2.40/2.44 WORST_CASE(?,O(n^2)) 2.40/2.44 2.40/2.44 Preprocessing Cost Relations 2.40/2.44 ===================================== 2.40/2.44 2.40/2.44 #### Computed strongly connected components 2.40/2.44 0. recursive : [evalrealheapsortbb2in/3,evalrealheapsortbb3in/3,evalrealheapsortbb4in/3] 2.40/2.44 1. recursive : [evalrealheapsortbb3in_loop_cont/7,evalrealheapsortbb5in/6,evalrealheapsortbb6in/6] 2.40/2.44 2. recursive : [evalrealheapsortbb10in/7,evalrealheapsortbb11in/7,evalrealheapsortbb12in/7,evalrealheapsortbb13in/7,evalrealheapsortbb14in/7,evalrealheapsortbb16in/7,evalrealheapsortbb9in/7] 2.40/2.44 3. recursive : [evalrealheapsortbb16in_loop_cont/9,evalrealheapsortbb17in/8,evalrealheapsortbb18in/8,evalrealheapsortbb8in/8] 2.40/2.44 4. non_recursive : [evalrealheapsortstop/5] 2.40/2.44 5. non_recursive : [evalrealheapsortreturnin/5] 2.40/2.44 6. non_recursive : [exit_location/1] 2.40/2.44 7. non_recursive : [evalrealheapsortbb18in_loop_cont/6] 2.40/2.44 8. non_recursive : [evalrealheapsortbb7in/5] 2.40/2.44 9. non_recursive : [evalrealheapsortbb6in_loop_cont/6] 2.40/2.44 10. non_recursive : [evalrealheapsortentryin/5] 2.40/2.44 11. non_recursive : [evalrealheapsortstart/5] 2.40/2.44 2.40/2.44 #### Obtained direct recursion through partial evaluation 2.40/2.44 0. SCC is partially evaluated into evalrealheapsortbb3in/3 2.40/2.44 1. SCC is partially evaluated into evalrealheapsortbb6in/6 2.40/2.44 2. SCC is partially evaluated into evalrealheapsortbb16in/7 2.40/2.44 3. SCC is partially evaluated into evalrealheapsortbb18in/8 2.40/2.44 4. SCC is completely evaluated into other SCCs 2.40/2.44 5. SCC is completely evaluated into other SCCs 2.40/2.44 6. SCC is completely evaluated into other SCCs 2.40/2.44 7. SCC is partially evaluated into evalrealheapsortbb18in_loop_cont/6 2.40/2.44 8. SCC is partially evaluated into evalrealheapsortbb7in/5 2.40/2.44 9. SCC is partially evaluated into evalrealheapsortbb6in_loop_cont/6 2.40/2.44 10. SCC is partially evaluated into evalrealheapsortentryin/5 2.40/2.44 11. SCC is partially evaluated into evalrealheapsortstart/5 2.40/2.44 2.40/2.44 Control-Flow Refinement of Cost Relations 2.40/2.44 ===================================== 2.40/2.44 2.40/2.44 ### Specialization of cost equations evalrealheapsortbb3in/3 2.40/2.44 * CE 10 is refined into CE [29] 2.40/2.44 * CE 12 is refined into CE [30] 2.40/2.44 * CE 13 is refined into CE [31] 2.40/2.44 * CE 11 is refined into CE [32] 2.40/2.44 2.40/2.44 2.40/2.44 ### Cost equations --> "Loop" of evalrealheapsortbb3in/3 2.40/2.44 * CEs [32] --> Loop 29 2.40/2.44 * CEs [29] --> Loop 30 2.40/2.44 * CEs [30] --> Loop 31 2.40/2.44 * CEs [31] --> Loop 32 2.40/2.44 2.40/2.44 ### Ranking functions of CR evalrealheapsortbb3in(C,H,I) 2.40/2.44 * RF of phase [29]: [C] 2.40/2.44 2.40/2.44 #### Partial ranking functions of CR evalrealheapsortbb3in(C,H,I) 2.40/2.44 * Partial RF of phase [29]: 2.40/2.44 - RF of loop [29:1]: 2.40/2.44 C 2.40/2.44 2.40/2.44 2.40/2.44 ### Specialization of cost equations evalrealheapsortbb6in/6 2.40/2.44 * CE 6 is refined into CE [33] 2.40/2.44 * CE 4 is refined into CE [34,35] 2.40/2.44 * CE 7 is refined into CE [36] 2.40/2.44 * CE 5 is refined into CE [37,38,39] 2.40/2.44 2.40/2.44 2.40/2.44 ### Cost equations --> "Loop" of evalrealheapsortbb6in/6 2.40/2.44 * CEs [39] --> Loop 33 2.40/2.44 * CEs [38] --> Loop 34 2.40/2.44 * CEs [37] --> Loop 35 2.40/2.44 * CEs [33] --> Loop 36 2.40/2.44 * CEs [34,35] --> Loop 37 2.40/2.44 * CEs [36] --> Loop 38 2.40/2.44 2.40/2.44 ### Ranking functions of CR evalrealheapsortbb6in(A,B,C,H,I,J) 2.40/2.44 * RF of phase [33,34,35]: [A-B] 2.40/2.44 2.40/2.44 #### Partial ranking functions of CR evalrealheapsortbb6in(A,B,C,H,I,J) 2.40/2.44 * Partial RF of phase [33,34,35]: 2.40/2.44 - RF of loop [33:1,34:1,35:1]: 2.40/2.44 A-B 2.40/2.44 2.40/2.44 2.40/2.44 ### Specialization of cost equations evalrealheapsortbb16in/7 2.40/2.44 * CE 28 is refined into CE [40] 2.40/2.44 * CE 27 is refined into CE [41] 2.40/2.44 * CE 26 is refined into CE [42] 2.40/2.44 * CE 23 is refined into CE [43] 2.40/2.44 * CE 24 is refined into CE [44] 2.40/2.44 * CE 22 is refined into CE [45] 2.40/2.44 * CE 25 is refined into CE [46] 2.40/2.44 * CE 21 is refined into CE [47] 2.40/2.44 2.40/2.44 2.40/2.44 ### Cost equations --> "Loop" of evalrealheapsortbb16in/7 2.40/2.44 * CEs [42] --> Loop 39 2.40/2.44 * CEs [43] --> Loop 40 2.40/2.44 * CEs [44] --> Loop 41 2.40/2.44 * CEs [45] --> Loop 42 2.40/2.44 * CEs [46] --> Loop 43 2.40/2.44 * CEs [47] --> Loop 44 2.40/2.44 * CEs [40] --> Loop 45 2.40/2.44 * CEs [41] --> Loop 46 2.40/2.44 2.40/2.44 ### Ranking functions of CR evalrealheapsortbb16in(A,B,C,D,H,I,J) 2.40/2.44 * RF of phase [42,44]: [A/2-B/2-C-3/2,A/2-C-3/2] 2.40/2.44 2.40/2.44 #### Partial ranking functions of CR evalrealheapsortbb16in(A,B,C,D,H,I,J) 2.40/2.44 * Partial RF of phase [42,44]: 2.40/2.44 - RF of loop [42:1,44:1]: 2.40/2.44 A/2-B/2-C-3/2 2.40/2.44 A/2-C-3/2 2.40/2.44 2.40/2.44 2.40/2.44 ### Specialization of cost equations evalrealheapsortbb18in/8 2.40/2.44 * CE 17 is refined into CE [48] 2.40/2.44 * CE 15 is refined into CE [49,50,51,52,53] 2.40/2.44 * CE 18 is refined into CE [54] 2.40/2.44 * CE 16 is refined into CE [55,56,57,58,59,60,61,62,63,64] 2.40/2.44 2.40/2.44 2.40/2.44 ### Cost equations --> "Loop" of evalrealheapsortbb18in/8 2.40/2.44 * CEs [64] --> Loop 47 2.40/2.44 * CEs [60] --> Loop 48 2.40/2.44 * CEs [63] --> Loop 49 2.40/2.44 * CEs [62] --> Loop 50 2.40/2.44 * CEs [61] --> Loop 51 2.40/2.44 * CEs [57] --> Loop 52 2.40/2.44 * CEs [58] --> Loop 53 2.40/2.44 * CEs [59] --> Loop 54 2.40/2.44 * CEs [55] --> Loop 55 2.40/2.44 * CEs [56] --> Loop 56 2.40/2.44 * CEs [48] --> Loop 57 2.40/2.44 * CEs [52] --> Loop 58 2.40/2.44 * CEs [51] --> Loop 59 2.40/2.44 * CEs [53] --> Loop 60 2.40/2.44 * CEs [50] --> Loop 61 2.40/2.44 * CEs [54] --> Loop 62 2.40/2.44 * CEs [49] --> Loop 63 2.40/2.44 2.40/2.44 ### Ranking functions of CR evalrealheapsortbb18in(A,B,C,D,H,I,J,K) 2.40/2.44 * RF of phase [47,48,49,50,51,52,53]: [A-B-3] 2.40/2.44 2.40/2.44 #### Partial ranking functions of CR evalrealheapsortbb18in(A,B,C,D,H,I,J,K) 2.40/2.44 * Partial RF of phase [47,48,49,50,51,52,53]: 2.40/2.44 - RF of loop [47:1,48:1]: 2.40/2.44 A-B-4 2.40/2.44 - RF of loop [49:1,52:1,53:1]: 2.40/2.44 A-B-3 2.40/2.44 - RF of loop [50:1,51:1]: 2.40/2.44 A-B-5 2.40/2.44 2.40/2.44 2.40/2.44 ### Specialization of cost equations evalrealheapsortbb18in_loop_cont/6 2.40/2.44 * CE 19 is refined into CE [65] 2.40/2.44 * CE 20 is refined into CE [66] 2.40/2.44 2.40/2.44 2.40/2.44 ### Cost equations --> "Loop" of evalrealheapsortbb18in_loop_cont/6 2.40/2.44 * CEs [65] --> Loop 64 2.40/2.44 * CEs [66] --> Loop 65 2.40/2.44 2.40/2.44 ### Ranking functions of CR evalrealheapsortbb18in_loop_cont(A,B,C,D,E,F) 2.40/2.44 2.40/2.44 #### Partial ranking functions of CR evalrealheapsortbb18in_loop_cont(A,B,C,D,E,F) 2.40/2.44 2.40/2.44 2.40/2.44 ### Specialization of cost equations evalrealheapsortbb7in/5 2.40/2.44 * CE 14 is refined into CE [67,68,69,70,71,72,73,74,75,76] 2.40/2.44 2.40/2.44 2.40/2.44 ### Cost equations --> "Loop" of evalrealheapsortbb7in/5 2.40/2.44 * CEs [74] --> Loop 66 2.40/2.44 * CEs [73] --> Loop 67 2.40/2.44 * CEs [72] --> Loop 68 2.40/2.44 * CEs [71,76] --> Loop 69 2.40/2.44 * CEs [69,70] --> Loop 70 2.40/2.44 * CEs [67,68,75] --> Loop 71 2.40/2.44 2.40/2.44 ### Ranking functions of CR evalrealheapsortbb7in(A,B,C,D,H) 2.40/2.44 2.40/2.44 #### Partial ranking functions of CR evalrealheapsortbb7in(A,B,C,D,H) 2.40/2.44 2.40/2.44 2.40/2.44 ### Specialization of cost equations evalrealheapsortbb6in_loop_cont/6 2.40/2.44 * CE 8 is refined into CE [77,78,79,80,81,82] 2.40/2.44 * CE 9 is refined into CE [83] 2.40/2.44 2.40/2.44 2.40/2.44 ### Cost equations --> "Loop" of evalrealheapsortbb6in_loop_cont/6 2.40/2.44 * CEs [82] --> Loop 72 2.40/2.44 * CEs [81] --> Loop 73 2.40/2.44 * CEs [80] --> Loop 74 2.40/2.44 * CEs [79] --> Loop 75 2.40/2.44 * CEs [78] --> Loop 76 2.40/2.44 * CEs [77] --> Loop 77 2.40/2.44 * CEs [83] --> Loop 78 2.40/2.44 2.40/2.44 ### Ranking functions of CR evalrealheapsortbb6in_loop_cont(A,B,C,D,E,F) 2.40/2.44 2.40/2.44 #### Partial ranking functions of CR evalrealheapsortbb6in_loop_cont(A,B,C,D,E,F) 2.40/2.44 2.40/2.44 2.40/2.44 ### Specialization of cost equations evalrealheapsortentryin/5 2.40/2.44 * CE 3 is refined into CE [84,85,86,87,88,89,90,91,92] 2.40/2.44 * CE 2 is refined into CE [93] 2.40/2.44 2.40/2.44 2.40/2.44 ### Cost equations --> "Loop" of evalrealheapsortentryin/5 2.40/2.44 * CEs [92] --> Loop 79 2.40/2.44 * CEs [91] --> Loop 80 2.40/2.44 * CEs [90] --> Loop 81 2.40/2.44 * CEs [89] --> Loop 82 2.40/2.44 * CEs [84,85,86,88] --> Loop 83 2.40/2.44 * CEs [93] --> Loop 84 2.40/2.44 * CEs [87] --> Loop 85 2.40/2.44 2.40/2.44 ### Ranking functions of CR evalrealheapsortentryin(A,B,C,D,H) 2.40/2.44 2.40/2.44 #### Partial ranking functions of CR evalrealheapsortentryin(A,B,C,D,H) 2.40/2.44 2.40/2.44 2.40/2.44 ### Specialization of cost equations evalrealheapsortstart/5 2.40/2.44 * CE 1 is refined into CE [94,95,96,97,98,99,100] 2.40/2.44 2.40/2.44 2.40/2.44 ### Cost equations --> "Loop" of evalrealheapsortstart/5 2.40/2.44 * CEs [100] --> Loop 86 2.40/2.44 * CEs [99] --> Loop 87 2.40/2.44 * CEs [98] --> Loop 88 2.40/2.44 * CEs [97] --> Loop 89 2.40/2.44 * CEs [96] --> Loop 90 2.40/2.44 * CEs [95] --> Loop 91 2.40/2.44 * CEs [94] --> Loop 92 2.40/2.44 2.40/2.44 ### Ranking functions of CR evalrealheapsortstart(A,B,C,D,H) 2.40/2.44 2.40/2.44 #### Partial ranking functions of CR evalrealheapsortstart(A,B,C,D,H) 2.40/2.44 2.40/2.44 2.40/2.44 Computing Bounds 2.40/2.44 ===================================== 2.40/2.44 2.40/2.44 #### Cost of chains of evalrealheapsortbb3in(C,H,I): 2.40/2.44 * Chain [[29],32]: 1*it(29)+0 2.40/2.44 Such that:it(29) =< C 2.40/2.44 2.40/2.44 with precondition: [H=3,C>=1] 2.40/2.44 2.40/2.44 * Chain [[29],31]: 1*it(29)+0 2.40/2.44 Such that:it(29) =< C 2.40/2.44 2.40/2.44 with precondition: [H=4,0>=I,C>=1,2*I+1>=0] 2.40/2.44 2.40/2.44 * Chain [[29],30]: 1*it(29)+0 2.40/2.44 Such that:it(29) =< C-I 2.40/2.44 2.40/2.44 with precondition: [H=4,I>=1,C>=2*I+1] 2.40/2.44 2.40/2.44 * Chain [32]: 0 2.40/2.44 with precondition: [H=3,2*C+1>=0] 2.40/2.44 2.40/2.44 * Chain [30]: 0 2.40/2.44 with precondition: [H=4,C=I,C>=1] 2.40/2.44 2.40/2.44 2.40/2.44 #### Cost of chains of evalrealheapsortbb6in(A,B,C,H,I,J): 2.40/2.44 * Chain [[33,34,35],38]: 3*it(33)+1*s(5)+1*s(6)+0 2.40/2.44 Such that:aux(1) =< A 2.40/2.44 aux(5) =< A-B 2.40/2.44 it(33) =< aux(5) 2.40/2.44 aux(2) =< aux(1)+1 2.40/2.44 s(5) =< it(33)*aux(1) 2.40/2.44 s(6) =< it(33)*aux(2) 2.40/2.44 2.40/2.44 with precondition: [H=3,A>=3,B>=1,A>=B+1] 2.40/2.44 2.40/2.44 * Chain [[33,34,35],37]: 3*it(33)+1*s(5)+1*s(6)+1*s(7)+0 2.40/2.44 Such that:aux(6) =< A 2.40/2.44 aux(7) =< A-B 2.40/2.44 s(7) =< aux(6) 2.40/2.44 it(33) =< aux(7) 2.40/2.44 aux(2) =< aux(6)+1 2.40/2.44 s(5) =< it(33)*aux(6) 2.40/2.44 s(6) =< it(33)*aux(2) 2.40/2.44 2.40/2.44 with precondition: [H=3,B>=1,A>=B+2] 2.40/2.44 2.40/2.44 * Chain [[33,34,35],36]: 3*it(33)+1*s(5)+1*s(6)+0 2.40/2.44 Such that:aux(1) =< I 2.40/2.44 aux(8) =< -B+I 2.40/2.44 it(33) =< aux(8) 2.40/2.44 aux(2) =< aux(1)+1 2.40/2.44 s(5) =< it(33)*aux(1) 2.40/2.44 s(6) =< it(33)*aux(2) 2.40/2.44 2.40/2.44 with precondition: [H=6,A=I,A>=3,B>=1,2*J+1>=0,A>=B+1,A>=J+1] 2.40/2.44 2.40/2.44 * Chain [38]: 0 2.40/2.44 with precondition: [H=3,A>=3,B>=1] 2.40/2.44 2.40/2.44 * Chain [37]: 1*s(7)+0 2.40/2.44 Such that:s(7) =< B 2.40/2.44 2.40/2.44 with precondition: [H=3,A>=3,B>=1,A>=B+1] 2.40/2.44 2.40/2.44 2.40/2.44 #### Cost of chains of evalrealheapsortbb16in(A,B,C,D,H,I,J): 2.40/2.44 * Chain [[42,44],46]: 2*it(42)+0 2.40/2.44 Such that:aux(9) =< A/2-B/2-C 2.40/2.44 aux(11) =< A/2-C 2.40/2.44 aux(13) =< -C+I 2.40/2.44 it(42) =< aux(9) 2.40/2.44 it(42) =< aux(13) 2.40/2.44 it(42) =< aux(11) 2.40/2.44 2.40/2.44 with precondition: [H=2,I=J,B>=0,C>=0,I>=2*C+1,A>=2*C+B+4,B+2*I+2>=A,A>=B+I+2] 2.40/2.44 2.40/2.44 * Chain [[42,44],45]: 2*it(42)+0 2.40/2.44 Such that:aux(9) =< A/2-B/2-C 2.40/2.44 aux(11) =< A/2-C 2.40/2.44 aux(14) =< A-B-C 2.40/2.44 it(42) =< aux(9) 2.40/2.44 it(42) =< aux(14) 2.40/2.44 it(42) =< aux(11) 2.40/2.44 2.40/2.44 with precondition: [H=3,B>=0,C>=0,A>=2*C+B+4] 2.40/2.44 2.40/2.44 * Chain [[42,44],43,46]: 2*it(42)+1 2.40/2.44 Such that:aux(11) =< A/2-C 2.40/2.44 aux(9) =< -C+I/2+1 2.40/2.44 aux(15) =< -C+I/2 2.40/2.44 it(42) =< aux(9) 2.40/2.44 it(42) =< aux(15) 2.40/2.44 it(42) =< aux(11) 2.40/2.44 2.40/2.44 with precondition: [H=2,A=B+I+2,A=B+J+2,B>=0,C>=0,A>=4*C+B+5] 2.40/2.44 2.40/2.44 * Chain [[42,44],43,45]: 2*it(42)+1 2.40/2.44 Such that:aux(11) =< A/2-C 2.40/2.44 aux(16) =< A/2-B/2-C 2.40/2.44 it(42) =< aux(16) 2.40/2.44 it(42) =< aux(11) 2.40/2.44 2.40/2.44 with precondition: [H=3,B>=0,C>=0,A>=4*C+B+5] 2.40/2.44 2.40/2.44 * Chain [[42,44],41,46]: 2*it(42)+1 2.40/2.44 Such that:aux(9) =< -B/2-C+I/2 2.40/2.44 aux(11) =< -C+I/2 2.40/2.44 aux(17) =< -C+J/2 2.40/2.44 it(42) =< aux(9) 2.40/2.44 it(42) =< aux(17) 2.40/2.44 it(42) =< aux(11) 2.40/2.44 2.40/2.44 with precondition: [H=2,A=I,B>=0,C>=0,J>=4*C+4,A>=B+J+2] 2.40/2.44 2.40/2.44 * Chain [[42,44],41,45]: 2*it(42)+1 2.40/2.44 Such that:aux(11) =< A/2-C 2.40/2.44 aux(18) =< A/2-B/2-C 2.40/2.44 it(42) =< aux(18) 2.40/2.44 it(42) =< aux(11) 2.40/2.44 2.40/2.44 with precondition: [H=3,B>=0,C>=0,A>=4*C+B+6] 2.40/2.44 2.40/2.44 * Chain [[42,44],40,46]: 2*it(42)+1 2.40/2.44 Such that:aux(9) =< -B/2-C+I/2 2.40/2.44 aux(11) =< -C+I/2 2.40/2.44 aux(19) =< -C+J/2 2.40/2.44 it(42) =< aux(9) 2.40/2.44 it(42) =< aux(19) 2.40/2.44 it(42) =< aux(11) 2.40/2.44 2.40/2.44 with precondition: [H=2,A=I,B>=0,C>=0,J>=4*C+3,A>=B+J+3] 2.40/2.44 2.40/2.44 * Chain [[42,44],40,45]: 2*it(42)+1 2.40/2.44 Such that:aux(11) =< A/2-C 2.40/2.44 aux(20) =< A/2-B/2-C 2.40/2.44 it(42) =< aux(20) 2.40/2.44 it(42) =< aux(11) 2.40/2.44 2.40/2.44 with precondition: [H=3,B>=0,C>=0,A>=4*C+B+6] 2.40/2.44 2.40/2.44 * Chain [[42,44],39,46]: 2*it(42)+1 2.40/2.44 Such that:aux(11) =< -C+I/2 2.40/2.44 aux(21) =< -B/2-C+I/2 2.40/2.44 it(42) =< aux(21) 2.40/2.44 it(42) =< aux(11) 2.40/2.44 2.40/2.44 with precondition: [H=2,A=I,A=B+J+2,B>=0,C>=0,A>=4*C+B+5] 2.40/2.44 2.40/2.44 * Chain [[42,44],39,45]: 2*it(42)+1 2.40/2.44 Such that:aux(11) =< A/2-C 2.40/2.44 aux(22) =< A/2-B/2-C 2.40/2.44 it(42) =< aux(22) 2.40/2.44 it(42) =< aux(11) 2.40/2.44 2.40/2.44 with precondition: [H=3,B>=0,C>=0,A>=4*C+B+5] 2.40/2.44 2.40/2.44 * Chain [46]: 0 2.40/2.44 with precondition: [H=2,J=D,C=I,A>=3,B>=0,A>=B+2,A>=C,4*A>=3*B+C+9,B+2*C+2>=A] 2.40/2.44 2.40/2.44 * Chain [45]: 0 2.40/2.44 with precondition: [H=3,A>=3,B>=0,C>=0,A>=B+2,A>=C,4*A>=3*B+C+9] 2.40/2.44 2.40/2.44 * Chain [43,46]: 1 2.40/2.44 with precondition: [H=2,I=2*C+1,I=J,B+I+2=A,I>=1,A>=I+2] 2.40/2.44 2.40/2.44 * Chain [43,45]: 1 2.40/2.44 with precondition: [H=3,A=2*C+B+3,C>=0,A>=2*C+3] 2.40/2.44 2.40/2.44 * Chain [41,46]: 1 2.40/2.44 with precondition: [H=2,A=I,2*C+2=J,B>=0,C>=0,A>=2*C+B+4] 2.40/2.44 2.40/2.44 * Chain [41,45]: 1 2.40/2.44 with precondition: [H=3,B>=0,C>=0,A>=2*C+B+4] 2.40/2.44 2.40/2.44 * Chain [40,46]: 1 2.40/2.44 with precondition: [H=2,A=I,2*C+1=J,B>=0,C>=0,A>=2*C+B+4] 2.40/2.44 2.40/2.44 * Chain [40,45]: 1 2.40/2.44 with precondition: [H=3,B>=0,C>=0,A>=2*C+B+4] 2.40/2.44 2.40/2.44 * Chain [39,46]: 1 2.40/2.44 with precondition: [H=2,A=I,A=2*C+B+3,A=B+J+2,B>=0,A>=B+3] 2.40/2.44 2.40/2.44 * Chain [39,45]: 1 2.40/2.44 with precondition: [H=3,A=2*C+B+3,C>=0,A>=2*C+3] 2.40/2.44 2.40/2.44 2.40/2.44 #### Cost of chains of evalrealheapsortbb18in(A,B,C,D,H,I,J,K): 2.40/2.44 * Chain [[47,48,49,50,51,52,53],63]: 13*it(47)+2*s(69)+2*s(73)+2*s(76)+2*s(80)+2*s(84)+1 2.40/2.44 Such that:aux(27) =< A/2 2.40/2.44 aux(28) =< A/2-B/2 2.40/2.44 aux(43) =< A-B 2.40/2.44 it(47) =< aux(43) 2.40/2.44 aux(40) =< aux(28)-1/2 2.40/2.44 aux(30) =< aux(27) 2.40/2.44 aux(29) =< aux(28)+1 2.40/2.44 aux(37) =< aux(28) 2.40/2.44 aux(34) =< aux(28)*2 2.40/2.44 s(71) =< it(47)*aux(28) 2.40/2.44 s(70) =< it(47)*aux(27) 2.40/2.44 s(86) =< it(47)*aux(40) 2.40/2.44 s(74) =< it(47)*aux(30) 2.40/2.44 s(72) =< it(47)*aux(29) 2.40/2.44 s(82) =< it(47)*aux(37) 2.40/2.44 s(78) =< it(47)*aux(34) 2.40/2.44 s(84) =< s(72) 2.40/2.44 s(84) =< s(86) 2.40/2.44 s(84) =< s(74) 2.40/2.44 s(80) =< s(72) 2.40/2.44 s(80) =< s(82) 2.40/2.44 s(80) =< s(74) 2.40/2.44 s(76) =< s(72) 2.40/2.44 s(76) =< s(78) 2.40/2.44 s(76) =< s(74) 2.40/2.44 s(73) =< s(72) 2.40/2.44 s(73) =< s(74) 2.40/2.44 s(69) =< s(72) 2.40/2.44 s(69) =< s(71) 2.40/2.44 s(69) =< s(70) 2.40/2.44 2.40/2.44 with precondition: [H=3,B>=0,A>=B+4] 2.40/2.44 2.40/2.44 * Chain [[47,48,49,50,51,52,53],62]: 13*it(47)+2*s(69)+2*s(73)+2*s(76)+2*s(80)+2*s(84)+0 2.40/2.44 Such that:aux(27) =< A/2 2.40/2.44 aux(28) =< A/2-B/2 2.40/2.44 aux(44) =< A-B 2.40/2.44 it(47) =< aux(44) 2.40/2.44 aux(40) =< aux(28)-1/2 2.40/2.44 aux(30) =< aux(27) 2.40/2.44 aux(29) =< aux(28)+1 2.40/2.44 aux(37) =< aux(28) 2.40/2.44 aux(34) =< aux(28)*2 2.40/2.44 s(71) =< it(47)*aux(28) 2.40/2.44 s(70) =< it(47)*aux(27) 2.40/2.44 s(86) =< it(47)*aux(40) 2.40/2.44 s(74) =< it(47)*aux(30) 2.40/2.44 s(72) =< it(47)*aux(29) 2.40/2.44 s(82) =< it(47)*aux(37) 2.40/2.44 s(78) =< it(47)*aux(34) 2.40/2.44 s(84) =< s(72) 2.40/2.44 s(84) =< s(86) 2.40/2.44 s(84) =< s(74) 2.40/2.44 s(80) =< s(72) 2.40/2.44 s(80) =< s(82) 2.40/2.44 s(80) =< s(74) 2.40/2.44 s(76) =< s(72) 2.40/2.44 s(76) =< s(78) 2.40/2.44 s(76) =< s(74) 2.40/2.44 s(73) =< s(72) 2.40/2.44 s(73) =< s(74) 2.40/2.44 s(69) =< s(72) 2.40/2.44 s(69) =< s(71) 2.40/2.44 s(69) =< s(70) 2.40/2.44 2.40/2.44 with precondition: [H=3,B>=0,A>=B+4] 2.40/2.44 2.40/2.44 * Chain [[47,48,49,50,51,52,53],61]: 13*it(47)+2*s(69)+2*s(73)+2*s(76)+2*s(80)+2*s(84)+0 2.40/2.44 Such that:aux(27) =< A/2 2.40/2.44 aux(28) =< A/2-B/2 2.40/2.44 aux(45) =< A-B 2.40/2.44 it(47) =< aux(45) 2.40/2.44 aux(40) =< aux(28)-1/2 2.40/2.44 aux(30) =< aux(27) 2.40/2.44 aux(29) =< aux(28)+1 2.40/2.44 aux(37) =< aux(28) 2.40/2.44 aux(34) =< aux(28)*2 2.40/2.44 s(71) =< it(47)*aux(28) 2.40/2.44 s(70) =< it(47)*aux(27) 2.40/2.44 s(86) =< it(47)*aux(40) 2.40/2.44 s(74) =< it(47)*aux(30) 2.40/2.44 s(72) =< it(47)*aux(29) 2.40/2.44 s(82) =< it(47)*aux(37) 2.40/2.44 s(78) =< it(47)*aux(34) 2.40/2.44 s(84) =< s(72) 2.40/2.44 s(84) =< s(86) 2.40/2.44 s(84) =< s(74) 2.40/2.44 s(80) =< s(72) 2.40/2.44 s(80) =< s(82) 2.40/2.44 s(80) =< s(74) 2.40/2.44 s(76) =< s(72) 2.40/2.44 s(76) =< s(78) 2.40/2.44 s(76) =< s(74) 2.40/2.44 s(73) =< s(72) 2.40/2.44 s(73) =< s(74) 2.40/2.44 s(69) =< s(72) 2.40/2.44 s(69) =< s(71) 2.40/2.44 s(69) =< s(70) 2.40/2.44 2.40/2.44 with precondition: [H=3,B>=0,A>=B+4] 2.40/2.44 2.40/2.44 * Chain [[47,48,49,50,51,52,53],60]: 13*it(47)+2*s(69)+2*s(73)+2*s(76)+2*s(80)+2*s(84)+2*s(91)+1 2.40/2.44 Such that:aux(46) =< A-B 2.40/2.44 aux(47) =< A/2 2.40/2.44 aux(48) =< A/2-B/2 2.40/2.44 s(89) =< aux(46) 2.40/2.44 s(89) =< aux(48) 2.40/2.44 s(91) =< s(89) 2.40/2.44 s(91) =< aux(46) 2.40/2.44 s(91) =< aux(47) 2.40/2.44 it(47) =< aux(46) 2.40/2.44 aux(40) =< aux(48)-1/2 2.40/2.44 aux(30) =< aux(47) 2.40/2.44 aux(29) =< aux(48)+1 2.40/2.44 aux(37) =< aux(48) 2.40/2.44 aux(34) =< aux(48)*2 2.40/2.44 s(71) =< it(47)*aux(48) 2.40/2.44 s(70) =< it(47)*aux(47) 2.40/2.44 s(86) =< it(47)*aux(40) 2.40/2.44 s(74) =< it(47)*aux(30) 2.40/2.44 s(72) =< it(47)*aux(29) 2.40/2.44 s(82) =< it(47)*aux(37) 2.40/2.44 s(78) =< it(47)*aux(34) 2.40/2.44 s(84) =< s(72) 2.40/2.44 s(84) =< s(86) 2.40/2.44 s(84) =< s(74) 2.40/2.44 s(80) =< s(72) 2.40/2.44 s(80) =< s(82) 2.40/2.44 s(80) =< s(74) 2.40/2.44 s(76) =< s(72) 2.40/2.44 s(76) =< s(78) 2.40/2.44 s(76) =< s(74) 2.40/2.44 s(73) =< s(72) 2.40/2.44 s(73) =< s(74) 2.40/2.44 s(69) =< s(72) 2.40/2.44 s(69) =< s(71) 2.40/2.44 s(69) =< s(70) 2.40/2.44 2.40/2.44 with precondition: [H=3,B>=0,A>=B+5] 2.40/2.44 2.40/2.44 * Chain [[47,48,49,50,51,52,53],59]: 13*it(47)+2*s(69)+2*s(73)+2*s(76)+2*s(80)+2*s(84)+4*s(94)+1 2.40/2.44 Such that:aux(49) =< A-B 2.40/2.44 aux(50) =< A/2 2.40/2.44 aux(51) =< A/2-B/2 2.40/2.44 s(92) =< aux(49) 2.40/2.44 s(92) =< aux(51) 2.40/2.44 s(94) =< s(92) 2.40/2.44 s(94) =< aux(50) 2.40/2.44 it(47) =< aux(49) 2.40/2.44 aux(40) =< aux(51)-1/2 2.40/2.44 aux(30) =< aux(50) 2.40/2.44 aux(29) =< aux(51)+1 2.40/2.44 aux(37) =< aux(51) 2.40/2.44 aux(34) =< aux(51)*2 2.40/2.44 s(71) =< it(47)*aux(51) 2.40/2.44 s(70) =< it(47)*aux(50) 2.40/2.44 s(86) =< it(47)*aux(40) 2.40/2.44 s(74) =< it(47)*aux(30) 2.40/2.44 s(72) =< it(47)*aux(29) 2.40/2.44 s(82) =< it(47)*aux(37) 2.40/2.44 s(78) =< it(47)*aux(34) 2.40/2.44 s(84) =< s(72) 2.40/2.44 s(84) =< s(86) 2.40/2.44 s(84) =< s(74) 2.40/2.44 s(80) =< s(72) 2.40/2.44 s(80) =< s(82) 2.40/2.44 s(80) =< s(74) 2.40/2.44 s(76) =< s(72) 2.40/2.44 s(76) =< s(78) 2.40/2.44 s(76) =< s(74) 2.40/2.44 s(73) =< s(72) 2.40/2.44 s(73) =< s(74) 2.40/2.44 s(69) =< s(72) 2.40/2.44 s(69) =< s(71) 2.40/2.44 s(69) =< s(70) 2.40/2.44 2.40/2.44 with precondition: [H=3,B>=0,A>=B+6] 2.40/2.44 2.40/2.44 * Chain [[47,48,49,50,51,52,53],58]: 13*it(47)+2*s(69)+2*s(73)+2*s(76)+2*s(80)+2*s(84)+4*s(97)+1 2.40/2.44 Such that:aux(52) =< A-B 2.40/2.44 aux(53) =< A/2 2.40/2.44 aux(54) =< A/2-B/2 2.40/2.44 s(95) =< aux(52) 2.40/2.44 s(95) =< aux(54) 2.40/2.44 s(97) =< s(95) 2.40/2.44 s(97) =< aux(53) 2.40/2.44 it(47) =< aux(52) 2.40/2.44 aux(40) =< aux(54)-1/2 2.40/2.44 aux(30) =< aux(53) 2.40/2.44 aux(29) =< aux(54)+1 2.40/2.44 aux(37) =< aux(54) 2.40/2.44 aux(34) =< aux(54)*2 2.40/2.44 s(71) =< it(47)*aux(54) 2.40/2.44 s(70) =< it(47)*aux(53) 2.40/2.44 s(86) =< it(47)*aux(40) 2.40/2.44 s(74) =< it(47)*aux(30) 2.40/2.44 s(72) =< it(47)*aux(29) 2.40/2.44 s(82) =< it(47)*aux(37) 2.40/2.44 s(78) =< it(47)*aux(34) 2.40/2.44 s(84) =< s(72) 2.40/2.44 s(84) =< s(86) 2.40/2.44 s(84) =< s(74) 2.40/2.44 s(80) =< s(72) 2.40/2.44 s(80) =< s(82) 2.40/2.44 s(80) =< s(74) 2.40/2.44 s(76) =< s(72) 2.40/2.44 s(76) =< s(78) 2.40/2.44 s(76) =< s(74) 2.40/2.44 s(73) =< s(72) 2.40/2.44 s(73) =< s(74) 2.40/2.44 s(69) =< s(72) 2.40/2.44 s(69) =< s(71) 2.40/2.44 s(69) =< s(70) 2.40/2.44 2.40/2.44 with precondition: [H=3,B>=0,A>=B+7] 2.40/2.44 2.40/2.44 * Chain [[47,48,49,50,51,52,53],55,62]: 13*it(47)+2*s(69)+2*s(73)+2*s(76)+2*s(80)+2*s(84)+2 2.40/2.44 Such that:aux(27) =< A/2 2.40/2.44 aux(28) =< A/2-B/2 2.40/2.44 aux(55) =< A-B 2.40/2.44 it(47) =< aux(55) 2.40/2.44 aux(40) =< aux(28)-1/2 2.40/2.44 aux(30) =< aux(27) 2.40/2.44 aux(29) =< aux(28)+1 2.40/2.44 aux(37) =< aux(28) 2.40/2.44 aux(34) =< aux(28)*2 2.40/2.44 s(71) =< it(47)*aux(28) 2.40/2.44 s(70) =< it(47)*aux(27) 2.40/2.44 s(86) =< it(47)*aux(40) 2.40/2.44 s(74) =< it(47)*aux(30) 2.40/2.44 s(72) =< it(47)*aux(29) 2.40/2.44 s(82) =< it(47)*aux(37) 2.40/2.44 s(78) =< it(47)*aux(34) 2.40/2.44 s(84) =< s(72) 2.40/2.44 s(84) =< s(86) 2.40/2.44 s(84) =< s(74) 2.40/2.44 s(80) =< s(72) 2.40/2.44 s(80) =< s(82) 2.40/2.44 s(80) =< s(74) 2.40/2.44 s(76) =< s(72) 2.40/2.44 s(76) =< s(78) 2.40/2.44 s(76) =< s(74) 2.40/2.44 s(73) =< s(72) 2.40/2.44 s(73) =< s(74) 2.40/2.44 s(69) =< s(72) 2.40/2.44 s(69) =< s(71) 2.40/2.44 s(69) =< s(70) 2.40/2.44 2.40/2.44 with precondition: [H=3,B>=0,A>=B+4] 2.40/2.44 2.40/2.44 * Chain [[47,48,49,50,51,52,53],55,61]: 13*it(47)+2*s(69)+2*s(73)+2*s(76)+2*s(80)+2*s(84)+2 2.40/2.44 Such that:aux(27) =< A/2 2.40/2.44 aux(28) =< A/2-B/2 2.40/2.44 aux(56) =< A-B 2.40/2.44 it(47) =< aux(56) 2.40/2.44 aux(40) =< aux(28)-1/2 2.40/2.44 aux(30) =< aux(27) 2.40/2.44 aux(29) =< aux(28)+1 2.40/2.44 aux(37) =< aux(28) 2.40/2.44 aux(34) =< aux(28)*2 2.40/2.44 s(71) =< it(47)*aux(28) 2.40/2.44 s(70) =< it(47)*aux(27) 2.40/2.44 s(86) =< it(47)*aux(40) 2.40/2.44 s(74) =< it(47)*aux(30) 2.40/2.44 s(72) =< it(47)*aux(29) 2.40/2.44 s(82) =< it(47)*aux(37) 2.40/2.44 s(78) =< it(47)*aux(34) 2.40/2.44 s(84) =< s(72) 2.40/2.44 s(84) =< s(86) 2.40/2.44 s(84) =< s(74) 2.40/2.44 s(80) =< s(72) 2.40/2.44 s(80) =< s(82) 2.40/2.44 s(80) =< s(74) 2.40/2.44 s(76) =< s(72) 2.40/2.44 s(76) =< s(78) 2.40/2.44 s(76) =< s(74) 2.40/2.44 s(73) =< s(72) 2.40/2.44 s(73) =< s(74) 2.40/2.44 s(69) =< s(72) 2.40/2.44 s(69) =< s(71) 2.40/2.44 s(69) =< s(70) 2.40/2.44 2.40/2.44 with precondition: [H=3,B>=0,A>=B+4] 2.40/2.44 2.40/2.44 * Chain [[47,48,49,50,51,52,53],55,56,62]: 13*it(47)+2*s(69)+2*s(73)+2*s(76)+2*s(80)+2*s(84)+3 2.40/2.44 Such that:aux(27) =< A/2 2.40/2.44 aux(28) =< A/2-B/2 2.40/2.44 aux(57) =< A-B 2.40/2.44 it(47) =< aux(57) 2.40/2.44 aux(40) =< aux(28)-1/2 2.40/2.44 aux(30) =< aux(27) 2.40/2.44 aux(29) =< aux(28)+1 2.40/2.44 aux(37) =< aux(28) 2.40/2.44 aux(34) =< aux(28)*2 2.40/2.44 s(71) =< it(47)*aux(28) 2.40/2.44 s(70) =< it(47)*aux(27) 2.40/2.44 s(86) =< it(47)*aux(40) 2.40/2.44 s(74) =< it(47)*aux(30) 2.40/2.44 s(72) =< it(47)*aux(29) 2.40/2.44 s(82) =< it(47)*aux(37) 2.40/2.44 s(78) =< it(47)*aux(34) 2.40/2.44 s(84) =< s(72) 2.40/2.44 s(84) =< s(86) 2.40/2.44 s(84) =< s(74) 2.40/2.44 s(80) =< s(72) 2.40/2.44 s(80) =< s(82) 2.40/2.44 s(80) =< s(74) 2.40/2.44 s(76) =< s(72) 2.40/2.44 s(76) =< s(78) 2.40/2.44 s(76) =< s(74) 2.40/2.44 s(73) =< s(72) 2.40/2.44 s(73) =< s(74) 2.40/2.44 s(69) =< s(72) 2.40/2.44 s(69) =< s(71) 2.40/2.44 s(69) =< s(70) 2.40/2.44 2.40/2.44 with precondition: [H=3,B>=0,A>=B+4] 2.40/2.44 2.40/2.44 * Chain [[47,48,49,50,51,52,53],55,56,57]: 13*it(47)+2*s(69)+2*s(73)+2*s(76)+2*s(80)+2*s(84)+3 2.40/2.44 Such that:aux(42) =< -B+I 2.40/2.44 aux(41) =< -B+I+1 2.40/2.44 aux(28) =< -B/2+I/2+1/2 2.40/2.44 aux(27) =< I/2+1/2 2.40/2.44 it(47) =< aux(41) 2.40/2.44 it(47) =< aux(42) 2.40/2.44 aux(40) =< aux(28)-1/2 2.40/2.44 aux(30) =< aux(27) 2.40/2.44 aux(29) =< aux(28)+1 2.40/2.44 aux(37) =< aux(28) 2.40/2.44 aux(34) =< aux(28)*2 2.40/2.44 s(71) =< it(47)*aux(28) 2.40/2.44 s(70) =< it(47)*aux(27) 2.40/2.44 s(86) =< it(47)*aux(40) 2.40/2.44 s(74) =< it(47)*aux(30) 2.40/2.44 s(72) =< it(47)*aux(29) 2.40/2.44 s(82) =< it(47)*aux(37) 2.40/2.44 s(78) =< it(47)*aux(34) 2.40/2.44 s(84) =< s(72) 2.40/2.44 s(84) =< s(86) 2.40/2.44 s(84) =< s(74) 2.40/2.44 s(80) =< s(72) 2.40/2.44 s(80) =< s(82) 2.40/2.44 s(80) =< s(74) 2.40/2.44 s(76) =< s(72) 2.40/2.44 s(76) =< s(78) 2.40/2.44 s(76) =< s(74) 2.40/2.44 s(73) =< s(72) 2.40/2.44 s(73) =< s(74) 2.40/2.44 s(69) =< s(72) 2.40/2.44 s(69) =< s(71) 2.40/2.44 s(69) =< s(70) 2.40/2.44 2.40/2.44 with precondition: [H=5,J=0,K=1,A=I+1,B>=0,A>=B+4] 2.40/2.44 2.40/2.44 * Chain [[47,48,49,50,51,52,53],54,62]: 13*it(47)+2*s(69)+2*s(73)+2*s(76)+2*s(80)+2*s(84)+2 2.40/2.44 Such that:aux(27) =< A/2 2.40/2.44 aux(28) =< A/2-B/2 2.40/2.44 aux(58) =< A-B 2.40/2.44 it(47) =< aux(58) 2.40/2.44 aux(40) =< aux(28)-1/2 2.40/2.44 aux(30) =< aux(27) 2.40/2.44 aux(29) =< aux(28)+1 2.40/2.44 aux(37) =< aux(28) 2.40/2.44 aux(34) =< aux(28)*2 2.40/2.44 s(71) =< it(47)*aux(28) 2.40/2.44 s(70) =< it(47)*aux(27) 2.40/2.44 s(86) =< it(47)*aux(40) 2.40/2.44 s(74) =< it(47)*aux(30) 2.40/2.44 s(72) =< it(47)*aux(29) 2.40/2.44 s(82) =< it(47)*aux(37) 2.40/2.44 s(78) =< it(47)*aux(34) 2.40/2.44 s(84) =< s(72) 2.40/2.44 s(84) =< s(86) 2.40/2.44 s(84) =< s(74) 2.40/2.44 s(80) =< s(72) 2.40/2.44 s(80) =< s(82) 2.40/2.44 s(80) =< s(74) 2.40/2.44 s(76) =< s(72) 2.40/2.44 s(76) =< s(78) 2.40/2.44 s(76) =< s(74) 2.40/2.44 s(73) =< s(72) 2.40/2.44 s(73) =< s(74) 2.40/2.44 s(69) =< s(72) 2.40/2.44 s(69) =< s(71) 2.40/2.44 s(69) =< s(70) 2.40/2.44 2.40/2.44 with precondition: [H=3,B>=0,A>=B+4] 2.40/2.44 2.40/2.44 * Chain [[47,48,49,50,51,52,53],54,61]: 13*it(47)+2*s(69)+2*s(73)+2*s(76)+2*s(80)+2*s(84)+2 2.40/2.44 Such that:aux(27) =< A/2 2.40/2.44 aux(28) =< A/2-B/2 2.40/2.44 aux(59) =< A-B 2.40/2.44 it(47) =< aux(59) 2.40/2.44 aux(40) =< aux(28)-1/2 2.40/2.44 aux(30) =< aux(27) 2.40/2.44 aux(29) =< aux(28)+1 2.40/2.44 aux(37) =< aux(28) 2.40/2.44 aux(34) =< aux(28)*2 2.40/2.44 s(71) =< it(47)*aux(28) 2.40/2.44 s(70) =< it(47)*aux(27) 2.40/2.44 s(86) =< it(47)*aux(40) 2.40/2.44 s(74) =< it(47)*aux(30) 2.40/2.44 s(72) =< it(47)*aux(29) 2.40/2.44 s(82) =< it(47)*aux(37) 2.40/2.44 s(78) =< it(47)*aux(34) 2.40/2.44 s(84) =< s(72) 2.40/2.44 s(84) =< s(86) 2.40/2.44 s(84) =< s(74) 2.40/2.44 s(80) =< s(72) 2.40/2.44 s(80) =< s(82) 2.40/2.44 s(80) =< s(74) 2.40/2.44 s(76) =< s(72) 2.40/2.44 s(76) =< s(78) 2.40/2.44 s(76) =< s(74) 2.40/2.44 s(73) =< s(72) 2.40/2.44 s(73) =< s(74) 2.40/2.44 s(69) =< s(72) 2.40/2.44 s(69) =< s(71) 2.40/2.44 s(69) =< s(70) 2.40/2.44 2.40/2.44 with precondition: [H=3,B>=0,A>=B+4] 2.40/2.44 2.40/2.44 * Chain [[47,48,49,50,51,52,53],54,56,62]: 13*it(47)+2*s(69)+2*s(73)+2*s(76)+2*s(80)+2*s(84)+3 2.40/2.44 Such that:aux(27) =< A/2 2.40/2.44 aux(28) =< A/2-B/2 2.40/2.44 aux(60) =< A-B 2.40/2.44 it(47) =< aux(60) 2.40/2.44 aux(40) =< aux(28)-1/2 2.40/2.44 aux(30) =< aux(27) 2.40/2.44 aux(29) =< aux(28)+1 2.40/2.44 aux(37) =< aux(28) 2.40/2.44 aux(34) =< aux(28)*2 2.40/2.44 s(71) =< it(47)*aux(28) 2.40/2.44 s(70) =< it(47)*aux(27) 2.40/2.44 s(86) =< it(47)*aux(40) 2.40/2.44 s(74) =< it(47)*aux(30) 2.40/2.44 s(72) =< it(47)*aux(29) 2.40/2.44 s(82) =< it(47)*aux(37) 2.40/2.44 s(78) =< it(47)*aux(34) 2.40/2.44 s(84) =< s(72) 2.40/2.44 s(84) =< s(86) 2.40/2.44 s(84) =< s(74) 2.40/2.44 s(80) =< s(72) 2.40/2.44 s(80) =< s(82) 2.40/2.44 s(80) =< s(74) 2.40/2.44 s(76) =< s(72) 2.40/2.44 s(76) =< s(78) 2.40/2.44 s(76) =< s(74) 2.40/2.44 s(73) =< s(72) 2.40/2.44 s(73) =< s(74) 2.40/2.44 s(69) =< s(72) 2.40/2.44 s(69) =< s(71) 2.40/2.44 s(69) =< s(70) 2.40/2.44 2.40/2.44 with precondition: [H=3,B>=0,A>=B+4] 2.40/2.44 2.40/2.44 * Chain [[47,48,49,50,51,52,53],54,56,57]: 13*it(47)+2*s(69)+2*s(73)+2*s(76)+2*s(80)+2*s(84)+3 2.40/2.44 Such that:aux(42) =< -B+I 2.40/2.44 aux(41) =< -B+I+1 2.40/2.44 aux(28) =< -B/2+I/2+1/2 2.40/2.44 aux(27) =< I/2+1/2 2.40/2.44 it(47) =< aux(41) 2.40/2.44 it(47) =< aux(42) 2.40/2.44 aux(40) =< aux(28)-1/2 2.40/2.44 aux(30) =< aux(27) 2.40/2.44 aux(29) =< aux(28)+1 2.40/2.44 aux(37) =< aux(28) 2.40/2.44 aux(34) =< aux(28)*2 2.40/2.44 s(71) =< it(47)*aux(28) 2.40/2.44 s(70) =< it(47)*aux(27) 2.40/2.44 s(86) =< it(47)*aux(40) 2.40/2.44 s(74) =< it(47)*aux(30) 2.40/2.44 s(72) =< it(47)*aux(29) 2.40/2.44 s(82) =< it(47)*aux(37) 2.40/2.44 s(78) =< it(47)*aux(34) 2.40/2.44 s(84) =< s(72) 2.40/2.44 s(84) =< s(86) 2.40/2.44 s(84) =< s(74) 2.40/2.44 s(80) =< s(72) 2.40/2.44 s(80) =< s(82) 2.40/2.44 s(80) =< s(74) 2.40/2.44 s(76) =< s(72) 2.40/2.44 s(76) =< s(78) 2.40/2.44 s(76) =< s(74) 2.40/2.44 s(73) =< s(72) 2.40/2.44 s(73) =< s(74) 2.40/2.44 s(69) =< s(72) 2.40/2.44 s(69) =< s(71) 2.40/2.44 s(69) =< s(70) 2.40/2.44 2.40/2.44 with precondition: [H=5,J=0,K=1,A=I+1,B>=0,A>=B+4] 2.40/2.44 2.40/2.44 * Chain [63]: 1 2.40/2.44 with precondition: [H=3,B+3=A,B>=0] 2.40/2.44 2.40/2.44 * Chain [62]: 0 2.40/2.44 with precondition: [H=3,A>=3,B>=0,A>=B+1] 2.40/2.44 2.40/2.44 * Chain [61]: 0 2.40/2.44 with precondition: [H=3,A>=3,B>=0,A>=B+2] 2.40/2.44 2.40/2.44 * Chain [60]: 2*s(91)+1 2.40/2.44 Such that:s(88) =< A-B 2.40/2.44 s(90) =< A/2 2.40/2.44 s(89) =< A/2-B/2 2.40/2.44 s(91) =< s(89) 2.40/2.44 s(91) =< s(88) 2.40/2.44 s(91) =< s(90) 2.40/2.44 2.40/2.44 with precondition: [H=3,B>=0,A>=B+4] 2.40/2.44 2.40/2.44 * Chain [59]: 4*s(94)+1 2.40/2.44 Such that:s(93) =< A/2 2.40/2.44 s(92) =< A/2-B/2 2.40/2.44 s(94) =< s(92) 2.40/2.44 s(94) =< s(93) 2.40/2.44 2.40/2.44 with precondition: [H=3,B>=0,A>=B+5] 2.40/2.44 2.40/2.44 * Chain [58]: 4*s(97)+1 2.40/2.44 Such that:s(96) =< A/2 2.40/2.44 s(95) =< A/2-B/2 2.40/2.44 s(97) =< s(95) 2.40/2.44 s(97) =< s(96) 2.40/2.44 2.40/2.44 with precondition: [H=3,B>=0,A>=B+6] 2.40/2.44 2.40/2.44 * Chain [55,62]: 2 2.40/2.44 with precondition: [H=3,A=B+3,A>=3] 2.40/2.44 2.40/2.44 * Chain [55,61]: 2 2.40/2.44 with precondition: [H=3,A=B+3,A>=3] 2.40/2.44 2.40/2.44 * Chain [55,56,62]: 3 2.40/2.44 with precondition: [H=3,A=B+3,A>=3] 2.40/2.44 2.40/2.44 * Chain [55,56,57]: 3 2.40/2.44 with precondition: [H=5,J=0,K=1,A=B+3,A=I+1,A>=3] 2.40/2.44 2.40/2.44 * Chain [54,62]: 2 2.40/2.44 with precondition: [H=3,A=B+3,A>=3] 2.40/2.44 2.40/2.44 * Chain [54,61]: 2 2.40/2.44 with precondition: [H=3,A=B+3,A>=3] 2.40/2.44 2.40/2.44 * Chain [54,56,62]: 3 2.40/2.44 with precondition: [H=3,A=B+3,A>=3] 2.40/2.44 2.40/2.44 * Chain [54,56,57]: 3 2.40/2.44 with precondition: [H=5,J=0,K=1,A=B+3,A=I+1,A>=3] 2.40/2.44 2.40/2.44 2.40/2.44 #### Cost of chains of evalrealheapsortbb18in_loop_cont(A,B,C,D,E,F): 2.40/2.44 * Chain [65]: 0 2.40/2.44 with precondition: [A=3,B>=3] 2.40/2.44 2.40/2.44 * Chain [64]: 0 2.40/2.44 with precondition: [A=5,B>=3] 2.40/2.44 2.40/2.44 2.40/2.44 #### Cost of chains of evalrealheapsortbb7in(A,B,C,D,H): 2.40/2.44 * Chain [71]: 3 2.40/2.44 with precondition: [A=3] 2.40/2.44 2.40/2.44 * Chain [70]: 0 2.40/2.44 with precondition: [A>=3] 2.40/2.44 2.40/2.44 * Chain [69]: 2*s(390)+143*s(391)+22*s(404)+44*s(405)+22*s(406)+22*s(408)+3 2.40/2.44 Such that:aux(75) =< A 2.40/2.44 aux(76) =< A/2 2.40/2.44 s(391) =< aux(75) 2.40/2.44 s(392) =< aux(76)-1/2 2.40/2.44 s(393) =< aux(76) 2.40/2.44 s(394) =< aux(76)+1 2.40/2.44 s(396) =< aux(76)*2 2.40/2.44 s(397) =< s(391)*aux(76) 2.40/2.44 s(399) =< s(391)*s(392) 2.40/2.44 s(400) =< s(391)*s(393) 2.40/2.44 s(401) =< s(391)*s(394) 2.40/2.44 s(403) =< s(391)*s(396) 2.40/2.44 s(404) =< s(401) 2.40/2.44 s(404) =< s(399) 2.40/2.44 s(404) =< s(400) 2.40/2.44 s(405) =< s(401) 2.40/2.44 s(405) =< s(400) 2.40/2.44 s(406) =< s(401) 2.40/2.44 s(406) =< s(403) 2.40/2.44 s(406) =< s(400) 2.40/2.44 s(408) =< s(401) 2.40/2.44 s(408) =< s(397) 2.40/2.44 s(390) =< aux(76) 2.40/2.44 s(390) =< aux(75) 2.40/2.44 2.40/2.44 with precondition: [A>=4] 2.40/2.44 2.40/2.44 * Chain [68]: 2*s(435)+13*s(436)+2*s(449)+4*s(450)+2*s(451)+2*s(453)+4*s(454)+1 2.40/2.44 Such that:s(431) =< A 2.40/2.44 aux(77) =< A/2 2.40/2.44 s(434) =< s(431) 2.40/2.44 s(434) =< aux(77) 2.40/2.44 s(435) =< s(434) 2.40/2.44 s(435) =< s(431) 2.40/2.44 s(435) =< aux(77) 2.40/2.44 s(436) =< s(431) 2.40/2.44 s(437) =< aux(77)-1/2 2.40/2.44 s(438) =< aux(77) 2.40/2.44 s(439) =< aux(77)+1 2.40/2.44 s(441) =< aux(77)*2 2.40/2.44 s(442) =< s(436)*aux(77) 2.40/2.44 s(444) =< s(436)*s(437) 2.40/2.45 s(445) =< s(436)*s(438) 2.40/2.45 s(446) =< s(436)*s(439) 2.40/2.45 s(448) =< s(436)*s(441) 2.40/2.45 s(449) =< s(446) 2.40/2.45 s(449) =< s(444) 2.40/2.45 s(449) =< s(445) 2.40/2.45 s(450) =< s(446) 2.40/2.45 s(450) =< s(445) 2.40/2.45 s(451) =< s(446) 2.40/2.45 s(451) =< s(448) 2.40/2.45 s(451) =< s(445) 2.40/2.45 s(453) =< s(446) 2.40/2.45 s(453) =< s(442) 2.40/2.45 s(454) =< aux(77) 2.40/2.45 2.40/2.45 with precondition: [A>=5] 2.40/2.45 2.40/2.45 * Chain [67]: 4*s(459)+13*s(460)+2*s(473)+4*s(474)+2*s(475)+2*s(477)+4*s(478)+1 2.40/2.45 Such that:s(455) =< A 2.40/2.45 aux(78) =< A/2 2.40/2.45 s(458) =< s(455) 2.40/2.45 s(458) =< aux(78) 2.40/2.45 s(459) =< s(458) 2.40/2.45 s(459) =< aux(78) 2.40/2.45 s(460) =< s(455) 2.40/2.45 s(461) =< aux(78)-1/2 2.40/2.45 s(462) =< aux(78) 2.40/2.45 s(463) =< aux(78)+1 2.40/2.45 s(465) =< aux(78)*2 2.40/2.45 s(466) =< s(460)*aux(78) 2.40/2.45 s(468) =< s(460)*s(461) 2.40/2.45 s(469) =< s(460)*s(462) 2.40/2.45 s(470) =< s(460)*s(463) 2.40/2.45 s(472) =< s(460)*s(465) 2.40/2.45 s(473) =< s(470) 2.40/2.45 s(473) =< s(468) 2.40/2.45 s(473) =< s(469) 2.40/2.45 s(474) =< s(470) 2.40/2.45 s(474) =< s(469) 2.40/2.45 s(475) =< s(470) 2.40/2.45 s(475) =< s(472) 2.40/2.45 s(475) =< s(469) 2.40/2.45 s(477) =< s(470) 2.40/2.45 s(477) =< s(466) 2.40/2.45 s(478) =< aux(78) 2.40/2.45 2.40/2.45 with precondition: [A>=6] 2.40/2.45 2.40/2.45 * Chain [66]: 4*s(483)+13*s(484)+2*s(497)+4*s(498)+2*s(499)+2*s(501)+1 2.40/2.45 Such that:s(479) =< A 2.40/2.45 aux(79) =< A/2 2.40/2.45 s(482) =< s(479) 2.40/2.45 s(482) =< aux(79) 2.40/2.45 s(483) =< s(482) 2.40/2.45 s(483) =< aux(79) 2.40/2.45 s(484) =< s(479) 2.40/2.45 s(485) =< aux(79)-1/2 2.40/2.45 s(486) =< aux(79) 2.40/2.45 s(487) =< aux(79)+1 2.40/2.45 s(489) =< aux(79)*2 2.40/2.45 s(490) =< s(484)*aux(79) 2.40/2.45 s(492) =< s(484)*s(485) 2.40/2.45 s(493) =< s(484)*s(486) 2.40/2.45 s(494) =< s(484)*s(487) 2.40/2.45 s(496) =< s(484)*s(489) 2.40/2.45 s(497) =< s(494) 2.40/2.45 s(497) =< s(492) 2.40/2.45 s(497) =< s(493) 2.40/2.45 s(498) =< s(494) 2.40/2.45 s(498) =< s(493) 2.40/2.45 s(499) =< s(494) 2.40/2.45 s(499) =< s(496) 2.40/2.45 s(499) =< s(493) 2.40/2.45 s(501) =< s(494) 2.40/2.45 s(501) =< s(490) 2.40/2.45 2.40/2.45 with precondition: [A>=7] 2.40/2.45 2.40/2.45 2.40/2.45 #### Cost of chains of evalrealheapsortbb6in_loop_cont(A,B,C,D,E,F): 2.40/2.45 * Chain [78]: 0 2.40/2.45 with precondition: [A=3,B>=3] 2.40/2.45 2.40/2.45 * Chain [77]: 3 2.40/2.45 with precondition: [A=6,B=3] 2.40/2.45 2.40/2.45 * Chain [76]: 0 2.40/2.45 with precondition: [A=6,B>=3] 2.40/2.45 2.40/2.45 * Chain [75]: 143*s(504)+22*s(514)+44*s(515)+22*s(516)+22*s(517)+2*s(518)+3 2.40/2.45 Such that:s(502) =< B 2.40/2.45 s(503) =< B/2 2.40/2.45 s(504) =< s(502) 2.40/2.45 s(505) =< s(503)-1/2 2.40/2.45 s(506) =< s(503) 2.40/2.45 s(507) =< s(503)+1 2.40/2.45 s(508) =< s(503)*2 2.40/2.45 s(509) =< s(504)*s(503) 2.40/2.45 s(510) =< s(504)*s(505) 2.40/2.45 s(511) =< s(504)*s(506) 2.40/2.45 s(512) =< s(504)*s(507) 2.40/2.45 s(513) =< s(504)*s(508) 2.40/2.45 s(514) =< s(512) 2.40/2.45 s(514) =< s(510) 2.40/2.45 s(514) =< s(511) 2.40/2.45 s(515) =< s(512) 2.40/2.45 s(515) =< s(511) 2.40/2.45 s(516) =< s(512) 2.40/2.45 s(516) =< s(513) 2.40/2.45 s(516) =< s(511) 2.40/2.45 s(517) =< s(512) 2.40/2.45 s(517) =< s(509) 2.40/2.45 s(518) =< s(503) 2.40/2.45 s(518) =< s(502) 2.40/2.45 2.40/2.45 with precondition: [A=6,B>=4] 2.40/2.45 2.40/2.45 * Chain [74]: 2*s(522)+13*s(523)+2*s(533)+4*s(534)+2*s(535)+2*s(536)+4*s(537)+1 2.40/2.45 Such that:s(519) =< B 2.40/2.45 s(520) =< B/2 2.40/2.45 s(521) =< s(519) 2.40/2.45 s(521) =< s(520) 2.40/2.45 s(522) =< s(521) 2.40/2.45 s(522) =< s(519) 2.40/2.45 s(522) =< s(520) 2.40/2.45 s(523) =< s(519) 2.40/2.45 s(524) =< s(520)-1/2 2.40/2.45 s(525) =< s(520) 2.40/2.45 s(526) =< s(520)+1 2.40/2.45 s(527) =< s(520)*2 2.40/2.45 s(528) =< s(523)*s(520) 2.40/2.45 s(529) =< s(523)*s(524) 2.40/2.45 s(530) =< s(523)*s(525) 2.40/2.45 s(531) =< s(523)*s(526) 2.40/2.45 s(532) =< s(523)*s(527) 2.40/2.45 s(533) =< s(531) 2.40/2.45 s(533) =< s(529) 2.40/2.45 s(533) =< s(530) 2.40/2.45 s(534) =< s(531) 2.40/2.45 s(534) =< s(530) 2.40/2.45 s(535) =< s(531) 2.40/2.45 s(535) =< s(532) 2.40/2.45 s(535) =< s(530) 2.40/2.45 s(536) =< s(531) 2.40/2.45 s(536) =< s(528) 2.40/2.45 s(537) =< s(520) 2.40/2.45 2.40/2.45 with precondition: [A=6,B>=5] 2.40/2.45 2.40/2.45 * Chain [73]: 4*s(541)+13*s(542)+2*s(552)+4*s(553)+2*s(554)+2*s(555)+4*s(556)+1 2.40/2.45 Such that:s(538) =< B 2.40/2.45 s(539) =< B/2 2.40/2.45 s(540) =< s(538) 2.40/2.45 s(540) =< s(539) 2.40/2.45 s(541) =< s(540) 2.40/2.45 s(541) =< s(539) 2.40/2.45 s(542) =< s(538) 2.40/2.45 s(543) =< s(539)-1/2 2.40/2.45 s(544) =< s(539) 2.40/2.45 s(545) =< s(539)+1 2.40/2.45 s(546) =< s(539)*2 2.40/2.45 s(547) =< s(542)*s(539) 2.40/2.45 s(548) =< s(542)*s(543) 2.40/2.45 s(549) =< s(542)*s(544) 2.40/2.45 s(550) =< s(542)*s(545) 2.40/2.45 s(551) =< s(542)*s(546) 2.40/2.45 s(552) =< s(550) 2.40/2.45 s(552) =< s(548) 2.40/2.45 s(552) =< s(549) 2.40/2.45 s(553) =< s(550) 2.40/2.45 s(553) =< s(549) 2.40/2.45 s(554) =< s(550) 2.40/2.45 s(554) =< s(551) 2.40/2.45 s(554) =< s(549) 2.40/2.45 s(555) =< s(550) 2.40/2.45 s(555) =< s(547) 2.40/2.45 s(556) =< s(539) 2.40/2.45 2.40/2.45 with precondition: [A=6,B>=6] 2.40/2.45 2.40/2.45 * Chain [72]: 4*s(560)+13*s(561)+2*s(571)+4*s(572)+2*s(573)+2*s(574)+1 2.40/2.45 Such that:s(557) =< B 2.40/2.45 s(558) =< B/2 2.40/2.45 s(559) =< s(557) 2.40/2.45 s(559) =< s(558) 2.40/2.45 s(560) =< s(559) 2.40/2.45 s(560) =< s(558) 2.40/2.45 s(561) =< s(557) 2.40/2.45 s(562) =< s(558)-1/2 2.40/2.45 s(563) =< s(558) 2.40/2.45 s(564) =< s(558)+1 2.40/2.45 s(565) =< s(558)*2 2.40/2.45 s(566) =< s(561)*s(558) 2.40/2.45 s(567) =< s(561)*s(562) 2.40/2.45 s(568) =< s(561)*s(563) 2.40/2.45 s(569) =< s(561)*s(564) 2.40/2.45 s(570) =< s(561)*s(565) 2.40/2.45 s(571) =< s(569) 2.40/2.45 s(571) =< s(567) 2.40/2.45 s(571) =< s(568) 2.40/2.45 s(572) =< s(569) 2.40/2.45 s(572) =< s(568) 2.40/2.45 s(573) =< s(569) 2.40/2.45 s(573) =< s(570) 2.40/2.45 s(573) =< s(568) 2.40/2.45 s(574) =< s(569) 2.40/2.45 s(574) =< s(566) 2.40/2.45 2.40/2.45 with precondition: [A=6,B>=7] 2.40/2.45 2.40/2.45 2.40/2.45 #### Cost of chains of evalrealheapsortentryin(A,B,C,D,H): 2.40/2.45 * Chain [85]: 3*s(577)+1*s(579)+1*s(580)+3 2.40/2.45 Such that:s(576) =< 2 2.40/2.45 s(575) =< 3 2.40/2.45 s(577) =< s(576) 2.40/2.45 s(578) =< s(575)+1 2.40/2.45 s(579) =< s(577)*s(575) 2.40/2.45 s(580) =< s(577)*s(578) 2.40/2.45 2.40/2.45 with precondition: [A=3] 2.40/2.45 2.40/2.45 * Chain [84]: 0 2.40/2.45 with precondition: [2>=A] 2.40/2.45 2.40/2.45 * Chain [83]: 1*s(583)+10*s(584)+3*s(586)+3*s(587)+0 2.40/2.45 Such that:s(583) =< 1 2.40/2.45 aux(83) =< A 2.40/2.45 s(584) =< aux(83) 2.40/2.45 s(585) =< aux(83)+1 2.40/2.45 s(586) =< s(584)*aux(83) 2.40/2.45 s(587) =< s(584)*s(585) 2.40/2.45 2.40/2.45 with precondition: [A>=3] 2.40/2.45 2.40/2.45 * Chain [82]: 146*s(603)+1*s(605)+1*s(606)+22*s(619)+44*s(620)+22*s(621)+22*s(622)+2*s(623)+3 2.40/2.45 Such that:s(608) =< A/2 2.40/2.45 aux(84) =< A 2.40/2.45 s(603) =< aux(84) 2.40/2.45 s(610) =< s(608)-1/2 2.40/2.45 s(611) =< s(608) 2.40/2.45 s(612) =< s(608)+1 2.40/2.45 s(613) =< s(608)*2 2.40/2.45 s(614) =< s(603)*s(608) 2.40/2.45 s(615) =< s(603)*s(610) 2.40/2.45 s(616) =< s(603)*s(611) 2.40/2.45 s(617) =< s(603)*s(612) 2.40/2.45 s(618) =< s(603)*s(613) 2.40/2.45 s(619) =< s(617) 2.40/2.45 s(619) =< s(615) 2.40/2.45 s(619) =< s(616) 2.40/2.45 s(620) =< s(617) 2.40/2.45 s(620) =< s(616) 2.40/2.45 s(621) =< s(617) 2.40/2.45 s(621) =< s(618) 2.40/2.45 s(621) =< s(616) 2.40/2.45 s(622) =< s(617) 2.40/2.45 s(622) =< s(614) 2.40/2.45 s(623) =< s(608) 2.40/2.45 s(623) =< aux(84) 2.40/2.45 s(604) =< aux(84)+1 2.40/2.45 s(605) =< s(603)*aux(84) 2.40/2.45 s(606) =< s(603)*s(604) 2.40/2.45 2.40/2.45 with precondition: [A>=4] 2.40/2.45 2.40/2.45 * Chain [81]: 16*s(626)+1*s(628)+1*s(629)+2*s(633)+2*s(644)+4*s(645)+2*s(646)+2*s(647)+4*s(648)+1 2.40/2.45 Such that:s(631) =< A/2 2.40/2.45 aux(85) =< A 2.40/2.45 s(632) =< aux(85) 2.40/2.45 s(632) =< s(631) 2.40/2.45 s(633) =< s(632) 2.40/2.45 s(633) =< aux(85) 2.40/2.45 s(633) =< s(631) 2.40/2.45 s(626) =< aux(85) 2.40/2.45 s(635) =< s(631)-1/2 2.40/2.45 s(636) =< s(631) 2.40/2.45 s(637) =< s(631)+1 2.40/2.45 s(638) =< s(631)*2 2.40/2.45 s(639) =< s(626)*s(631) 2.40/2.45 s(640) =< s(626)*s(635) 2.40/2.45 s(641) =< s(626)*s(636) 2.40/2.45 s(642) =< s(626)*s(637) 2.40/2.45 s(643) =< s(626)*s(638) 2.40/2.45 s(644) =< s(642) 2.40/2.45 s(644) =< s(640) 2.40/2.45 s(644) =< s(641) 2.40/2.45 s(645) =< s(642) 2.40/2.45 s(645) =< s(641) 2.40/2.45 s(646) =< s(642) 2.40/2.45 s(646) =< s(643) 2.40/2.45 s(646) =< s(641) 2.40/2.45 s(647) =< s(642) 2.40/2.45 s(647) =< s(639) 2.40/2.45 s(648) =< s(631) 2.40/2.45 s(627) =< aux(85)+1 2.40/2.45 s(628) =< s(626)*aux(85) 2.40/2.45 s(629) =< s(626)*s(627) 2.40/2.45 2.40/2.45 with precondition: [A>=5] 2.40/2.45 2.40/2.45 * Chain [80]: 16*s(651)+1*s(653)+1*s(654)+4*s(658)+2*s(669)+4*s(670)+2*s(671)+2*s(672)+4*s(673)+1 2.40/2.45 Such that:s(656) =< A/2 2.40/2.45 aux(86) =< A 2.40/2.45 s(657) =< aux(86) 2.40/2.45 s(657) =< s(656) 2.40/2.45 s(658) =< s(657) 2.40/2.45 s(658) =< s(656) 2.40/2.45 s(651) =< aux(86) 2.40/2.45 s(660) =< s(656)-1/2 2.40/2.45 s(661) =< s(656) 2.40/2.45 s(662) =< s(656)+1 2.40/2.45 s(663) =< s(656)*2 2.40/2.45 s(664) =< s(651)*s(656) 2.40/2.45 s(665) =< s(651)*s(660) 2.40/2.45 s(666) =< s(651)*s(661) 2.40/2.45 s(667) =< s(651)*s(662) 2.40/2.45 s(668) =< s(651)*s(663) 2.40/2.45 s(669) =< s(667) 2.40/2.45 s(669) =< s(665) 2.40/2.45 s(669) =< s(666) 2.40/2.45 s(670) =< s(667) 2.40/2.45 s(670) =< s(666) 2.40/2.45 s(671) =< s(667) 2.40/2.45 s(671) =< s(668) 2.40/2.45 s(671) =< s(666) 2.40/2.45 s(672) =< s(667) 2.40/2.45 s(672) =< s(664) 2.40/2.45 s(673) =< s(656) 2.40/2.45 s(652) =< aux(86)+1 2.40/2.45 s(653) =< s(651)*aux(86) 2.40/2.45 s(654) =< s(651)*s(652) 2.40/2.45 2.40/2.45 with precondition: [A>=6] 2.40/2.45 2.40/2.45 * Chain [79]: 16*s(676)+1*s(678)+1*s(679)+4*s(683)+2*s(694)+4*s(695)+2*s(696)+2*s(697)+1 2.40/2.45 Such that:s(681) =< A/2 2.40/2.45 aux(87) =< A 2.40/2.45 s(682) =< aux(87) 2.40/2.45 s(682) =< s(681) 2.40/2.45 s(683) =< s(682) 2.40/2.45 s(683) =< s(681) 2.40/2.45 s(676) =< aux(87) 2.40/2.45 s(685) =< s(681)-1/2 2.40/2.45 s(686) =< s(681) 2.40/2.45 s(687) =< s(681)+1 2.40/2.45 s(688) =< s(681)*2 2.40/2.45 s(689) =< s(676)*s(681) 2.40/2.45 s(690) =< s(676)*s(685) 2.40/2.45 s(691) =< s(676)*s(686) 2.40/2.45 s(692) =< s(676)*s(687) 2.40/2.45 s(693) =< s(676)*s(688) 2.40/2.45 s(694) =< s(692) 2.40/2.45 s(694) =< s(690) 2.40/2.45 s(694) =< s(691) 2.40/2.45 s(695) =< s(692) 2.40/2.45 s(695) =< s(691) 2.40/2.45 s(696) =< s(692) 2.40/2.45 s(696) =< s(693) 2.40/2.45 s(696) =< s(691) 2.40/2.45 s(697) =< s(692) 2.40/2.45 s(697) =< s(689) 2.40/2.45 s(677) =< aux(87)+1 2.40/2.45 s(678) =< s(676)*aux(87) 2.40/2.45 s(679) =< s(676)*s(677) 2.40/2.45 2.40/2.45 with precondition: [A>=7] 2.40/2.45 2.40/2.45 2.40/2.45 #### Cost of chains of evalrealheapsortstart(A,B,C,D,H): 2.40/2.45 * Chain [92]: 3*s(700)+1*s(702)+1*s(703)+3 2.40/2.45 Such that:s(698) =< 2 2.40/2.45 s(699) =< 3 2.40/2.45 s(700) =< s(698) 2.40/2.45 s(701) =< s(699)+1 2.40/2.45 s(702) =< s(700)*s(699) 2.40/2.45 s(703) =< s(700)*s(701) 2.40/2.45 2.40/2.45 with precondition: [A=3] 2.40/2.45 2.40/2.45 * Chain [91]: 0 2.40/2.45 with precondition: [2>=A] 2.40/2.45 2.40/2.45 * Chain [90]: 1*s(704)+10*s(706)+3*s(708)+3*s(709)+0 2.40/2.45 Such that:s(704) =< 1 2.40/2.45 s(705) =< A 2.40/2.45 s(706) =< s(705) 2.40/2.45 s(707) =< s(705)+1 2.40/2.45 s(708) =< s(706)*s(705) 2.40/2.45 s(709) =< s(706)*s(707) 2.40/2.45 2.40/2.45 with precondition: [A>=3] 2.40/2.45 2.40/2.45 * Chain [89]: 146*s(712)+22*s(722)+44*s(723)+22*s(724)+22*s(725)+2*s(726)+1*s(728)+1*s(729)+3 2.40/2.45 Such that:s(711) =< A 2.40/2.45 s(710) =< A/2 2.40/2.45 s(712) =< s(711) 2.40/2.45 s(713) =< s(710)-1/2 2.40/2.45 s(714) =< s(710) 2.40/2.45 s(715) =< s(710)+1 2.40/2.45 s(716) =< s(710)*2 2.40/2.45 s(717) =< s(712)*s(710) 2.40/2.45 s(718) =< s(712)*s(713) 2.40/2.45 s(719) =< s(712)*s(714) 2.40/2.45 s(720) =< s(712)*s(715) 2.40/2.45 s(721) =< s(712)*s(716) 2.40/2.45 s(722) =< s(720) 2.40/2.45 s(722) =< s(718) 2.40/2.45 s(722) =< s(719) 2.40/2.45 s(723) =< s(720) 2.40/2.45 s(723) =< s(719) 2.40/2.45 s(724) =< s(720) 2.40/2.45 s(724) =< s(721) 2.40/2.45 s(724) =< s(719) 2.40/2.45 s(725) =< s(720) 2.40/2.45 s(725) =< s(717) 2.40/2.45 s(726) =< s(710) 2.40/2.45 s(726) =< s(711) 2.40/2.45 s(727) =< s(711)+1 2.40/2.45 s(728) =< s(712)*s(711) 2.40/2.45 s(729) =< s(712)*s(727) 2.40/2.45 2.40/2.45 with precondition: [A>=4] 2.40/2.45 2.40/2.45 * Chain [88]: 2*s(733)+16*s(734)+2*s(744)+4*s(745)+2*s(746)+2*s(747)+4*s(748)+1*s(750)+1*s(751)+1 2.40/2.45 Such that:s(731) =< A 2.40/2.45 s(730) =< A/2 2.40/2.45 s(732) =< s(731) 2.40/2.45 s(732) =< s(730) 2.40/2.45 s(733) =< s(732) 2.40/2.45 s(733) =< s(731) 2.40/2.45 s(733) =< s(730) 2.40/2.45 s(734) =< s(731) 2.40/2.45 s(735) =< s(730)-1/2 2.40/2.45 s(736) =< s(730) 2.40/2.45 s(737) =< s(730)+1 2.40/2.45 s(738) =< s(730)*2 2.40/2.45 s(739) =< s(734)*s(730) 2.40/2.45 s(740) =< s(734)*s(735) 2.40/2.45 s(741) =< s(734)*s(736) 2.40/2.45 s(742) =< s(734)*s(737) 2.40/2.45 s(743) =< s(734)*s(738) 2.40/2.45 s(744) =< s(742) 2.40/2.45 s(744) =< s(740) 2.40/2.45 s(744) =< s(741) 2.40/2.45 s(745) =< s(742) 2.40/2.45 s(745) =< s(741) 2.40/2.45 s(746) =< s(742) 2.40/2.45 s(746) =< s(743) 2.40/2.45 s(746) =< s(741) 2.40/2.45 s(747) =< s(742) 2.40/2.45 s(747) =< s(739) 2.40/2.45 s(748) =< s(730) 2.40/2.45 s(749) =< s(731)+1 2.40/2.45 s(750) =< s(734)*s(731) 2.40/2.45 s(751) =< s(734)*s(749) 2.40/2.45 2.40/2.45 with precondition: [A>=5] 2.40/2.45 2.40/2.45 * Chain [87]: 4*s(755)+16*s(756)+2*s(766)+4*s(767)+2*s(768)+2*s(769)+4*s(770)+1*s(772)+1*s(773)+1 2.40/2.45 Such that:s(753) =< A 2.40/2.45 s(752) =< A/2 2.40/2.45 s(754) =< s(753) 2.40/2.45 s(754) =< s(752) 2.40/2.45 s(755) =< s(754) 2.40/2.45 s(755) =< s(752) 2.40/2.45 s(756) =< s(753) 2.40/2.45 s(757) =< s(752)-1/2 2.40/2.45 s(758) =< s(752) 2.40/2.45 s(759) =< s(752)+1 2.40/2.45 s(760) =< s(752)*2 2.40/2.45 s(761) =< s(756)*s(752) 2.40/2.45 s(762) =< s(756)*s(757) 2.40/2.45 s(763) =< s(756)*s(758) 2.40/2.45 s(764) =< s(756)*s(759) 2.40/2.45 s(765) =< s(756)*s(760) 2.40/2.45 s(766) =< s(764) 2.40/2.45 s(766) =< s(762) 2.40/2.45 s(766) =< s(763) 2.40/2.45 s(767) =< s(764) 2.40/2.45 s(767) =< s(763) 2.40/2.45 s(768) =< s(764) 2.40/2.45 s(768) =< s(765) 2.40/2.45 s(768) =< s(763) 2.40/2.45 s(769) =< s(764) 2.40/2.45 s(769) =< s(761) 2.40/2.45 s(770) =< s(752) 2.40/2.45 s(771) =< s(753)+1 2.40/2.45 s(772) =< s(756)*s(753) 2.40/2.45 s(773) =< s(756)*s(771) 2.40/2.45 2.40/2.45 with precondition: [A>=6] 2.40/2.45 2.40/2.45 * Chain [86]: 4*s(777)+16*s(778)+2*s(788)+4*s(789)+2*s(790)+2*s(791)+1*s(793)+1*s(794)+1 2.40/2.45 Such that:s(775) =< A 2.40/2.45 s(774) =< A/2 2.40/2.45 s(776) =< s(775) 2.40/2.45 s(776) =< s(774) 2.40/2.45 s(777) =< s(776) 2.40/2.45 s(777) =< s(774) 2.40/2.45 s(778) =< s(775) 2.40/2.45 s(779) =< s(774)-1/2 2.40/2.45 s(780) =< s(774) 2.40/2.45 s(781) =< s(774)+1 2.40/2.45 s(782) =< s(774)*2 2.40/2.45 s(783) =< s(778)*s(774) 2.40/2.45 s(784) =< s(778)*s(779) 2.40/2.45 s(785) =< s(778)*s(780) 2.40/2.45 s(786) =< s(778)*s(781) 2.40/2.45 s(787) =< s(778)*s(782) 2.40/2.45 s(788) =< s(786) 2.40/2.45 s(788) =< s(784) 2.40/2.45 s(788) =< s(785) 2.40/2.45 s(789) =< s(786) 2.40/2.45 s(789) =< s(785) 2.40/2.45 s(790) =< s(786) 2.40/2.45 s(790) =< s(787) 2.40/2.45 s(790) =< s(785) 2.40/2.45 s(791) =< s(786) 2.40/2.45 s(791) =< s(783) 2.40/2.45 s(792) =< s(775)+1 2.40/2.45 s(793) =< s(778)*s(775) 2.40/2.45 s(794) =< s(778)*s(792) 2.40/2.45 2.40/2.45 with precondition: [A>=7] 2.40/2.45 2.40/2.45 2.40/2.45 Closed-form bounds of evalrealheapsortstart(A,B,C,D,H): 2.40/2.45 ------------------------------------- 2.40/2.45 * Chain [92] with precondition: [A=3] 2.40/2.45 - Upper bound: 23 2.40/2.45 - Complexity: constant 2.40/2.45 * Chain [91] with precondition: [2>=A] 2.40/2.45 - Upper bound: 0 2.40/2.45 - Complexity: constant 2.40/2.45 * Chain [90] with precondition: [A>=3] 2.40/2.45 - Upper bound: 13*A+1+6*A*A 2.40/2.45 - Complexity: n^2 2.40/2.45 * Chain [89] with precondition: [A>=4] 2.40/2.45 - Upper bound: 257*A+3+2*A*A+A/2*(110*A)+A 2.40/2.45 - Complexity: n^2 2.40/2.45 * Chain [88] with precondition: [A>=5] 2.40/2.45 - Upper bound: 29*A+1+2*A*A+A/2*(10*A)+2*A 2.40/2.45 - Complexity: n^2 2.40/2.45 * Chain [87] with precondition: [A>=6] 2.40/2.45 - Upper bound: 31*A+1+2*A*A+A/2*(10*A)+2*A 2.40/2.45 - Complexity: n^2 2.40/2.45 * Chain [86] with precondition: [A>=7] 2.40/2.45 - Upper bound: 31*A+1+2*A*A+A/2*(10*A) 2.40/2.45 - Complexity: n^2 2.40/2.45 2.40/2.45 ### Maximum cost of evalrealheapsortstart(A,B,C,D,H): max([22,nat(A)*2*nat(A)+nat(A)*13+max([nat(A)*4*nat(A),nat(A)*10*nat(A/2)+nat(A)*16+max([nat(A/2)*4,nat(A/2)*2+max([nat(A/2)*2,nat(A)*226+2+nat(A)*100*nat(A/2)])+nat(A)*2])])])+1 2.40/2.45 Asymptotic class: n^2 2.40/2.45 * Total analysis performed in 2218 ms. 2.40/2.45 2.45/2.55 EOF