] YES(?,PRIMREC)