2.77/2.76 WORST_CASE(?,O(n^2)) 2.77/2.76 2.77/2.76 Preprocessing Cost Relations 2.77/2.76 ===================================== 2.77/2.76 2.77/2.76 #### Computed strongly connected components 2.77/2.76 0. non_recursive : [eval_realheapsort_stop/9] 2.77/2.76 1. non_recursive : [eval_realheapsort_bb16_in/9] 2.77/2.76 2. recursive : [eval_realheapsort_bb2_in/3,eval_realheapsort_bb3_in/3,eval_realheapsort_bb4_in/3] 2.77/2.76 3. recursive : [eval_realheapsort_28/8,eval_realheapsort_29/8,eval_realheapsort__critedge_in/8,eval_realheapsort_bb1_in/8,eval_realheapsort_bb2_in_loop_cont/9] 2.77/2.76 4. recursive : [eval_realheapsort_bb10_in/7,eval_realheapsort_bb11_in/7,eval_realheapsort_bb12_in/7,eval_realheapsort_bb13_in/7,eval_realheapsort_bb14_in/7,eval_realheapsort_bb8_in/7,eval_realheapsort_bb9_in/7] 2.77/2.76 5. recursive : [eval_realheapsort_85/10,eval_realheapsort_86/10,eval_realheapsort_bb15_in/10,eval_realheapsort_bb6_in/10,eval_realheapsort_bb7_in/10,eval_realheapsort_bb8_in_loop_cont/11] 2.77/2.76 6. non_recursive : [exit_location/1] 2.77/2.76 7. non_recursive : [eval_realheapsort_bb6_in_loop_cont/10] 2.77/2.76 8. non_recursive : [eval_realheapsort_39/9] 2.77/2.76 9. non_recursive : [eval_realheapsort_38/9] 2.77/2.76 10. non_recursive : [eval_realheapsort_37/9] 2.77/2.76 11. non_recursive : [eval_realheapsort_36/9] 2.77/2.76 12. non_recursive : [eval_realheapsort_35/9] 2.77/2.76 13. non_recursive : [eval_realheapsort_34/9] 2.77/2.76 14. non_recursive : [eval_realheapsort_33/9] 2.77/2.76 15. non_recursive : [eval_realheapsort_32/9] 2.77/2.76 16. non_recursive : [eval_realheapsort_31/9] 2.77/2.76 17. non_recursive : [eval_realheapsort_30/9] 2.77/2.76 18. non_recursive : [eval_realheapsort_bb5_in/9] 2.77/2.76 19. non_recursive : [eval_realheapsort_bb1_in_loop_cont/10] 2.77/2.76 20. non_recursive : [eval_realheapsort_2/9] 2.77/2.76 21. non_recursive : [eval_realheapsort_1/9] 2.77/2.76 22. non_recursive : [eval_realheapsort_0/9] 2.77/2.76 23. non_recursive : [eval_realheapsort_bb0_in/9] 2.77/2.76 24. non_recursive : [eval_realheapsort_start/9] 2.77/2.76 2.77/2.76 #### Obtained direct recursion through partial evaluation 2.77/2.76 0. SCC is completely evaluated into other SCCs 2.77/2.76 1. SCC is completely evaluated into other SCCs 2.77/2.76 2. SCC is partially evaluated into eval_realheapsort_bb2_in/3 2.77/2.76 3. SCC is partially evaluated into eval_realheapsort_bb1_in/8 2.77/2.76 4. SCC is partially evaluated into eval_realheapsort_bb8_in/7 2.77/2.76 5. SCC is partially evaluated into eval_realheapsort_bb6_in/10 2.77/2.76 6. SCC is completely evaluated into other SCCs 2.77/2.76 7. SCC is partially evaluated into eval_realheapsort_bb6_in_loop_cont/10 2.77/2.76 8. SCC is partially evaluated into eval_realheapsort_39/9 2.77/2.76 9. SCC is completely evaluated into other SCCs 2.77/2.76 10. SCC is completely evaluated into other SCCs 2.77/2.76 11. SCC is completely evaluated into other SCCs 2.77/2.76 12. SCC is completely evaluated into other SCCs 2.77/2.76 13. SCC is completely evaluated into other SCCs 2.77/2.76 14. SCC is completely evaluated into other SCCs 2.77/2.76 15. SCC is completely evaluated into other SCCs 2.77/2.76 16. SCC is completely evaluated into other SCCs 2.77/2.76 17. SCC is completely evaluated into other SCCs 2.77/2.76 18. SCC is completely evaluated into other SCCs 2.77/2.76 19. SCC is partially evaluated into eval_realheapsort_bb1_in_loop_cont/10 2.77/2.76 20. SCC is partially evaluated into eval_realheapsort_2/9 2.77/2.76 21. SCC is completely evaluated into other SCCs 2.77/2.76 22. SCC is completely evaluated into other SCCs 2.77/2.76 23. SCC is completely evaluated into other SCCs 2.77/2.76 24. SCC is partially evaluated into eval_realheapsort_start/9 2.77/2.76 2.77/2.76 Control-Flow Refinement of Cost Relations 2.77/2.76 ===================================== 2.77/2.76 2.77/2.76 ### Specialization of cost equations eval_realheapsort_bb2_in/3 2.77/2.76 * CE 13 is refined into CE [29] 2.77/2.76 * CE 10 is refined into CE [30] 2.77/2.76 * CE 12 is refined into CE [31] 2.77/2.76 * CE 11 is refined into CE [32] 2.77/2.76 2.77/2.76 2.77/2.76 ### Cost equations --> "Loop" of eval_realheapsort_bb2_in/3 2.77/2.76 * CEs [32] --> Loop 29 2.77/2.76 * CEs [29] --> Loop 30 2.77/2.76 * CEs [30] --> Loop 31 2.77/2.76 * CEs [31] --> Loop 32 2.77/2.76 2.77/2.76 ### Ranking functions of CR eval_realheapsort_bb2_in(V_j_0,B,C) 2.77/2.76 * RF of phase [29]: [V_j_0] 2.77/2.76 2.77/2.76 #### Partial ranking functions of CR eval_realheapsort_bb2_in(V_j_0,B,C) 2.77/2.76 * Partial RF of phase [29]: 2.77/2.76 - RF of loop [29:1]: 2.77/2.76 V_j_0 2.77/2.76 2.77/2.76 2.77/2.76 ### Specialization of cost equations eval_realheapsort_bb1_in/8 2.77/2.76 * CE 6 is refined into CE [33] 2.77/2.76 * CE 4 is refined into CE [34,35] 2.77/2.76 * CE 7 is refined into CE [36] 2.77/2.76 * CE 5 is refined into CE [37,38,39] 2.77/2.76 2.77/2.76 2.77/2.76 ### Cost equations --> "Loop" of eval_realheapsort_bb1_in/8 2.77/2.76 * CEs [39] --> Loop 33 2.77/2.76 * CEs [38] --> Loop 34 2.77/2.76 * CEs [37] --> Loop 35 2.77/2.76 * CEs [33] --> Loop 36 2.77/2.76 * CEs [34,35] --> Loop 37 2.77/2.76 * CEs [36] --> Loop 38 2.77/2.76 2.77/2.76 ### Ranking functions of CR eval_realheapsort_bb1_in(V_33,V_N,V_j_0,V_k_0,B,C,D,E) 2.77/2.76 * RF of phase [33,34,35]: [V_N-V_k_0] 2.77/2.76 2.77/2.76 #### Partial ranking functions of CR eval_realheapsort_bb1_in(V_33,V_N,V_j_0,V_k_0,B,C,D,E) 2.77/2.76 * Partial RF of phase [33,34,35]: 2.77/2.76 - RF of loop [33:1,34:1,35:1]: 2.77/2.76 V_N-V_k_0 2.77/2.76 2.77/2.76 2.77/2.76 ### Specialization of cost equations eval_realheapsort_bb8_in/7 2.77/2.76 * CE 27 is refined into CE [40] 2.77/2.76 * CE 28 is refined into CE [41] 2.77/2.76 * CE 26 is refined into CE [42] 2.77/2.76 * CE 23 is refined into CE [43] 2.77/2.76 * CE 24 is refined into CE [44] 2.77/2.76 * CE 22 is refined into CE [45] 2.77/2.76 * CE 25 is refined into CE [46] 2.77/2.76 * CE 21 is refined into CE [47] 2.77/2.76 2.77/2.76 2.77/2.76 ### Cost equations --> "Loop" of eval_realheapsort_bb8_in/7 2.77/2.76 * CEs [42] --> Loop 39 2.77/2.76 * CEs [43] --> Loop 40 2.77/2.76 * CEs [44] --> Loop 41 2.77/2.76 * CEs [45] --> Loop 42 2.77/2.76 * CEs [46] --> Loop 43 2.77/2.76 * CEs [47] --> Loop 44 2.77/2.76 * CEs [40] --> Loop 45 2.77/2.76 * CEs [41] --> Loop 46 2.77/2.76 2.77/2.76 ### Ranking functions of CR eval_realheapsort_bb8_in(V_N,V_j_1,V_k_1,V_m_0,B,C,D) 2.77/2.76 * RF of phase [42,44]: [V_N/2-V_j_1-3/2,V_N/2-V_j_1-V_k_1/2-3/2] 2.77/2.76 2.77/2.76 #### Partial ranking functions of CR eval_realheapsort_bb8_in(V_N,V_j_1,V_k_1,V_m_0,B,C,D) 2.77/2.76 * Partial RF of phase [42,44]: 2.77/2.76 - RF of loop [42:1,44:1]: 2.77/2.76 V_N/2-V_j_1-3/2 2.77/2.76 V_N/2-V_j_1-V_k_1/2-3/2 2.77/2.76 2.77/2.76 2.77/2.76 ### Specialization of cost equations eval_realheapsort_bb6_in/10 2.77/2.76 * CE 17 is refined into CE [48] 2.77/2.76 * CE 15 is refined into CE [49,50,51,52,53] 2.77/2.76 * CE 18 is refined into CE [54] 2.77/2.76 * CE 16 is refined into CE [55,56,57,58,59,60,61,62,63,64] 2.77/2.76 2.77/2.76 2.77/2.76 ### Cost equations --> "Loop" of eval_realheapsort_bb6_in/10 2.77/2.76 * CEs [64] --> Loop 47 2.77/2.76 * CEs [60] --> Loop 48 2.77/2.76 * CEs [63] --> Loop 49 2.77/2.76 * CEs [62] --> Loop 50 2.77/2.76 * CEs [61] --> Loop 51 2.77/2.76 * CEs [58] --> Loop 52 2.77/2.76 * CEs [59] --> Loop 53 2.77/2.76 * CEs [56] --> Loop 54 2.77/2.76 * CEs [55] --> Loop 55 2.77/2.76 * CEs [57] --> Loop 56 2.77/2.76 * CEs [48] --> Loop 57 2.77/2.76 * CEs [52] --> Loop 58 2.77/2.76 * CEs [51] --> Loop 59 2.77/2.76 * CEs [53] --> Loop 60 2.77/2.76 * CEs [50] --> Loop 61 2.77/2.76 * CEs [54] --> Loop 62 2.77/2.76 * CEs [49] --> Loop 63 2.77/2.76 2.77/2.76 ### Ranking functions of CR eval_realheapsort_bb6_in(V_90,V_N,V_j_1,V_k_1,V_m_0,B,C,D,E,F) 2.77/2.76 * RF of phase [47,48,49,50,51,52,53]: [V_N-V_k_1-3] 2.77/2.76 2.77/2.76 #### Partial ranking functions of CR eval_realheapsort_bb6_in(V_90,V_N,V_j_1,V_k_1,V_m_0,B,C,D,E,F) 2.77/2.76 * Partial RF of phase [47,48,49,50,51,52,53]: 2.77/2.76 - RF of loop [47:1,48:1]: 2.77/2.76 V_N-V_k_1-4 2.77/2.76 - RF of loop [49:1,52:1,53:1]: 2.77/2.76 V_N-V_k_1-3 2.77/2.76 - RF of loop [50:1,51:1]: 2.77/2.76 V_N-V_k_1-5 2.77/2.76 2.77/2.76 2.77/2.76 ### Specialization of cost equations eval_realheapsort_bb6_in_loop_cont/10 2.77/2.76 * CE 19 is refined into CE [65] 2.77/2.76 * CE 20 is refined into CE [66] 2.77/2.76 2.77/2.76 2.77/2.76 ### Cost equations --> "Loop" of eval_realheapsort_bb6_in_loop_cont/10 2.77/2.76 * CEs [65] --> Loop 64 2.77/2.76 * CEs [66] --> Loop 65 2.77/2.76 2.77/2.76 ### Ranking functions of CR eval_realheapsort_bb6_in_loop_cont(A,B,C,D,E,F,G,H,I,J) 2.77/2.76 2.77/2.76 #### Partial ranking functions of CR eval_realheapsort_bb6_in_loop_cont(A,B,C,D,E,F,G,H,I,J) 2.77/2.76 2.77/2.76 2.77/2.76 ### Specialization of cost equations eval_realheapsort_39/9 2.77/2.76 * CE 14 is refined into CE [67,68,69,70,71,72,73,74,75,76] 2.77/2.76 2.77/2.76 2.77/2.76 ### Cost equations --> "Loop" of eval_realheapsort_39/9 2.77/2.76 * CEs [74] --> Loop 66 2.77/2.76 * CEs [73] --> Loop 67 2.77/2.76 * CEs [72] --> Loop 68 2.77/2.76 * CEs [71,76] --> Loop 69 2.77/2.76 * CEs [69,70] --> Loop 70 2.77/2.76 * CEs [67,68,75] --> Loop 71 2.77/2.76 2.77/2.76 ### Ranking functions of CR eval_realheapsort_39(V_33,V_90,V_N,V_j_0,V_j_1,V_k_0,V_k_1,V_m_0,B) 2.77/2.76 2.77/2.76 #### Partial ranking functions of CR eval_realheapsort_39(V_33,V_90,V_N,V_j_0,V_j_1,V_k_0,V_k_1,V_m_0,B) 2.77/2.76 2.77/2.76 2.77/2.76 ### Specialization of cost equations eval_realheapsort_bb1_in_loop_cont/10 2.77/2.76 * CE 8 is refined into CE [77,78,79,80,81,82] 2.77/2.76 * CE 9 is refined into CE [83] 2.77/2.76 2.77/2.76 2.77/2.76 ### Cost equations --> "Loop" of eval_realheapsort_bb1_in_loop_cont/10 2.77/2.76 * CEs [82] --> Loop 72 2.77/2.76 * CEs [81] --> Loop 73 2.77/2.76 * CEs [80] --> Loop 74 2.77/2.76 * CEs [79] --> Loop 75 2.77/2.76 * CEs [78] --> Loop 76 2.77/2.76 * CEs [77] --> Loop 77 2.77/2.76 * CEs [83] --> Loop 78 2.77/2.76 2.77/2.76 ### Ranking functions of CR eval_realheapsort_bb1_in_loop_cont(A,B,C,D,E,F,G,H,I,J) 2.77/2.76 2.77/2.76 #### Partial ranking functions of CR eval_realheapsort_bb1_in_loop_cont(A,B,C,D,E,F,G,H,I,J) 2.77/2.76 2.77/2.76 2.77/2.76 ### Specialization of cost equations eval_realheapsort_2/9 2.77/2.76 * CE 3 is refined into CE [84,85,86,87,88,89,90,91,92] 2.77/2.76 * CE 2 is refined into CE [93] 2.77/2.76 2.77/2.76 2.77/2.76 ### Cost equations --> "Loop" of eval_realheapsort_2/9 2.77/2.76 * CEs [92] --> Loop 79 2.77/2.76 * CEs [91] --> Loop 80 2.77/2.76 * CEs [90] --> Loop 81 2.77/2.76 * CEs [89] --> Loop 82 2.77/2.76 * CEs [84,85,86,88] --> Loop 83 2.77/2.76 * CEs [93] --> Loop 84 2.77/2.76 * CEs [87] --> Loop 85 2.77/2.76 2.77/2.76 ### Ranking functions of CR eval_realheapsort_2(V_33,V_90,V_N,V_j_0,V_j_1,V_k_0,V_k_1,V_m_0,B) 2.77/2.76 2.77/2.76 #### Partial ranking functions of CR eval_realheapsort_2(V_33,V_90,V_N,V_j_0,V_j_1,V_k_0,V_k_1,V_m_0,B) 2.77/2.76 2.77/2.76 2.77/2.76 ### Specialization of cost equations eval_realheapsort_start/9 2.77/2.76 * CE 1 is refined into CE [94,95,96,97,98,99,100] 2.77/2.76 2.77/2.76 2.77/2.76 ### Cost equations --> "Loop" of eval_realheapsort_start/9 2.77/2.76 * CEs [100] --> Loop 86 2.77/2.76 * CEs [99] --> Loop 87 2.77/2.76 * CEs [98] --> Loop 88 2.77/2.76 * CEs [97] --> Loop 89 2.77/2.76 * CEs [96] --> Loop 90 2.77/2.76 * CEs [95] --> Loop 91 2.77/2.76 * CEs [94] --> Loop 92 2.77/2.76 2.77/2.76 ### Ranking functions of CR eval_realheapsort_start(V_33,V_90,V_N,V_j_0,V_j_1,V_k_0,V_k_1,V_m_0,B) 2.77/2.76 2.77/2.76 #### Partial ranking functions of CR eval_realheapsort_start(V_33,V_90,V_N,V_j_0,V_j_1,V_k_0,V_k_1,V_m_0,B) 2.77/2.76 2.77/2.76 2.77/2.76 Computing Bounds 2.77/2.76 ===================================== 2.77/2.76 2.77/2.76 #### Cost of chains of eval_realheapsort_bb2_in(V_j_0,B,C): 2.77/2.76 * Chain [[29],32]: 1*it(29)+0 2.77/2.76 Such that:it(29) =< V_j_0 2.77/2.76 2.77/2.76 with precondition: [B=2,0>=C,V_j_0>=1,2*C+1>=0] 2.77/2.76 2.77/2.76 * Chain [[29],31]: 1*it(29)+0 2.77/2.76 Such that:it(29) =< V_j_0-C 2.77/2.76 2.77/2.76 with precondition: [B=2,C>=1,V_j_0>=2*C+1] 2.77/2.76 2.77/2.76 * Chain [[29],30]: 1*it(29)+0 2.77/2.76 Such that:it(29) =< V_j_0 2.77/2.76 2.77/2.76 with precondition: [B=3,V_j_0>=1] 2.77/2.76 2.77/2.76 * Chain [31]: 0 2.77/2.76 with precondition: [B=2,V_j_0=C,V_j_0>=1] 2.77/2.76 2.77/2.76 * Chain [30]: 0 2.77/2.76 with precondition: [B=3,2*V_j_0+1>=0] 2.77/2.76 2.77/2.76 2.77/2.76 #### Cost of chains of eval_realheapsort_bb1_in(V_33,V_N,V_j_0,V_k_0,B,C,D,E): 2.77/2.76 * Chain [[33,34,35],38]: 3*it(33)+1*s(5)+1*s(6)+0 2.77/2.76 Such that:aux(1) =< V_N 2.77/2.76 aux(5) =< V_N-V_k_0 2.77/2.76 it(33) =< aux(5) 2.77/2.76 aux(2) =< aux(1)+1 2.77/2.76 s(5) =< it(33)*aux(1) 2.77/2.76 s(6) =< it(33)*aux(2) 2.77/2.76 2.77/2.76 with precondition: [B=3,V_N>=3,V_k_0>=1,V_N>=V_k_0+1] 2.77/2.76 2.77/2.76 * Chain [[33,34,35],37]: 3*it(33)+1*s(5)+1*s(6)+1*s(7)+0 2.77/2.76 Such that:aux(6) =< V_N 2.77/2.76 aux(7) =< V_N-V_k_0 2.77/2.76 s(7) =< aux(6) 2.77/2.76 it(33) =< aux(7) 2.77/2.76 aux(2) =< aux(6)+1 2.77/2.76 s(5) =< it(33)*aux(6) 2.77/2.76 s(6) =< it(33)*aux(2) 2.77/2.76 2.77/2.76 with precondition: [B=3,V_k_0>=1,V_N>=V_k_0+2] 2.77/2.76 2.77/2.76 * Chain [[33,34,35],36]: 3*it(33)+1*s(5)+1*s(6)+0 2.77/2.76 Such that:aux(1) =< C 2.77/2.76 aux(8) =< -V_k_0+C 2.77/2.76 it(33) =< aux(8) 2.77/2.76 aux(2) =< aux(1)+1 2.77/2.76 s(5) =< it(33)*aux(1) 2.77/2.76 s(6) =< it(33)*aux(2) 2.77/2.76 2.77/2.76 with precondition: [B=5,V_N=C,V_N=E,V_N>=3,V_k_0>=1,2*D+1>=0,V_N>=V_k_0+1,V_N>=D+1] 2.77/2.76 2.77/2.76 * Chain [38]: 0 2.77/2.76 with precondition: [B=3,V_N>=3,V_k_0>=1] 2.77/2.76 2.77/2.76 * Chain [37]: 1*s(7)+0 2.77/2.76 Such that:s(7) =< V_k_0 2.77/2.76 2.77/2.76 with precondition: [B=3,V_N>=3,V_k_0>=1,V_N>=V_k_0+1] 2.77/2.76 2.77/2.76 2.77/2.76 #### Cost of chains of eval_realheapsort_bb8_in(V_N,V_j_1,V_k_1,V_m_0,B,C,D): 2.77/2.76 * Chain [[42,44],46]: 2*it(42)+0 2.77/2.76 Such that:aux(9) =< V_N/2-V_j_1 2.77/2.76 aux(10) =< V_N/2-V_j_1-V_k_1/2 2.77/2.76 aux(13) =< V_N-V_j_1-V_k_1 2.77/2.76 it(42) =< aux(9) 2.77/2.76 it(42) =< aux(10) 2.77/2.76 it(42) =< aux(13) 2.77/2.76 2.77/2.76 with precondition: [B=3,V_j_1>=0,V_k_1>=0,V_N>=2*V_j_1+V_k_1+4] 2.77/2.76 2.77/2.76 * Chain [[42,44],45]: 2*it(42)+0 2.77/2.76 Such that:aux(9) =< V_N/2-V_j_1 2.77/2.76 aux(10) =< V_N/2-V_j_1-V_k_1/2 2.77/2.76 aux(14) =< -V_j_1+C 2.77/2.76 it(42) =< aux(9) 2.77/2.76 it(42) =< aux(10) 2.77/2.76 it(42) =< aux(14) 2.77/2.76 2.77/2.76 with precondition: [B=4,C=D,V_j_1>=0,V_k_1>=0,C>=2*V_j_1+1,V_N>=2*V_j_1+V_k_1+4,V_k_1+2*C+2>=V_N,V_N>=V_k_1+C+2] 2.77/2.76 2.77/2.76 * Chain [[42,44],43,46]: 2*it(42)+1 2.77/2.76 Such that:aux(9) =< V_N/2-V_j_1 2.77/2.76 aux(15) =< V_N/2-V_j_1-V_k_1/2 2.77/2.76 it(42) =< aux(9) 2.77/2.76 it(42) =< aux(15) 2.77/2.76 2.77/2.76 with precondition: [B=3,V_j_1>=0,V_k_1>=0,V_N>=4*V_j_1+V_k_1+5] 2.77/2.76 2.77/2.76 * Chain [[42,44],43,45]: 2*it(42)+1 2.77/2.76 Such that:aux(9) =< -V_j_1+V_k_1/2+C/2+1 2.77/2.76 aux(10) =< -V_j_1+C/2+1 2.77/2.76 aux(16) =< -V_j_1+C/2 2.77/2.76 it(42) =< aux(9) 2.77/2.76 it(42) =< aux(10) 2.77/2.76 it(42) =< aux(16) 2.77/2.76 2.77/2.76 with precondition: [B=4,V_N=V_k_1+C+2,V_N=V_k_1+D+2,V_j_1>=0,V_k_1>=0,V_N>=4*V_j_1+V_k_1+5] 2.77/2.76 2.77/2.76 * Chain [[42,44],41,46]: 2*it(42)+1 2.77/2.76 Such that:aux(9) =< V_N/2-V_j_1 2.77/2.76 aux(17) =< V_N/2-V_j_1-V_k_1/2 2.77/2.76 it(42) =< aux(9) 2.77/2.76 it(42) =< aux(17) 2.77/2.76 2.77/2.76 with precondition: [B=3,V_j_1>=0,V_k_1>=0,V_N>=4*V_j_1+V_k_1+6] 2.77/2.76 2.77/2.76 * Chain [[42,44],41,45]: 2*it(42)+1 2.77/2.76 Such that:aux(10) =< -V_j_1-V_k_1/2+C/2 2.77/2.76 aux(9) =< -V_j_1+C/2 2.77/2.76 aux(18) =< -V_j_1+D/2 2.77/2.76 it(42) =< aux(9) 2.77/2.76 it(42) =< aux(10) 2.77/2.76 it(42) =< aux(18) 2.77/2.76 2.77/2.76 with precondition: [B=4,V_N=C,V_j_1>=0,V_k_1>=0,D>=4*V_j_1+4,V_N>=V_k_1+D+2] 2.77/2.76 2.77/2.76 * Chain [[42,44],40,46]: 2*it(42)+1 2.77/2.76 Such that:aux(9) =< V_N/2-V_j_1 2.77/2.76 aux(19) =< V_N/2-V_j_1-V_k_1/2 2.77/2.76 it(42) =< aux(9) 2.77/2.76 it(42) =< aux(19) 2.77/2.76 2.77/2.76 with precondition: [B=3,V_j_1>=0,V_k_1>=0,V_N>=4*V_j_1+V_k_1+6] 2.77/2.76 2.77/2.76 * Chain [[42,44],40,45]: 2*it(42)+1 2.77/2.76 Such that:aux(10) =< -V_j_1-V_k_1/2+C/2 2.77/2.76 aux(9) =< -V_j_1+C/2 2.77/2.76 aux(20) =< -V_j_1+D/2 2.77/2.76 it(42) =< aux(9) 2.77/2.76 it(42) =< aux(10) 2.77/2.76 it(42) =< aux(20) 2.77/2.76 2.77/2.76 with precondition: [B=4,V_N=C,V_j_1>=0,V_k_1>=0,D>=4*V_j_1+3,V_N>=V_k_1+D+3] 2.77/2.76 2.77/2.76 * Chain [[42,44],39,46]: 2*it(42)+1 2.77/2.76 Such that:aux(9) =< V_N/2-V_j_1 2.77/2.76 aux(21) =< V_N/2-V_j_1-V_k_1/2 2.77/2.76 it(42) =< aux(9) 2.77/2.76 it(42) =< aux(21) 2.77/2.76 2.77/2.76 with precondition: [B=3,V_j_1>=0,V_k_1>=0,V_N>=4*V_j_1+V_k_1+5] 2.77/2.76 2.77/2.76 * Chain [[42,44],39,45]: 2*it(42)+1 2.77/2.76 Such that:aux(9) =< -V_j_1+C/2 2.77/2.76 aux(10) =< -V_j_1+D/2+1 2.77/2.76 aux(22) =< -V_j_1+D/2 2.77/2.76 it(42) =< aux(9) 2.77/2.76 it(42) =< aux(10) 2.77/2.76 it(42) =< aux(22) 2.77/2.76 2.77/2.76 with precondition: [B=4,V_N=C,V_N=V_k_1+D+2,V_j_1>=0,V_k_1>=0,V_N>=4*V_j_1+V_k_1+5] 2.77/2.76 2.77/2.76 * Chain [46]: 0 2.77/2.76 with precondition: [B=3,V_N>=3,V_j_1>=0,V_k_1>=0,V_N>=V_j_1,V_N>=V_k_1+2,4*V_N>=3*V_k_1+V_j_1+9] 2.77/2.76 2.77/2.76 * Chain [45]: 0 2.77/2.76 with precondition: [B=4,D=V_m_0,V_j_1=C,V_N>=3,V_k_1>=0,V_N>=V_j_1,V_N>=V_k_1+2,4*V_N>=3*V_k_1+V_j_1+9,V_k_1+2*V_j_1+2>=V_N] 2.77/2.76 2.77/2.76 * Chain [43,46]: 1 2.77/2.76 with precondition: [B=3,V_k_1+2*V_j_1+3=V_N,V_k_1>=0,V_N>=V_k_1+3] 2.77/2.76 2.77/2.76 * Chain [43,45]: 1 2.77/2.76 with precondition: [B=4,C=2*V_j_1+1,C=D,V_k_1+C+2=V_N,C>=1,V_N>=C+2] 2.77/2.76 2.77/2.76 * Chain [41,46]: 1 2.77/2.76 with precondition: [B=3,V_j_1>=0,V_k_1>=0,V_N>=2*V_j_1+V_k_1+4] 2.77/2.76 2.77/2.76 * Chain [41,45]: 1 2.77/2.76 with precondition: [B=4,V_N=C,2*V_j_1+2=D,V_j_1>=0,V_k_1>=0,V_N>=2*V_j_1+V_k_1+4] 2.77/2.76 2.77/2.76 * Chain [40,46]: 1 2.77/2.76 with precondition: [B=3,V_j_1>=0,V_k_1>=0,V_N>=2*V_j_1+V_k_1+4] 2.77/2.76 2.77/2.76 * Chain [40,45]: 1 2.77/2.76 with precondition: [B=4,V_N=C,2*V_j_1+1=D,V_j_1>=0,V_k_1>=0,V_N>=2*V_j_1+V_k_1+4] 2.77/2.76 2.77/2.76 * Chain [39,46]: 1 2.77/2.76 with precondition: [B=3,V_k_1+2*V_j_1+3=V_N,V_k_1>=0,V_N>=V_k_1+3] 2.77/2.76 2.77/2.76 * Chain [39,45]: 1 2.77/2.76 with precondition: [B=4,D=2*V_j_1+1,V_N=C,V_N=V_k_1+D+2,D>=1,V_N>=D+2] 2.77/2.76 2.77/2.76 2.77/2.76 #### Cost of chains of eval_realheapsort_bb6_in(V_90,V_N,V_j_1,V_k_1,V_m_0,B,C,D,E,F): 2.77/2.76 * Chain [[47,48,49,50,51,52,53],63]: 13*it(47)+2*s(69)+2*s(72)+2*s(75)+2*s(79)+2*s(83)+1 2.77/2.76 Such that:aux(30) =< V_N/2 2.77/2.76 aux(29) =< V_N/2-V_k_1/2 2.77/2.76 aux(44) =< V_N-V_k_1 2.77/2.76 it(47) =< aux(44) 2.77/2.76 aux(41) =< aux(29)-3/2 2.77/2.76 aux(32) =< aux(30) 2.77/2.76 aux(31) =< aux(29) 2.77/2.76 aux(38) =< aux(29)-1 2.77/2.76 aux(35) =< aux(29)*2-2 2.77/2.76 s(71) =< it(47)*aux(30) 2.77/2.76 s(70) =< it(47)*aux(29) 2.77/2.76 s(84) =< it(47)*aux(41) 2.77/2.76 s(74) =< it(47)*aux(32) 2.77/2.76 s(73) =< it(47)*aux(31) 2.77/2.76 s(80) =< it(47)*aux(38) 2.77/2.76 s(76) =< it(47)*aux(35) 2.77/2.76 s(83) =< s(74) 2.77/2.76 s(83) =< s(73) 2.77/2.76 s(83) =< s(84) 2.77/2.76 s(79) =< s(74) 2.77/2.76 s(79) =< s(73) 2.77/2.76 s(79) =< s(80) 2.77/2.76 s(75) =< s(74) 2.77/2.76 s(75) =< s(73) 2.77/2.76 s(75) =< s(76) 2.77/2.76 s(72) =< s(74) 2.77/2.76 s(72) =< s(73) 2.77/2.76 s(69) =< s(71) 2.77/2.76 s(69) =< s(70) 2.77/2.76 2.77/2.76 with precondition: [B=3,V_k_1>=0,V_N>=V_k_1+4] 2.77/2.76 2.77/2.76 * Chain [[47,48,49,50,51,52,53],62]: 13*it(47)+2*s(69)+2*s(72)+2*s(75)+2*s(79)+2*s(83)+0 2.77/2.76 Such that:aux(30) =< V_N/2 2.77/2.76 aux(29) =< V_N/2-V_k_1/2 2.77/2.76 aux(45) =< V_N-V_k_1 2.77/2.76 it(47) =< aux(45) 2.77/2.76 aux(41) =< aux(29)-3/2 2.77/2.76 aux(32) =< aux(30) 2.77/2.76 aux(31) =< aux(29) 2.77/2.76 aux(38) =< aux(29)-1 2.77/2.76 aux(35) =< aux(29)*2-2 2.77/2.76 s(71) =< it(47)*aux(30) 2.77/2.76 s(70) =< it(47)*aux(29) 2.77/2.76 s(84) =< it(47)*aux(41) 2.77/2.76 s(74) =< it(47)*aux(32) 2.77/2.76 s(73) =< it(47)*aux(31) 2.77/2.76 s(80) =< it(47)*aux(38) 2.77/2.76 s(76) =< it(47)*aux(35) 2.77/2.76 s(83) =< s(74) 2.77/2.76 s(83) =< s(73) 2.77/2.76 s(83) =< s(84) 2.77/2.76 s(79) =< s(74) 2.77/2.76 s(79) =< s(73) 2.77/2.76 s(79) =< s(80) 2.77/2.76 s(75) =< s(74) 2.77/2.76 s(75) =< s(73) 2.77/2.76 s(75) =< s(76) 2.77/2.76 s(72) =< s(74) 2.77/2.76 s(72) =< s(73) 2.77/2.76 s(69) =< s(71) 2.77/2.76 s(69) =< s(70) 2.77/2.76 2.77/2.76 with precondition: [B=3,V_k_1>=0,V_N>=V_k_1+4] 2.77/2.76 2.77/2.76 * Chain [[47,48,49,50,51,52,53],61]: 13*it(47)+2*s(69)+2*s(72)+2*s(75)+2*s(79)+2*s(83)+0 2.77/2.76 Such that:aux(30) =< V_N/2 2.77/2.76 aux(29) =< V_N/2-V_k_1/2 2.77/2.76 aux(46) =< V_N-V_k_1 2.77/2.76 it(47) =< aux(46) 2.77/2.76 aux(41) =< aux(29)-3/2 2.77/2.77 aux(32) =< aux(30) 2.77/2.77 aux(31) =< aux(29) 2.77/2.77 aux(38) =< aux(29)-1 2.77/2.77 aux(35) =< aux(29)*2-2 2.77/2.77 s(71) =< it(47)*aux(30) 2.77/2.77 s(70) =< it(47)*aux(29) 2.77/2.77 s(84) =< it(47)*aux(41) 2.77/2.77 s(74) =< it(47)*aux(32) 2.77/2.77 s(73) =< it(47)*aux(31) 2.77/2.77 s(80) =< it(47)*aux(38) 2.77/2.77 s(76) =< it(47)*aux(35) 2.77/2.77 s(83) =< s(74) 2.77/2.77 s(83) =< s(73) 2.77/2.77 s(83) =< s(84) 2.77/2.77 s(79) =< s(74) 2.77/2.77 s(79) =< s(73) 2.77/2.77 s(79) =< s(80) 2.77/2.77 s(75) =< s(74) 2.77/2.77 s(75) =< s(73) 2.77/2.77 s(75) =< s(76) 2.77/2.77 s(72) =< s(74) 2.77/2.77 s(72) =< s(73) 2.77/2.77 s(69) =< s(71) 2.77/2.77 s(69) =< s(70) 2.77/2.77 2.77/2.77 with precondition: [B=3,V_k_1>=0,V_N>=V_k_1+4] 2.77/2.77 2.77/2.77 * Chain [[47,48,49,50,51,52,53],60]: 13*it(47)+2*s(69)+2*s(72)+2*s(75)+2*s(79)+2*s(83)+2*s(90)+1 2.77/2.77 Such that:aux(47) =< V_N-V_k_1 2.77/2.77 aux(48) =< V_N/2 2.77/2.77 aux(49) =< V_N/2-V_k_1/2 2.77/2.77 s(89) =< aux(47) 2.77/2.77 s(89) =< aux(49) 2.77/2.77 s(90) =< aux(48) 2.77/2.77 s(90) =< s(89) 2.77/2.77 s(90) =< aux(47) 2.77/2.77 it(47) =< aux(47) 2.77/2.77 aux(41) =< aux(49)-3/2 2.77/2.77 aux(32) =< aux(48) 2.77/2.77 aux(31) =< aux(49) 2.77/2.77 aux(38) =< aux(49)-1 2.77/2.77 aux(35) =< aux(49)*2-2 2.77/2.77 s(71) =< it(47)*aux(48) 2.77/2.77 s(70) =< it(47)*aux(49) 2.77/2.77 s(84) =< it(47)*aux(41) 2.77/2.77 s(74) =< it(47)*aux(32) 2.77/2.77 s(73) =< it(47)*aux(31) 2.77/2.77 s(80) =< it(47)*aux(38) 2.77/2.77 s(76) =< it(47)*aux(35) 2.77/2.77 s(83) =< s(74) 2.77/2.77 s(83) =< s(73) 2.77/2.77 s(83) =< s(84) 2.77/2.77 s(79) =< s(74) 2.77/2.77 s(79) =< s(73) 2.77/2.77 s(79) =< s(80) 2.77/2.77 s(75) =< s(74) 2.77/2.77 s(75) =< s(73) 2.77/2.77 s(75) =< s(76) 2.77/2.77 s(72) =< s(74) 2.77/2.77 s(72) =< s(73) 2.77/2.77 s(69) =< s(71) 2.77/2.77 s(69) =< s(70) 2.77/2.77 2.77/2.77 with precondition: [B=3,V_k_1>=0,V_N>=V_k_1+5] 2.77/2.77 2.77/2.77 * Chain [[47,48,49,50,51,52,53],59]: 13*it(47)+2*s(69)+2*s(72)+2*s(75)+2*s(79)+2*s(83)+4*s(93)+1 2.77/2.77 Such that:aux(50) =< V_N-V_k_1 2.77/2.77 aux(51) =< V_N/2 2.77/2.77 aux(52) =< V_N/2-V_k_1/2 2.77/2.77 s(92) =< aux(50) 2.77/2.77 s(92) =< aux(52) 2.77/2.77 s(93) =< aux(51) 2.77/2.77 s(93) =< s(92) 2.77/2.77 it(47) =< aux(50) 2.77/2.77 aux(41) =< aux(52)-3/2 2.77/2.77 aux(32) =< aux(51) 2.77/2.77 aux(31) =< aux(52) 2.77/2.77 aux(38) =< aux(52)-1 2.77/2.77 aux(35) =< aux(52)*2-2 2.77/2.77 s(71) =< it(47)*aux(51) 2.77/2.77 s(70) =< it(47)*aux(52) 2.77/2.77 s(84) =< it(47)*aux(41) 2.77/2.77 s(74) =< it(47)*aux(32) 2.77/2.77 s(73) =< it(47)*aux(31) 2.77/2.77 s(80) =< it(47)*aux(38) 2.77/2.77 s(76) =< it(47)*aux(35) 2.77/2.77 s(83) =< s(74) 2.77/2.77 s(83) =< s(73) 2.77/2.77 s(83) =< s(84) 2.77/2.77 s(79) =< s(74) 2.77/2.77 s(79) =< s(73) 2.77/2.77 s(79) =< s(80) 2.77/2.77 s(75) =< s(74) 2.77/2.77 s(75) =< s(73) 2.77/2.77 s(75) =< s(76) 2.77/2.77 s(72) =< s(74) 2.77/2.77 s(72) =< s(73) 2.77/2.77 s(69) =< s(71) 2.77/2.77 s(69) =< s(70) 2.77/2.77 2.77/2.77 with precondition: [B=3,V_k_1>=0,V_N>=V_k_1+6] 2.77/2.77 2.77/2.77 * Chain [[47,48,49,50,51,52,53],58]: 13*it(47)+2*s(69)+2*s(72)+2*s(75)+2*s(79)+2*s(83)+4*s(96)+1 2.77/2.77 Such that:aux(53) =< V_N-V_k_1 2.77/2.77 aux(54) =< V_N/2 2.77/2.77 aux(55) =< V_N/2-V_k_1/2 2.77/2.77 s(95) =< aux(53) 2.77/2.77 s(95) =< aux(55) 2.77/2.77 s(96) =< aux(54) 2.77/2.77 s(96) =< s(95) 2.77/2.77 it(47) =< aux(53) 2.77/2.77 aux(41) =< aux(55)-3/2 2.77/2.77 aux(32) =< aux(54) 2.77/2.77 aux(31) =< aux(55) 2.77/2.77 aux(38) =< aux(55)-1 2.77/2.77 aux(35) =< aux(55)*2-2 2.77/2.77 s(71) =< it(47)*aux(54) 2.77/2.77 s(70) =< it(47)*aux(55) 2.77/2.77 s(84) =< it(47)*aux(41) 2.77/2.77 s(74) =< it(47)*aux(32) 2.77/2.77 s(73) =< it(47)*aux(31) 2.77/2.77 s(80) =< it(47)*aux(38) 2.77/2.77 s(76) =< it(47)*aux(35) 2.77/2.77 s(83) =< s(74) 2.77/2.77 s(83) =< s(73) 2.77/2.77 s(83) =< s(84) 2.77/2.77 s(79) =< s(74) 2.77/2.77 s(79) =< s(73) 2.77/2.77 s(79) =< s(80) 2.77/2.77 s(75) =< s(74) 2.77/2.77 s(75) =< s(73) 2.77/2.77 s(75) =< s(76) 2.77/2.77 s(72) =< s(74) 2.77/2.77 s(72) =< s(73) 2.77/2.77 s(69) =< s(71) 2.77/2.77 s(69) =< s(70) 2.77/2.77 2.77/2.77 with precondition: [B=3,V_k_1>=0,V_N>=V_k_1+7] 2.77/2.77 2.77/2.77 * Chain [[47,48,49,50,51,52,53],55,62]: 13*it(47)+2*s(69)+2*s(72)+2*s(75)+2*s(79)+2*s(83)+2 2.77/2.77 Such that:aux(30) =< V_N/2 2.77/2.77 aux(29) =< V_N/2-V_k_1/2 2.77/2.77 aux(56) =< V_N-V_k_1 2.77/2.77 it(47) =< aux(56) 2.77/2.77 aux(41) =< aux(29)-3/2 2.77/2.77 aux(32) =< aux(30) 2.77/2.77 aux(31) =< aux(29) 2.77/2.77 aux(38) =< aux(29)-1 2.77/2.77 aux(35) =< aux(29)*2-2 2.77/2.77 s(71) =< it(47)*aux(30) 2.77/2.77 s(70) =< it(47)*aux(29) 2.77/2.77 s(84) =< it(47)*aux(41) 2.77/2.77 s(74) =< it(47)*aux(32) 2.77/2.77 s(73) =< it(47)*aux(31) 2.77/2.77 s(80) =< it(47)*aux(38) 2.77/2.77 s(76) =< it(47)*aux(35) 2.77/2.77 s(83) =< s(74) 2.77/2.77 s(83) =< s(73) 2.77/2.77 s(83) =< s(84) 2.77/2.77 s(79) =< s(74) 2.77/2.77 s(79) =< s(73) 2.77/2.77 s(79) =< s(80) 2.77/2.77 s(75) =< s(74) 2.77/2.77 s(75) =< s(73) 2.77/2.77 s(75) =< s(76) 2.77/2.77 s(72) =< s(74) 2.77/2.77 s(72) =< s(73) 2.77/2.77 s(69) =< s(71) 2.77/2.77 s(69) =< s(70) 2.77/2.77 2.77/2.77 with precondition: [B=3,V_k_1>=0,V_N>=V_k_1+4] 2.77/2.77 2.77/2.77 * Chain [[47,48,49,50,51,52,53],55,61]: 13*it(47)+2*s(69)+2*s(72)+2*s(75)+2*s(79)+2*s(83)+2 2.77/2.77 Such that:aux(30) =< V_N/2 2.77/2.77 aux(29) =< V_N/2-V_k_1/2 2.77/2.77 aux(57) =< V_N-V_k_1 2.77/2.77 it(47) =< aux(57) 2.77/2.77 aux(41) =< aux(29)-3/2 2.77/2.77 aux(32) =< aux(30) 2.77/2.77 aux(31) =< aux(29) 2.77/2.77 aux(38) =< aux(29)-1 2.77/2.77 aux(35) =< aux(29)*2-2 2.77/2.77 s(71) =< it(47)*aux(30) 2.77/2.77 s(70) =< it(47)*aux(29) 2.77/2.77 s(84) =< it(47)*aux(41) 2.77/2.77 s(74) =< it(47)*aux(32) 2.77/2.77 s(73) =< it(47)*aux(31) 2.77/2.77 s(80) =< it(47)*aux(38) 2.77/2.77 s(76) =< it(47)*aux(35) 2.77/2.77 s(83) =< s(74) 2.77/2.77 s(83) =< s(73) 2.77/2.77 s(83) =< s(84) 2.77/2.77 s(79) =< s(74) 2.77/2.77 s(79) =< s(73) 2.77/2.77 s(79) =< s(80) 2.77/2.77 s(75) =< s(74) 2.77/2.77 s(75) =< s(73) 2.77/2.77 s(75) =< s(76) 2.77/2.77 s(72) =< s(74) 2.77/2.77 s(72) =< s(73) 2.77/2.77 s(69) =< s(71) 2.77/2.77 s(69) =< s(70) 2.77/2.77 2.77/2.77 with precondition: [B=3,V_k_1>=0,V_N>=V_k_1+4] 2.77/2.77 2.77/2.77 * Chain [[47,48,49,50,51,52,53],55,56,62]: 13*it(47)+2*s(69)+2*s(72)+2*s(75)+2*s(79)+2*s(83)+3 2.77/2.77 Such that:aux(30) =< V_N/2 2.77/2.77 aux(29) =< V_N/2-V_k_1/2 2.77/2.77 aux(58) =< V_N-V_k_1 2.77/2.77 it(47) =< aux(58) 2.77/2.77 aux(41) =< aux(29)-3/2 2.77/2.77 aux(32) =< aux(30) 2.77/2.77 aux(31) =< aux(29) 2.77/2.77 aux(38) =< aux(29)-1 2.77/2.77 aux(35) =< aux(29)*2-2 2.77/2.77 s(71) =< it(47)*aux(30) 2.77/2.77 s(70) =< it(47)*aux(29) 2.77/2.77 s(84) =< it(47)*aux(41) 2.77/2.77 s(74) =< it(47)*aux(32) 2.77/2.77 s(73) =< it(47)*aux(31) 2.77/2.77 s(80) =< it(47)*aux(38) 2.77/2.77 s(76) =< it(47)*aux(35) 2.77/2.77 s(83) =< s(74) 2.77/2.77 s(83) =< s(73) 2.77/2.77 s(83) =< s(84) 2.77/2.77 s(79) =< s(74) 2.77/2.77 s(79) =< s(73) 2.77/2.77 s(79) =< s(80) 2.77/2.77 s(75) =< s(74) 2.77/2.77 s(75) =< s(73) 2.77/2.77 s(75) =< s(76) 2.77/2.77 s(72) =< s(74) 2.77/2.77 s(72) =< s(73) 2.77/2.77 s(69) =< s(71) 2.77/2.77 s(69) =< s(70) 2.77/2.77 2.77/2.77 with precondition: [B=3,V_k_1>=0,V_N>=V_k_1+4] 2.77/2.77 2.77/2.77 * Chain [[47,48,49,50,51,52,53],55,56,57]: 13*it(47)+2*s(69)+2*s(72)+2*s(75)+2*s(79)+2*s(83)+3 2.77/2.77 Such that:aux(43) =< -V_k_1+C 2.77/2.77 aux(42) =< -V_k_1+C+1 2.77/2.77 aux(29) =< -V_k_1/2+C/2+1/2 2.77/2.77 aux(30) =< C/2+1/2 2.77/2.77 it(47) =< aux(42) 2.77/2.77 it(47) =< aux(43) 2.77/2.77 aux(41) =< aux(29)-3/2 2.77/2.77 aux(32) =< aux(30) 2.77/2.77 aux(31) =< aux(29) 2.77/2.77 aux(38) =< aux(29)-1 2.77/2.77 aux(35) =< aux(29)*2-2 2.77/2.77 s(71) =< it(47)*aux(30) 2.77/2.77 s(70) =< it(47)*aux(29) 2.77/2.77 s(84) =< it(47)*aux(41) 2.77/2.77 s(74) =< it(47)*aux(32) 2.77/2.77 s(73) =< it(47)*aux(31) 2.77/2.77 s(80) =< it(47)*aux(38) 2.77/2.77 s(76) =< it(47)*aux(35) 2.77/2.77 s(83) =< s(74) 2.77/2.77 s(83) =< s(73) 2.77/2.77 s(83) =< s(84) 2.77/2.77 s(79) =< s(74) 2.77/2.77 s(79) =< s(73) 2.77/2.77 s(79) =< s(80) 2.77/2.77 s(75) =< s(74) 2.77/2.77 s(75) =< s(73) 2.77/2.77 s(75) =< s(76) 2.77/2.77 s(72) =< s(74) 2.77/2.77 s(72) =< s(73) 2.77/2.77 s(69) =< s(71) 2.77/2.77 s(69) =< s(70) 2.77/2.77 2.77/2.77 with precondition: [B=6,D=0,F=1,V_N=C+1,V_N=E+1,V_k_1>=0,V_N>=V_k_1+4] 2.77/2.77 2.77/2.77 * Chain [[47,48,49,50,51,52,53],54,62]: 13*it(47)+2*s(69)+2*s(72)+2*s(75)+2*s(79)+2*s(83)+2 2.77/2.77 Such that:aux(30) =< V_N/2 2.77/2.77 aux(29) =< V_N/2-V_k_1/2 2.77/2.77 aux(59) =< V_N-V_k_1 2.77/2.77 it(47) =< aux(59) 2.77/2.77 aux(41) =< aux(29)-3/2 2.77/2.77 aux(32) =< aux(30) 2.77/2.77 aux(31) =< aux(29) 2.77/2.77 aux(38) =< aux(29)-1 2.77/2.77 aux(35) =< aux(29)*2-2 2.77/2.77 s(71) =< it(47)*aux(30) 2.77/2.77 s(70) =< it(47)*aux(29) 2.77/2.77 s(84) =< it(47)*aux(41) 2.77/2.77 s(74) =< it(47)*aux(32) 2.77/2.77 s(73) =< it(47)*aux(31) 2.77/2.77 s(80) =< it(47)*aux(38) 2.77/2.77 s(76) =< it(47)*aux(35) 2.77/2.77 s(83) =< s(74) 2.77/2.77 s(83) =< s(73) 2.77/2.77 s(83) =< s(84) 2.77/2.77 s(79) =< s(74) 2.77/2.77 s(79) =< s(73) 2.77/2.77 s(79) =< s(80) 2.77/2.77 s(75) =< s(74) 2.77/2.77 s(75) =< s(73) 2.77/2.77 s(75) =< s(76) 2.77/2.77 s(72) =< s(74) 2.77/2.77 s(72) =< s(73) 2.77/2.77 s(69) =< s(71) 2.77/2.77 s(69) =< s(70) 2.77/2.77 2.77/2.77 with precondition: [B=3,V_k_1>=0,V_N>=V_k_1+4] 2.77/2.77 2.77/2.77 * Chain [[47,48,49,50,51,52,53],54,61]: 13*it(47)+2*s(69)+2*s(72)+2*s(75)+2*s(79)+2*s(83)+2 2.77/2.77 Such that:aux(30) =< V_N/2 2.77/2.77 aux(29) =< V_N/2-V_k_1/2 2.77/2.77 aux(60) =< V_N-V_k_1 2.77/2.77 it(47) =< aux(60) 2.77/2.77 aux(41) =< aux(29)-3/2 2.77/2.77 aux(32) =< aux(30) 2.77/2.77 aux(31) =< aux(29) 2.77/2.77 aux(38) =< aux(29)-1 2.77/2.77 aux(35) =< aux(29)*2-2 2.77/2.77 s(71) =< it(47)*aux(30) 2.77/2.77 s(70) =< it(47)*aux(29) 2.77/2.77 s(84) =< it(47)*aux(41) 2.77/2.77 s(74) =< it(47)*aux(32) 2.77/2.77 s(73) =< it(47)*aux(31) 2.77/2.77 s(80) =< it(47)*aux(38) 2.77/2.77 s(76) =< it(47)*aux(35) 2.77/2.77 s(83) =< s(74) 2.77/2.77 s(83) =< s(73) 2.77/2.77 s(83) =< s(84) 2.77/2.77 s(79) =< s(74) 2.77/2.77 s(79) =< s(73) 2.77/2.77 s(79) =< s(80) 2.77/2.77 s(75) =< s(74) 2.77/2.77 s(75) =< s(73) 2.77/2.77 s(75) =< s(76) 2.77/2.77 s(72) =< s(74) 2.77/2.77 s(72) =< s(73) 2.77/2.77 s(69) =< s(71) 2.77/2.77 s(69) =< s(70) 2.77/2.77 2.77/2.77 with precondition: [B=3,V_k_1>=0,V_N>=V_k_1+4] 2.77/2.77 2.77/2.77 * Chain [[47,48,49,50,51,52,53],54,56,62]: 13*it(47)+2*s(69)+2*s(72)+2*s(75)+2*s(79)+2*s(83)+3 2.77/2.77 Such that:aux(30) =< V_N/2 2.77/2.77 aux(29) =< V_N/2-V_k_1/2 2.77/2.77 aux(61) =< V_N-V_k_1 2.77/2.77 it(47) =< aux(61) 2.77/2.77 aux(41) =< aux(29)-3/2 2.77/2.77 aux(32) =< aux(30) 2.77/2.77 aux(31) =< aux(29) 2.77/2.77 aux(38) =< aux(29)-1 2.77/2.77 aux(35) =< aux(29)*2-2 2.77/2.77 s(71) =< it(47)*aux(30) 2.77/2.77 s(70) =< it(47)*aux(29) 2.77/2.77 s(84) =< it(47)*aux(41) 2.77/2.77 s(74) =< it(47)*aux(32) 2.77/2.77 s(73) =< it(47)*aux(31) 2.77/2.77 s(80) =< it(47)*aux(38) 2.77/2.77 s(76) =< it(47)*aux(35) 2.77/2.77 s(83) =< s(74) 2.77/2.77 s(83) =< s(73) 2.77/2.77 s(83) =< s(84) 2.77/2.77 s(79) =< s(74) 2.77/2.77 s(79) =< s(73) 2.77/2.77 s(79) =< s(80) 2.77/2.77 s(75) =< s(74) 2.77/2.77 s(75) =< s(73) 2.77/2.77 s(75) =< s(76) 2.77/2.77 s(72) =< s(74) 2.77/2.77 s(72) =< s(73) 2.77/2.77 s(69) =< s(71) 2.77/2.77 s(69) =< s(70) 2.77/2.77 2.77/2.77 with precondition: [B=3,V_k_1>=0,V_N>=V_k_1+4] 2.77/2.77 2.77/2.77 * Chain [[47,48,49,50,51,52,53],54,56,57]: 13*it(47)+2*s(69)+2*s(72)+2*s(75)+2*s(79)+2*s(83)+3 2.77/2.77 Such that:aux(43) =< -V_k_1+C 2.77/2.77 aux(42) =< -V_k_1+C+1 2.77/2.77 aux(29) =< -V_k_1/2+C/2+1/2 2.77/2.77 aux(30) =< C/2+1/2 2.77/2.77 it(47) =< aux(42) 2.77/2.77 it(47) =< aux(43) 2.77/2.77 aux(41) =< aux(29)-3/2 2.77/2.77 aux(32) =< aux(30) 2.77/2.77 aux(31) =< aux(29) 2.77/2.77 aux(38) =< aux(29)-1 2.77/2.77 aux(35) =< aux(29)*2-2 2.77/2.77 s(71) =< it(47)*aux(30) 2.77/2.77 s(70) =< it(47)*aux(29) 2.77/2.77 s(84) =< it(47)*aux(41) 2.77/2.77 s(74) =< it(47)*aux(32) 2.77/2.77 s(73) =< it(47)*aux(31) 2.77/2.77 s(80) =< it(47)*aux(38) 2.77/2.77 s(76) =< it(47)*aux(35) 2.77/2.77 s(83) =< s(74) 2.77/2.77 s(83) =< s(73) 2.77/2.77 s(83) =< s(84) 2.77/2.77 s(79) =< s(74) 2.77/2.77 s(79) =< s(73) 2.77/2.77 s(79) =< s(80) 2.77/2.77 s(75) =< s(74) 2.77/2.77 s(75) =< s(73) 2.77/2.77 s(75) =< s(76) 2.77/2.77 s(72) =< s(74) 2.77/2.77 s(72) =< s(73) 2.77/2.77 s(69) =< s(71) 2.77/2.77 s(69) =< s(70) 2.77/2.77 2.77/2.77 with precondition: [B=6,D=0,F=1,V_N=C+1,V_N=E+1,V_k_1>=0,V_N>=V_k_1+4] 2.77/2.77 2.77/2.77 * Chain [63]: 1 2.77/2.77 with precondition: [B=3,V_k_1+3=V_N,V_k_1>=0] 2.77/2.77 2.77/2.77 * Chain [62]: 0 2.77/2.77 with precondition: [B=3,V_N>=3,V_k_1>=0,V_N>=V_k_1+1] 2.77/2.77 2.77/2.77 * Chain [61]: 0 2.77/2.77 with precondition: [B=3,V_N>=3,V_k_1>=0,V_N>=V_k_1+2] 2.77/2.77 2.77/2.77 * Chain [60]: 2*s(90)+1 2.77/2.77 Such that:s(87) =< V_N-V_k_1 2.77/2.77 s(88) =< V_N/2 2.77/2.77 s(89) =< V_N/2-V_k_1/2 2.77/2.77 s(90) =< s(88) 2.77/2.77 s(90) =< s(89) 2.77/2.77 s(90) =< s(87) 2.77/2.77 2.77/2.77 with precondition: [B=3,V_k_1>=0,V_N>=V_k_1+4] 2.77/2.77 2.77/2.77 * Chain [59]: 4*s(93)+1 2.77/2.77 Such that:s(91) =< V_N/2 2.77/2.77 s(92) =< V_N/2-V_k_1/2 2.77/2.77 s(93) =< s(91) 2.77/2.77 s(93) =< s(92) 2.77/2.77 2.77/2.77 with precondition: [B=3,V_k_1>=0,V_N>=V_k_1+5] 2.77/2.77 2.77/2.77 * Chain [58]: 4*s(96)+1 2.77/2.77 Such that:s(94) =< V_N/2 2.77/2.77 s(95) =< V_N/2-V_k_1/2 2.77/2.77 s(96) =< s(94) 2.77/2.77 s(96) =< s(95) 2.77/2.77 2.77/2.77 with precondition: [B=3,V_k_1>=0,V_N>=V_k_1+6] 2.77/2.77 2.77/2.77 * Chain [55,62]: 2 2.77/2.77 with precondition: [B=3,V_N=V_k_1+3,V_N>=3] 2.77/2.77 2.77/2.77 * Chain [55,61]: 2 2.77/2.77 with precondition: [B=3,V_N=V_k_1+3,V_N>=3] 2.77/2.77 2.77/2.77 * Chain [55,56,62]: 3 2.77/2.77 with precondition: [B=3,V_N=V_k_1+3,V_N>=3] 2.77/2.77 2.77/2.77 * Chain [55,56,57]: 3 2.77/2.77 with precondition: [B=6,D=0,F=1,C+1=V_N,C=V_k_1+2,C=E,C>=2] 2.77/2.77 2.77/2.77 * Chain [54,62]: 2 2.77/2.77 with precondition: [B=3,V_N=V_k_1+3,V_N>=3] 2.77/2.77 2.77/2.77 * Chain [54,61]: 2 2.77/2.77 with precondition: [B=3,V_N=V_k_1+3,V_N>=3] 2.77/2.77 2.77/2.77 * Chain [54,56,62]: 3 2.77/2.77 with precondition: [B=3,V_N=V_k_1+3,V_N>=3] 2.77/2.77 2.77/2.77 * Chain [54,56,57]: 3 2.77/2.77 with precondition: [B=6,D=0,F=1,C+1=V_N,C=V_k_1+2,C=E,C>=2] 2.77/2.77 2.77/2.77 2.77/2.77 #### Cost of chains of eval_realheapsort_bb6_in_loop_cont(A,B,C,D,E,F,G,H,I,J): 2.77/2.77 * Chain [65]: 0 2.77/2.77 with precondition: [A=3,D>=3] 2.77/2.77 2.77/2.77 * Chain [64]: 0 2.77/2.77 with precondition: [A=6,D>=3] 2.77/2.77 2.77/2.77 2.77/2.77 #### Cost of chains of eval_realheapsort_39(V_33,V_90,V_N,V_j_0,V_j_1,V_k_0,V_k_1,V_m_0,B): 2.77/2.77 * Chain [71]: 3 2.77/2.77 with precondition: [V_N=3] 2.77/2.77 2.77/2.77 * Chain [70]: 0 2.77/2.77 with precondition: [V_N>=3] 2.77/2.77 2.77/2.77 * Chain [69]: 2*s(389)+143*s(390)+22*s(403)+22*s(404)+22*s(405)+22*s(406)+22*s(407)+3 2.77/2.77 Such that:aux(76) =< V_N 2.77/2.77 aux(77) =< V_N/2 2.77/2.77 s(390) =< aux(76) 2.77/2.77 s(391) =< aux(77)-3/2 2.77/2.77 s(392) =< aux(77) 2.77/2.77 s(394) =< aux(77)-1 2.77/2.77 s(395) =< aux(77)*2-2 2.77/2.77 s(396) =< s(390)*aux(77) 2.77/2.77 s(398) =< s(390)*s(391) 2.77/2.77 s(399) =< s(390)*s(392) 2.77/2.77 s(401) =< s(390)*s(394) 2.77/2.77 s(402) =< s(390)*s(395) 2.77/2.77 s(403) =< s(399) 2.77/2.77 s(403) =< s(398) 2.77/2.77 s(404) =< s(399) 2.77/2.77 s(404) =< s(401) 2.77/2.77 s(405) =< s(399) 2.77/2.77 s(405) =< s(402) 2.77/2.77 s(406) =< s(399) 2.77/2.77 s(407) =< s(396) 2.77/2.77 s(389) =< aux(77) 2.77/2.77 s(389) =< aux(76) 2.77/2.77 2.77/2.77 with precondition: [V_N>=4] 2.77/2.77 2.77/2.77 * Chain [68]: 2*s(434)+13*s(435)+2*s(448)+2*s(449)+2*s(450)+2*s(451)+2*s(452)+4*s(453)+1 2.77/2.77 Such that:s(430) =< V_N 2.77/2.77 aux(78) =< V_N/2 2.77/2.77 s(433) =< s(430) 2.77/2.77 s(433) =< aux(78) 2.77/2.77 s(434) =< aux(78) 2.77/2.77 s(434) =< s(433) 2.77/2.77 s(434) =< s(430) 2.77/2.77 s(435) =< s(430) 2.77/2.77 s(436) =< aux(78)-3/2 2.77/2.77 s(437) =< aux(78) 2.77/2.77 s(439) =< aux(78)-1 2.77/2.77 s(440) =< aux(78)*2-2 2.77/2.77 s(441) =< s(435)*aux(78) 2.77/2.77 s(443) =< s(435)*s(436) 2.77/2.77 s(444) =< s(435)*s(437) 2.77/2.77 s(446) =< s(435)*s(439) 2.77/2.77 s(447) =< s(435)*s(440) 2.77/2.77 s(448) =< s(444) 2.77/2.77 s(448) =< s(443) 2.77/2.77 s(449) =< s(444) 2.77/2.77 s(449) =< s(446) 2.77/2.77 s(450) =< s(444) 2.77/2.77 s(450) =< s(447) 2.77/2.77 s(451) =< s(444) 2.77/2.77 s(452) =< s(441) 2.77/2.77 s(453) =< aux(78) 2.77/2.77 2.77/2.77 with precondition: [V_N>=5] 2.77/2.77 2.77/2.77 * Chain [67]: 4*s(458)+13*s(459)+2*s(472)+2*s(473)+2*s(474)+2*s(475)+2*s(476)+4*s(477)+1 2.77/2.77 Such that:s(454) =< V_N 2.77/2.77 aux(79) =< V_N/2 2.77/2.77 s(457) =< s(454) 2.77/2.77 s(457) =< aux(79) 2.77/2.77 s(458) =< aux(79) 2.77/2.77 s(458) =< s(457) 2.77/2.77 s(459) =< s(454) 2.77/2.77 s(460) =< aux(79)-3/2 2.77/2.77 s(461) =< aux(79) 2.77/2.77 s(463) =< aux(79)-1 2.77/2.77 s(464) =< aux(79)*2-2 2.77/2.77 s(465) =< s(459)*aux(79) 2.77/2.77 s(467) =< s(459)*s(460) 2.77/2.77 s(468) =< s(459)*s(461) 2.77/2.77 s(470) =< s(459)*s(463) 2.77/2.77 s(471) =< s(459)*s(464) 2.77/2.77 s(472) =< s(468) 2.77/2.77 s(472) =< s(467) 2.77/2.77 s(473) =< s(468) 2.77/2.77 s(473) =< s(470) 2.77/2.77 s(474) =< s(468) 2.77/2.77 s(474) =< s(471) 2.77/2.77 s(475) =< s(468) 2.77/2.77 s(476) =< s(465) 2.77/2.77 s(477) =< aux(79) 2.77/2.77 2.77/2.77 with precondition: [V_N>=6] 2.77/2.77 2.77/2.77 * Chain [66]: 4*s(482)+13*s(483)+2*s(496)+2*s(497)+2*s(498)+2*s(499)+2*s(500)+1 2.77/2.77 Such that:s(478) =< V_N 2.77/2.77 aux(80) =< V_N/2 2.77/2.77 s(481) =< s(478) 2.77/2.77 s(481) =< aux(80) 2.77/2.77 s(482) =< aux(80) 2.77/2.77 s(482) =< s(481) 2.77/2.77 s(483) =< s(478) 2.77/2.77 s(484) =< aux(80)-3/2 2.77/2.77 s(485) =< aux(80) 2.77/2.77 s(487) =< aux(80)-1 2.77/2.77 s(488) =< aux(80)*2-2 2.77/2.77 s(489) =< s(483)*aux(80) 2.77/2.77 s(491) =< s(483)*s(484) 2.77/2.77 s(492) =< s(483)*s(485) 2.77/2.77 s(494) =< s(483)*s(487) 2.77/2.77 s(495) =< s(483)*s(488) 2.77/2.77 s(496) =< s(492) 2.77/2.77 s(496) =< s(491) 2.77/2.77 s(497) =< s(492) 2.77/2.77 s(497) =< s(494) 2.77/2.77 s(498) =< s(492) 2.77/2.77 s(498) =< s(495) 2.77/2.77 s(499) =< s(492) 2.77/2.77 s(500) =< s(489) 2.77/2.77 2.77/2.77 with precondition: [V_N>=7] 2.77/2.77 2.77/2.77 2.77/2.77 #### Cost of chains of eval_realheapsort_bb1_in_loop_cont(A,B,C,D,E,F,G,H,I,J): 2.77/2.77 * Chain [78]: 0 2.77/2.77 with precondition: [A=3,D>=3] 2.77/2.77 2.77/2.77 * Chain [77]: 3 2.77/2.77 with precondition: [A=5,D=3] 2.77/2.77 2.77/2.77 * Chain [76]: 0 2.77/2.77 with precondition: [A=5,D>=3] 2.77/2.77 2.77/2.77 * Chain [75]: 143*s(503)+22*s(513)+22*s(514)+22*s(515)+22*s(516)+22*s(517)+2*s(518)+3 2.77/2.77 Such that:s(501) =< D 2.77/2.77 s(502) =< D/2 2.77/2.77 s(503) =< s(501) 2.77/2.77 s(504) =< s(502)-3/2 2.77/2.77 s(505) =< s(502) 2.77/2.77 s(506) =< s(502)-1 2.77/2.77 s(507) =< s(502)*2-2 2.77/2.77 s(508) =< s(503)*s(502) 2.77/2.77 s(509) =< s(503)*s(504) 2.77/2.77 s(510) =< s(503)*s(505) 2.77/2.77 s(511) =< s(503)*s(506) 2.77/2.77 s(512) =< s(503)*s(507) 2.77/2.77 s(513) =< s(510) 2.77/2.77 s(513) =< s(509) 2.77/2.77 s(514) =< s(510) 2.77/2.77 s(514) =< s(511) 2.77/2.77 s(515) =< s(510) 2.77/2.77 s(515) =< s(512) 2.77/2.77 s(516) =< s(510) 2.77/2.77 s(517) =< s(508) 2.77/2.77 s(518) =< s(502) 2.77/2.77 s(518) =< s(501) 2.77/2.77 2.77/2.77 with precondition: [A=5,D>=4] 2.77/2.77 2.77/2.77 * Chain [74]: 2*s(522)+13*s(523)+2*s(533)+2*s(534)+2*s(535)+2*s(536)+2*s(537)+4*s(538)+1 2.77/2.77 Such that:s(519) =< D 2.77/2.77 s(520) =< D/2 2.77/2.77 s(521) =< s(519) 2.77/2.77 s(521) =< s(520) 2.77/2.77 s(522) =< s(520) 2.77/2.77 s(522) =< s(521) 2.77/2.77 s(522) =< s(519) 2.77/2.77 s(523) =< s(519) 2.77/2.77 s(524) =< s(520)-3/2 2.77/2.77 s(525) =< s(520) 2.77/2.77 s(526) =< s(520)-1 2.77/2.77 s(527) =< s(520)*2-2 2.77/2.77 s(528) =< s(523)*s(520) 2.77/2.77 s(529) =< s(523)*s(524) 2.77/2.77 s(530) =< s(523)*s(525) 2.77/2.77 s(531) =< s(523)*s(526) 2.77/2.77 s(532) =< s(523)*s(527) 2.77/2.77 s(533) =< s(530) 2.77/2.77 s(533) =< s(529) 2.77/2.77 s(534) =< s(530) 2.77/2.77 s(534) =< s(531) 2.77/2.77 s(535) =< s(530) 2.77/2.77 s(535) =< s(532) 2.77/2.77 s(536) =< s(530) 2.77/2.77 s(537) =< s(528) 2.77/2.77 s(538) =< s(520) 2.77/2.77 2.77/2.77 with precondition: [A=5,D>=5] 2.77/2.77 2.77/2.77 * Chain [73]: 4*s(542)+13*s(543)+2*s(553)+2*s(554)+2*s(555)+2*s(556)+2*s(557)+4*s(558)+1 2.77/2.77 Such that:s(539) =< D 2.77/2.77 s(540) =< D/2 2.77/2.77 s(541) =< s(539) 2.77/2.77 s(541) =< s(540) 2.77/2.77 s(542) =< s(540) 2.77/2.77 s(542) =< s(541) 2.77/2.77 s(543) =< s(539) 2.77/2.77 s(544) =< s(540)-3/2 2.77/2.77 s(545) =< s(540) 2.77/2.77 s(546) =< s(540)-1 2.77/2.77 s(547) =< s(540)*2-2 2.77/2.77 s(548) =< s(543)*s(540) 2.77/2.77 s(549) =< s(543)*s(544) 2.77/2.77 s(550) =< s(543)*s(545) 2.77/2.77 s(551) =< s(543)*s(546) 2.77/2.77 s(552) =< s(543)*s(547) 2.77/2.77 s(553) =< s(550) 2.77/2.77 s(553) =< s(549) 2.77/2.77 s(554) =< s(550) 2.77/2.77 s(554) =< s(551) 2.77/2.77 s(555) =< s(550) 2.77/2.77 s(555) =< s(552) 2.77/2.77 s(556) =< s(550) 2.77/2.77 s(557) =< s(548) 2.77/2.77 s(558) =< s(540) 2.77/2.77 2.77/2.77 with precondition: [A=5,D>=6] 2.77/2.77 2.77/2.77 * Chain [72]: 4*s(562)+13*s(563)+2*s(573)+2*s(574)+2*s(575)+2*s(576)+2*s(577)+1 2.77/2.77 Such that:s(559) =< D 2.77/2.77 s(560) =< D/2 2.77/2.77 s(561) =< s(559) 2.77/2.77 s(561) =< s(560) 2.77/2.77 s(562) =< s(560) 2.77/2.77 s(562) =< s(561) 2.77/2.77 s(563) =< s(559) 2.77/2.77 s(564) =< s(560)-3/2 2.77/2.77 s(565) =< s(560) 2.77/2.77 s(566) =< s(560)-1 2.77/2.77 s(567) =< s(560)*2-2 2.77/2.77 s(568) =< s(563)*s(560) 2.77/2.77 s(569) =< s(563)*s(564) 2.77/2.77 s(570) =< s(563)*s(565) 2.77/2.77 s(571) =< s(563)*s(566) 2.77/2.77 s(572) =< s(563)*s(567) 2.77/2.77 s(573) =< s(570) 2.77/2.77 s(573) =< s(569) 2.77/2.77 s(574) =< s(570) 2.77/2.77 s(574) =< s(571) 2.77/2.77 s(575) =< s(570) 2.77/2.77 s(575) =< s(572) 2.77/2.77 s(576) =< s(570) 2.77/2.77 s(577) =< s(568) 2.77/2.77 2.77/2.77 with precondition: [A=5,D>=7] 2.77/2.77 2.77/2.77 2.77/2.77 #### Cost of chains of eval_realheapsort_2(V_33,V_90,V_N,V_j_0,V_j_1,V_k_0,V_k_1,V_m_0,B): 2.77/2.77 * Chain [85]: 3*s(580)+1*s(582)+1*s(583)+3 2.77/2.77 Such that:s(579) =< 2 2.77/2.77 s(578) =< 3 2.77/2.77 s(580) =< s(579) 2.77/2.77 s(581) =< s(578)+1 2.77/2.77 s(582) =< s(580)*s(578) 2.77/2.77 s(583) =< s(580)*s(581) 2.77/2.77 2.77/2.77 with precondition: [V_N=3] 2.77/2.77 2.77/2.77 * Chain [84]: 0 2.77/2.77 with precondition: [2>=V_N] 2.77/2.77 2.77/2.77 * Chain [83]: 1*s(586)+10*s(587)+3*s(589)+3*s(590)+0 2.77/2.77 Such that:s(586) =< 1 2.77/2.77 aux(84) =< V_N 2.77/2.77 s(587) =< aux(84) 2.77/2.77 s(588) =< aux(84)+1 2.77/2.77 s(589) =< s(587)*aux(84) 2.77/2.77 s(590) =< s(587)*s(588) 2.77/2.77 2.77/2.77 with precondition: [V_N>=3] 2.77/2.77 2.77/2.77 * Chain [82]: 146*s(606)+1*s(608)+1*s(609)+22*s(622)+22*s(623)+22*s(624)+22*s(625)+22*s(626)+2*s(627)+3 2.77/2.77 Such that:s(611) =< V_N/2 2.77/2.77 aux(85) =< V_N 2.77/2.77 s(606) =< aux(85) 2.77/2.77 s(613) =< s(611)-3/2 2.77/2.77 s(614) =< s(611) 2.77/2.77 s(615) =< s(611)-1 2.77/2.77 s(616) =< s(611)*2-2 2.77/2.77 s(617) =< s(606)*s(611) 2.77/2.77 s(618) =< s(606)*s(613) 2.77/2.77 s(619) =< s(606)*s(614) 2.77/2.77 s(620) =< s(606)*s(615) 2.77/2.77 s(621) =< s(606)*s(616) 2.77/2.77 s(622) =< s(619) 2.77/2.77 s(622) =< s(618) 2.77/2.77 s(623) =< s(619) 2.77/2.77 s(623) =< s(620) 2.77/2.77 s(624) =< s(619) 2.77/2.77 s(624) =< s(621) 2.77/2.77 s(625) =< s(619) 2.77/2.77 s(626) =< s(617) 2.77/2.77 s(627) =< s(611) 2.77/2.77 s(627) =< aux(85) 2.77/2.77 s(607) =< aux(85)+1 2.77/2.77 s(608) =< s(606)*aux(85) 2.77/2.77 s(609) =< s(606)*s(607) 2.77/2.77 2.77/2.77 with precondition: [V_N>=4] 2.77/2.77 2.77/2.77 * Chain [81]: 16*s(630)+1*s(632)+1*s(633)+2*s(637)+2*s(648)+2*s(649)+2*s(650)+2*s(651)+2*s(652)+4*s(653)+1 2.77/2.77 Such that:s(635) =< V_N/2 2.77/2.77 aux(86) =< V_N 2.77/2.77 s(636) =< aux(86) 2.77/2.77 s(636) =< s(635) 2.77/2.77 s(637) =< s(635) 2.77/2.77 s(637) =< s(636) 2.77/2.77 s(637) =< aux(86) 2.77/2.77 s(630) =< aux(86) 2.77/2.77 s(639) =< s(635)-3/2 2.77/2.77 s(640) =< s(635) 2.77/2.77 s(641) =< s(635)-1 2.77/2.77 s(642) =< s(635)*2-2 2.77/2.77 s(643) =< s(630)*s(635) 2.77/2.77 s(644) =< s(630)*s(639) 2.77/2.77 s(645) =< s(630)*s(640) 2.77/2.77 s(646) =< s(630)*s(641) 2.77/2.77 s(647) =< s(630)*s(642) 2.77/2.77 s(648) =< s(645) 2.77/2.77 s(648) =< s(644) 2.77/2.77 s(649) =< s(645) 2.77/2.77 s(649) =< s(646) 2.77/2.77 s(650) =< s(645) 2.77/2.77 s(650) =< s(647) 2.77/2.77 s(651) =< s(645) 2.77/2.77 s(652) =< s(643) 2.77/2.77 s(653) =< s(635) 2.77/2.77 s(631) =< aux(86)+1 2.77/2.77 s(632) =< s(630)*aux(86) 2.77/2.77 s(633) =< s(630)*s(631) 2.77/2.77 2.77/2.77 with precondition: [V_N>=5] 2.77/2.77 2.77/2.77 * Chain [80]: 16*s(656)+1*s(658)+1*s(659)+4*s(663)+2*s(674)+2*s(675)+2*s(676)+2*s(677)+2*s(678)+4*s(679)+1 2.77/2.77 Such that:s(661) =< V_N/2 2.77/2.77 aux(87) =< V_N 2.77/2.77 s(662) =< aux(87) 2.77/2.77 s(662) =< s(661) 2.77/2.77 s(663) =< s(661) 2.77/2.77 s(663) =< s(662) 2.77/2.77 s(656) =< aux(87) 2.77/2.77 s(665) =< s(661)-3/2 2.77/2.77 s(666) =< s(661) 2.77/2.77 s(667) =< s(661)-1 2.77/2.77 s(668) =< s(661)*2-2 2.77/2.77 s(669) =< s(656)*s(661) 2.77/2.77 s(670) =< s(656)*s(665) 2.77/2.77 s(671) =< s(656)*s(666) 2.77/2.77 s(672) =< s(656)*s(667) 2.77/2.77 s(673) =< s(656)*s(668) 2.77/2.77 s(674) =< s(671) 2.77/2.77 s(674) =< s(670) 2.77/2.77 s(675) =< s(671) 2.77/2.77 s(675) =< s(672) 2.77/2.77 s(676) =< s(671) 2.77/2.77 s(676) =< s(673) 2.77/2.77 s(677) =< s(671) 2.77/2.77 s(678) =< s(669) 2.77/2.77 s(679) =< s(661) 2.77/2.77 s(657) =< aux(87)+1 2.77/2.77 s(658) =< s(656)*aux(87) 2.77/2.77 s(659) =< s(656)*s(657) 2.77/2.77 2.77/2.77 with precondition: [V_N>=6] 2.77/2.77 2.77/2.77 * Chain [79]: 16*s(682)+1*s(684)+1*s(685)+4*s(689)+2*s(700)+2*s(701)+2*s(702)+2*s(703)+2*s(704)+1 2.77/2.77 Such that:s(687) =< V_N/2 2.77/2.77 aux(88) =< V_N 2.77/2.77 s(688) =< aux(88) 2.77/2.77 s(688) =< s(687) 2.77/2.77 s(689) =< s(687) 2.77/2.77 s(689) =< s(688) 2.77/2.77 s(682) =< aux(88) 2.77/2.77 s(691) =< s(687)-3/2 2.77/2.77 s(692) =< s(687) 2.77/2.77 s(693) =< s(687)-1 2.77/2.77 s(694) =< s(687)*2-2 2.77/2.77 s(695) =< s(682)*s(687) 2.77/2.77 s(696) =< s(682)*s(691) 2.77/2.77 s(697) =< s(682)*s(692) 2.77/2.77 s(698) =< s(682)*s(693) 2.77/2.77 s(699) =< s(682)*s(694) 2.77/2.77 s(700) =< s(697) 2.77/2.77 s(700) =< s(696) 2.77/2.77 s(701) =< s(697) 2.77/2.77 s(701) =< s(698) 2.77/2.77 s(702) =< s(697) 2.77/2.77 s(702) =< s(699) 2.77/2.77 s(703) =< s(697) 2.77/2.77 s(704) =< s(695) 2.77/2.77 s(683) =< aux(88)+1 2.77/2.77 s(684) =< s(682)*aux(88) 2.77/2.77 s(685) =< s(682)*s(683) 2.77/2.77 2.77/2.77 with precondition: [V_N>=7] 2.77/2.77 2.77/2.77 2.77/2.77 #### Cost of chains of eval_realheapsort_start(V_33,V_90,V_N,V_j_0,V_j_1,V_k_0,V_k_1,V_m_0,B): 2.77/2.77 * Chain [92]: 3*s(707)+1*s(709)+1*s(710)+3 2.77/2.77 Such that:s(705) =< 2 2.77/2.77 s(706) =< 3 2.77/2.77 s(707) =< s(705) 2.77/2.77 s(708) =< s(706)+1 2.77/2.77 s(709) =< s(707)*s(706) 2.77/2.77 s(710) =< s(707)*s(708) 2.77/2.77 2.77/2.77 with precondition: [V_N=3] 2.77/2.77 2.77/2.77 * Chain [91]: 0 2.77/2.77 with precondition: [2>=V_N] 2.77/2.77 2.77/2.77 * Chain [90]: 1*s(711)+10*s(713)+3*s(715)+3*s(716)+0 2.77/2.77 Such that:s(711) =< 1 2.77/2.77 s(712) =< V_N 2.77/2.77 s(713) =< s(712) 2.77/2.77 s(714) =< s(712)+1 2.77/2.77 s(715) =< s(713)*s(712) 2.77/2.77 s(716) =< s(713)*s(714) 2.77/2.77 2.77/2.77 with precondition: [V_N>=3] 2.77/2.77 2.77/2.77 * Chain [89]: 146*s(719)+22*s(729)+22*s(730)+22*s(731)+22*s(732)+22*s(733)+2*s(734)+1*s(736)+1*s(737)+3 2.77/2.77 Such that:s(718) =< V_N 2.77/2.77 s(717) =< V_N/2 2.77/2.77 s(719) =< s(718) 2.77/2.77 s(720) =< s(717)-3/2 2.77/2.77 s(721) =< s(717) 2.77/2.77 s(722) =< s(717)-1 2.77/2.77 s(723) =< s(717)*2-2 2.77/2.77 s(724) =< s(719)*s(717) 2.77/2.77 s(725) =< s(719)*s(720) 2.77/2.77 s(726) =< s(719)*s(721) 2.77/2.77 s(727) =< s(719)*s(722) 2.77/2.77 s(728) =< s(719)*s(723) 2.77/2.77 s(729) =< s(726) 2.77/2.77 s(729) =< s(725) 2.77/2.77 s(730) =< s(726) 2.77/2.77 s(730) =< s(727) 2.77/2.77 s(731) =< s(726) 2.77/2.77 s(731) =< s(728) 2.77/2.77 s(732) =< s(726) 2.77/2.77 s(733) =< s(724) 2.77/2.77 s(734) =< s(717) 2.77/2.77 s(734) =< s(718) 2.77/2.77 s(735) =< s(718)+1 2.77/2.77 s(736) =< s(719)*s(718) 2.77/2.77 s(737) =< s(719)*s(735) 2.77/2.77 2.77/2.77 with precondition: [V_N>=4] 2.77/2.77 2.77/2.77 * Chain [88]: 2*s(741)+16*s(742)+2*s(752)+2*s(753)+2*s(754)+2*s(755)+2*s(756)+4*s(757)+1*s(759)+1*s(760)+1 2.77/2.77 Such that:s(739) =< V_N 2.77/2.77 s(738) =< V_N/2 2.77/2.77 s(740) =< s(739) 2.77/2.77 s(740) =< s(738) 2.77/2.77 s(741) =< s(738) 2.77/2.77 s(741) =< s(740) 2.77/2.77 s(741) =< s(739) 2.77/2.77 s(742) =< s(739) 2.77/2.77 s(743) =< s(738)-3/2 2.77/2.77 s(744) =< s(738) 2.77/2.77 s(745) =< s(738)-1 2.77/2.77 s(746) =< s(738)*2-2 2.77/2.77 s(747) =< s(742)*s(738) 2.77/2.77 s(748) =< s(742)*s(743) 2.77/2.77 s(749) =< s(742)*s(744) 2.77/2.77 s(750) =< s(742)*s(745) 2.77/2.77 s(751) =< s(742)*s(746) 2.77/2.77 s(752) =< s(749) 2.77/2.77 s(752) =< s(748) 2.77/2.77 s(753) =< s(749) 2.77/2.77 s(753) =< s(750) 2.77/2.77 s(754) =< s(749) 2.77/2.77 s(754) =< s(751) 2.77/2.77 s(755) =< s(749) 2.77/2.77 s(756) =< s(747) 2.77/2.77 s(757) =< s(738) 2.77/2.77 s(758) =< s(739)+1 2.77/2.77 s(759) =< s(742)*s(739) 2.77/2.77 s(760) =< s(742)*s(758) 2.77/2.77 2.77/2.77 with precondition: [V_N>=5] 2.77/2.77 2.77/2.77 * Chain [87]: 4*s(764)+16*s(765)+2*s(775)+2*s(776)+2*s(777)+2*s(778)+2*s(779)+4*s(780)+1*s(782)+1*s(783)+1 2.77/2.77 Such that:s(762) =< V_N 2.77/2.77 s(761) =< V_N/2 2.77/2.77 s(763) =< s(762) 2.77/2.77 s(763) =< s(761) 2.77/2.77 s(764) =< s(761) 2.77/2.77 s(764) =< s(763) 2.77/2.77 s(765) =< s(762) 2.77/2.77 s(766) =< s(761)-3/2 2.77/2.77 s(767) =< s(761) 2.77/2.77 s(768) =< s(761)-1 2.77/2.77 s(769) =< s(761)*2-2 2.77/2.77 s(770) =< s(765)*s(761) 2.77/2.77 s(771) =< s(765)*s(766) 2.77/2.77 s(772) =< s(765)*s(767) 2.77/2.77 s(773) =< s(765)*s(768) 2.77/2.77 s(774) =< s(765)*s(769) 2.77/2.77 s(775) =< s(772) 2.77/2.77 s(775) =< s(771) 2.77/2.77 s(776) =< s(772) 2.77/2.77 s(776) =< s(773) 2.77/2.77 s(777) =< s(772) 2.77/2.77 s(777) =< s(774) 2.77/2.77 s(778) =< s(772) 2.77/2.77 s(779) =< s(770) 2.77/2.77 s(780) =< s(761) 2.77/2.77 s(781) =< s(762)+1 2.77/2.77 s(782) =< s(765)*s(762) 2.77/2.77 s(783) =< s(765)*s(781) 2.77/2.77 2.77/2.77 with precondition: [V_N>=6] 2.77/2.77 2.77/2.77 * Chain [86]: 4*s(787)+16*s(788)+2*s(798)+2*s(799)+2*s(800)+2*s(801)+2*s(802)+1*s(804)+1*s(805)+1 2.77/2.77 Such that:s(785) =< V_N 2.77/2.77 s(784) =< V_N/2 2.77/2.77 s(786) =< s(785) 2.77/2.77 s(786) =< s(784) 2.77/2.77 s(787) =< s(784) 2.77/2.77 s(787) =< s(786) 2.77/2.77 s(788) =< s(785) 2.77/2.77 s(789) =< s(784)-3/2 2.77/2.77 s(790) =< s(784) 2.77/2.77 s(791) =< s(784)-1 2.77/2.77 s(792) =< s(784)*2-2 2.77/2.77 s(793) =< s(788)*s(784) 2.77/2.77 s(794) =< s(788)*s(789) 2.77/2.77 s(795) =< s(788)*s(790) 2.77/2.77 s(796) =< s(788)*s(791) 2.77/2.77 s(797) =< s(788)*s(792) 2.77/2.77 s(798) =< s(795) 2.77/2.77 s(798) =< s(794) 2.77/2.77 s(799) =< s(795) 2.77/2.77 s(799) =< s(796) 2.77/2.77 s(800) =< s(795) 2.77/2.77 s(800) =< s(797) 2.77/2.77 s(801) =< s(795) 2.77/2.77 s(802) =< s(793) 2.77/2.77 s(803) =< s(785)+1 2.77/2.77 s(804) =< s(788)*s(785) 2.77/2.77 s(805) =< s(788)*s(803) 2.77/2.77 2.77/2.77 with precondition: [V_N>=7] 2.77/2.77 2.77/2.77 2.77/2.77 Closed-form bounds of eval_realheapsort_start(V_33,V_90,V_N,V_j_0,V_j_1,V_k_0,V_k_1,V_m_0,B): 2.77/2.77 ------------------------------------- 2.77/2.77 * Chain [92] with precondition: [V_N=3] 2.77/2.77 - Upper bound: 23 2.77/2.77 - Complexity: constant 2.77/2.77 * Chain [91] with precondition: [2>=V_N] 2.77/2.77 - Upper bound: 0 2.77/2.77 - Complexity: constant 2.77/2.77 * Chain [90] with precondition: [V_N>=3] 2.77/2.77 - Upper bound: 13*V_N+1+6*V_N*V_N 2.77/2.77 - Complexity: n^2 2.77/2.77 * Chain [89] with precondition: [V_N>=4] 2.77/2.77 - Upper bound: 147*V_N+3+2*V_N*V_N+V_N/2*(110*V_N)+V_N 2.77/2.77 - Complexity: n^2 2.77/2.77 * Chain [88] with precondition: [V_N>=5] 2.77/2.77 - Upper bound: 17*V_N+1+2*V_N*V_N+V_N/2*(10*V_N)+3*V_N 2.77/2.77 - Complexity: n^2 2.77/2.77 * Chain [87] with precondition: [V_N>=6] 2.77/2.77 - Upper bound: 17*V_N+1+2*V_N*V_N+V_N/2*(10*V_N)+4*V_N 2.77/2.77 - Complexity: n^2 2.77/2.77 * Chain [86] with precondition: [V_N>=7] 2.77/2.77 - Upper bound: 17*V_N+1+2*V_N*V_N+V_N/2*(10*V_N)+2*V_N 2.77/2.77 - Complexity: n^2 2.77/2.77 2.77/2.77 ### Maximum cost of eval_realheapsort_start(V_33,V_90,V_N,V_j_0,V_j_1,V_k_0,V_k_1,V_m_0,B): max([22,nat(V_N)*2*nat(V_N)+nat(V_N)*13+max([nat(V_N)*4*nat(V_N),nat(V_N)*10*nat(V_N/2)+nat(V_N)*4+nat(V_N/2)*2+max([nat(V_N/2)*6,nat(V_N)*130+2+nat(V_N)*100*nat(V_N/2)])])])+1 2.77/2.77 Asymptotic class: n^2 2.77/2.77 * Total analysis performed in 2529 ms. 2.77/2.77 2.78/2.87 EOF