/export/starexec/sandbox/solver/bin/starexec_run_its /export/starexec/sandbox/benchmark/theBenchmark.koat /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?,O(n^2)) Preprocessing Cost Relations ===================================== #### Computed strongly connected components 0. recursive : [evalrealheapsortbb2in/3,evalrealheapsortbb3in/3,evalrealheapsortbb4in/3] 1. recursive : [evalrealheapsortbb3in_loop_cont/7,evalrealheapsortbb5in/6,evalrealheapsortbb6in/6] 2. recursive : [evalrealheapsortbb10in/7,evalrealheapsortbb11in/7,evalrealheapsortbb12in/7,evalrealheapsortbb13in/7,evalrealheapsortbb14in/7,evalrealheapsortbb16in/7,evalrealheapsortbb9in/7] 3. recursive : [evalrealheapsortbb16in_loop_cont/9,evalrealheapsortbb17in/8,evalrealheapsortbb18in/8,evalrealheapsortbb8in/8] 4. non_recursive : [evalrealheapsortstop/5] 5. non_recursive : [evalrealheapsortreturnin/5] 6. non_recursive : [exit_location/1] 7. non_recursive : [evalrealheapsortbb18in_loop_cont/6] 8. non_recursive : [evalrealheapsortbb7in/5] 9. non_recursive : [evalrealheapsortbb6in_loop_cont/6] 10. non_recursive : [evalrealheapsortentryin/5] 11. non_recursive : [evalrealheapsortstart/5] #### Obtained direct recursion through partial evaluation 0. SCC is partially evaluated into evalrealheapsortbb3in/3 1. SCC is partially evaluated into evalrealheapsortbb6in/6 2. SCC is partially evaluated into evalrealheapsortbb16in/7 3. SCC is partially evaluated into evalrealheapsortbb18in/8 4. SCC is completely evaluated into other SCCs 5. SCC is completely evaluated into other SCCs 6. SCC is completely evaluated into other SCCs 7. SCC is partially evaluated into evalrealheapsortbb18in_loop_cont/6 8. SCC is partially evaluated into evalrealheapsortbb7in/5 9. SCC is partially evaluated into evalrealheapsortbb6in_loop_cont/6 10. SCC is partially evaluated into evalrealheapsortentryin/5 11. SCC is partially evaluated into evalrealheapsortstart/5 Control-Flow Refinement of Cost Relations ===================================== ### Specialization of cost equations evalrealheapsortbb3in/3 * CE 10 is refined into CE [29] * CE 12 is refined into CE [30] * CE 13 is refined into CE [31] * CE 11 is refined into CE [32] ### Cost equations --> "Loop" of evalrealheapsortbb3in/3 * CEs [32] --> Loop 29 * CEs [29] --> Loop 30 * CEs [30] --> Loop 31 * CEs [31] --> Loop 32 ### Ranking functions of CR evalrealheapsortbb3in(C,H,I) * RF of phase [29]: [C] #### Partial ranking functions of CR evalrealheapsortbb3in(C,H,I) * Partial RF of phase [29]: - RF of loop [29:1]: C ### Specialization of cost equations evalrealheapsortbb6in/6 * CE 6 is refined into CE [33] * CE 4 is refined into CE [34,35] * CE 7 is refined into CE [36] * CE 5 is refined into CE [37,38,39] ### Cost equations --> "Loop" of evalrealheapsortbb6in/6 * CEs [39] --> Loop 33 * CEs [38] --> Loop 34 * CEs [37] --> Loop 35 * CEs [33] --> Loop 36 * CEs [34,35] --> Loop 37 * CEs [36] --> Loop 38 ### Ranking functions of CR evalrealheapsortbb6in(A,B,C,H,I,J) * RF of phase [33,34,35]: [A-B] #### Partial ranking functions of CR evalrealheapsortbb6in(A,B,C,H,I,J) * Partial RF of phase [33,34,35]: - RF of loop [33:1,34:1,35:1]: A-B ### Specialization of cost equations evalrealheapsortbb16in/7 * CE 28 is refined into CE [40] * CE 27 is refined into CE [41] * CE 26 is refined into CE [42] * CE 23 is refined into CE [43] * CE 24 is refined into CE [44] * CE 22 is refined into CE [45] * CE 25 is refined into CE [46] * CE 21 is refined into CE [47] ### Cost equations --> "Loop" of evalrealheapsortbb16in/7 * CEs [42] --> Loop 39 * CEs [43] --> Loop 40 * CEs [44] --> Loop 41 * CEs [45] --> Loop 42 * CEs [46] --> Loop 43 * CEs [47] --> Loop 44 * CEs [40] --> Loop 45 * CEs [41] --> Loop 46 ### Ranking functions of CR evalrealheapsortbb16in(A,B,C,D,H,I,J) * RF of phase [42,44]: [A/2-B/2-C-3/2,A/2-C-3/2] #### Partial ranking functions of CR evalrealheapsortbb16in(A,B,C,D,H,I,J) * Partial RF of phase [42,44]: - RF of loop [42:1,44:1]: A/2-B/2-C-3/2 A/2-C-3/2 ### Specialization of cost equations evalrealheapsortbb18in/8 * CE 17 is refined into CE [48] * CE 15 is refined into CE [49,50,51,52,53] * CE 18 is refined into CE [54] * CE 16 is refined into CE [55,56,57,58,59,60,61,62,63,64] ### Cost equations --> "Loop" of evalrealheapsortbb18in/8 * CEs [64] --> Loop 47 * CEs [60] --> Loop 48 * CEs [63] --> Loop 49 * CEs [62] --> Loop 50 * CEs [61] --> Loop 51 * CEs [57] --> Loop 52 * CEs [58] --> Loop 53 * CEs [59] --> Loop 54 * CEs [55] --> Loop 55 * CEs [56] --> Loop 56 * CEs [48] --> Loop 57 * CEs [52] --> Loop 58 * CEs [51] --> Loop 59 * CEs [53] --> Loop 60 * CEs [50] --> Loop 61 * CEs [54] --> Loop 62 * CEs [49] --> Loop 63 ### Ranking functions of CR evalrealheapsortbb18in(A,B,C,D,H,I,J,K) * RF of phase [47,48,49,50,51,52,53]: [A-B-3] #### Partial ranking functions of CR evalrealheapsortbb18in(A,B,C,D,H,I,J,K) * Partial RF of phase [47,48,49,50,51,52,53]: - RF of loop [47:1,48:1]: A-B-4 - RF of loop [49:1,52:1,53:1]: A-B-3 - RF of loop [50:1,51:1]: A-B-5 ### Specialization of cost equations evalrealheapsortbb18in_loop_cont/6 * CE 19 is refined into CE [65] * CE 20 is refined into CE [66] ### Cost equations --> "Loop" of evalrealheapsortbb18in_loop_cont/6 * CEs [65] --> Loop 64 * CEs [66] --> Loop 65 ### Ranking functions of CR evalrealheapsortbb18in_loop_cont(A,B,C,D,E,F) #### Partial ranking functions of CR evalrealheapsortbb18in_loop_cont(A,B,C,D,E,F) ### Specialization of cost equations evalrealheapsortbb7in/5 * CE 14 is refined into CE [67,68,69,70,71,72,73,74,75,76] ### Cost equations --> "Loop" of evalrealheapsortbb7in/5 * CEs [74] --> Loop 66 * CEs [73] --> Loop 67 * CEs [72] --> Loop 68 * CEs [71,76] --> Loop 69 * CEs [69,70] --> Loop 70 * CEs [67,68,75] --> Loop 71 ### Ranking functions of CR evalrealheapsortbb7in(A,B,C,D,H) #### Partial ranking functions of CR evalrealheapsortbb7in(A,B,C,D,H) ### Specialization of cost equations evalrealheapsortbb6in_loop_cont/6 * CE 8 is refined into CE [77,78,79,80,81,82] * CE 9 is refined into CE [83] ### Cost equations --> "Loop" of evalrealheapsortbb6in_loop_cont/6 * CEs [82] --> Loop 72 * CEs [81] --> Loop 73 * CEs [80] --> Loop 74 * CEs [79] --> Loop 75 * CEs [78] --> Loop 76 * CEs [77] --> Loop 77 * CEs [83] --> Loop 78 ### Ranking functions of CR evalrealheapsortbb6in_loop_cont(A,B,C,D,E,F) #### Partial ranking functions of CR evalrealheapsortbb6in_loop_cont(A,B,C,D,E,F) ### Specialization of cost equations evalrealheapsortentryin/5 * CE 3 is refined into CE [84,85,86,87,88,89,90,91,92] * CE 2 is refined into CE [93] ### Cost equations --> "Loop" of evalrealheapsortentryin/5 * CEs [92] --> Loop 79 * CEs [91] --> Loop 80 * CEs [90] --> Loop 81 * CEs [89] --> Loop 82 * CEs [84,85,86,88] --> Loop 83 * CEs [93] --> Loop 84 * CEs [87] --> Loop 85 ### Ranking functions of CR evalrealheapsortentryin(A,B,C,D,H) #### Partial ranking functions of CR evalrealheapsortentryin(A,B,C,D,H) ### Specialization of cost equations evalrealheapsortstart/5 * CE 1 is refined into CE [94,95,96,97,98,99,100] ### Cost equations --> "Loop" of evalrealheapsortstart/5 * CEs [100] --> Loop 86 * CEs [99] --> Loop 87 * CEs [98] --> Loop 88 * CEs [97] --> Loop 89 * CEs [96] --> Loop 90 * CEs [95] --> Loop 91 * CEs [94] --> Loop 92 ### Ranking functions of CR evalrealheapsortstart(A,B,C,D,H) #### Partial ranking functions of CR evalrealheapsortstart(A,B,C,D,H) Computing Bounds ===================================== #### Cost of chains of evalrealheapsortbb3in(C,H,I): * Chain [[29],32]: 1*it(29)+0 Such that:it(29) =< C with precondition: [H=3,C>=1] * Chain [[29],31]: 1*it(29)+0 Such that:it(29) =< C with precondition: [H=4,0>=I,C>=1,2*I+1>=0] * Chain [[29],30]: 1*it(29)+0 Such that:it(29) =< C-I with precondition: [H=4,I>=1,C>=2*I+1] * Chain [32]: 0 with precondition: [H=3,2*C+1>=0] * Chain [30]: 0 with precondition: [H=4,C=I,C>=1] #### Cost of chains of evalrealheapsortbb6in(A,B,C,H,I,J): * Chain [[33,34,35],38]: 3*it(33)+1*s(5)+1*s(6)+0 Such that:aux(1) =< A aux(5) =< A-B it(33) =< aux(5) aux(2) =< aux(1)+1 s(5) =< it(33)*aux(1) s(6) =< it(33)*aux(2) with precondition: [H=3,A>=3,B>=1,A>=B+1] * Chain [[33,34,35],37]: 3*it(33)+1*s(5)+1*s(6)+1*s(7)+0 Such that:aux(6) =< A aux(7) =< A-B s(7) =< aux(6) it(33) =< aux(7) aux(2) =< aux(6)+1 s(5) =< it(33)*aux(6) s(6) =< it(33)*aux(2) with precondition: [H=3,B>=1,A>=B+2] * Chain [[33,34,35],36]: 3*it(33)+1*s(5)+1*s(6)+0 Such that:aux(1) =< I aux(8) =< -B+I it(33) =< aux(8) aux(2) =< aux(1)+1 s(5) =< it(33)*aux(1) s(6) =< it(33)*aux(2) with precondition: [H=6,A=I,A>=3,B>=1,2*J+1>=0,A>=B+1,A>=J+1] * Chain [38]: 0 with precondition: [H=3,A>=3,B>=1] * Chain [37]: 1*s(7)+0 Such that:s(7) =< B with precondition: [H=3,A>=3,B>=1,A>=B+1] #### Cost of chains of evalrealheapsortbb16in(A,B,C,D,H,I,J): * Chain [[42,44],46]: 2*it(42)+0 Such that:aux(9) =< A/2-B/2-C aux(11) =< A/2-C aux(13) =< -C+I it(42) =< aux(9) it(42) =< aux(13) it(42) =< aux(11) 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] * Chain [[42,44],45]: 2*it(42)+0 Such that:aux(9) =< A/2-B/2-C aux(11) =< A/2-C aux(14) =< A-B-C it(42) =< aux(9) it(42) =< aux(14) it(42) =< aux(11) with precondition: [H=3,B>=0,C>=0,A>=2*C+B+4] * Chain [[42,44],43,46]: 2*it(42)+1 Such that:aux(11) =< A/2-C aux(9) =< -C+I/2+1 aux(15) =< -C+I/2 it(42) =< aux(9) it(42) =< aux(15) it(42) =< aux(11) with precondition: [H=2,A=B+I+2,A=B+J+2,B>=0,C>=0,A>=4*C+B+5] * Chain [[42,44],43,45]: 2*it(42)+1 Such that:aux(11) =< A/2-C aux(16) =< A/2-B/2-C it(42) =< aux(16) it(42) =< aux(11) with precondition: [H=3,B>=0,C>=0,A>=4*C+B+5] * Chain [[42,44],41,46]: 2*it(42)+1 Such that:aux(9) =< -B/2-C+I/2 aux(11) =< -C+I/2 aux(17) =< -C+J/2 it(42) =< aux(9) it(42) =< aux(17) it(42) =< aux(11) with precondition: [H=2,A=I,B>=0,C>=0,J>=4*C+4,A>=B+J+2] * Chain [[42,44],41,45]: 2*it(42)+1 Such that:aux(11) =< A/2-C aux(18) =< A/2-B/2-C it(42) =< aux(18) it(42) =< aux(11) with precondition: [H=3,B>=0,C>=0,A>=4*C+B+6] * Chain [[42,44],40,46]: 2*it(42)+1 Such that:aux(9) =< -B/2-C+I/2 aux(11) =< -C+I/2 aux(19) =< -C+J/2 it(42) =< aux(9) it(42) =< aux(19) it(42) =< aux(11) with precondition: [H=2,A=I,B>=0,C>=0,J>=4*C+3,A>=B+J+3] * Chain [[42,44],40,45]: 2*it(42)+1 Such that:aux(11) =< A/2-C aux(20) =< A/2-B/2-C it(42) =< aux(20) it(42) =< aux(11) with precondition: [H=3,B>=0,C>=0,A>=4*C+B+6] * Chain [[42,44],39,46]: 2*it(42)+1 Such that:aux(11) =< -C+I/2 aux(21) =< -B/2-C+I/2 it(42) =< aux(21) it(42) =< aux(11) with precondition: [H=2,A=I,A=B+J+2,B>=0,C>=0,A>=4*C+B+5] * Chain [[42,44],39,45]: 2*it(42)+1 Such that:aux(11) =< A/2-C aux(22) =< A/2-B/2-C it(42) =< aux(22) it(42) =< aux(11) with precondition: [H=3,B>=0,C>=0,A>=4*C+B+5] * Chain [46]: 0 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] * Chain [45]: 0 with precondition: [H=3,A>=3,B>=0,C>=0,A>=B+2,A>=C,4*A>=3*B+C+9] * Chain [43,46]: 1 with precondition: [H=2,I=2*C+1,I=J,B+I+2=A,I>=1,A>=I+2] * Chain [43,45]: 1 with precondition: [H=3,A=2*C+B+3,C>=0,A>=2*C+3] * Chain [41,46]: 1 with precondition: [H=2,A=I,2*C+2=J,B>=0,C>=0,A>=2*C+B+4] * Chain [41,45]: 1 with precondition: [H=3,B>=0,C>=0,A>=2*C+B+4] * Chain [40,46]: 1 with precondition: [H=2,A=I,2*C+1=J,B>=0,C>=0,A>=2*C+B+4] * Chain [40,45]: 1 with precondition: [H=3,B>=0,C>=0,A>=2*C+B+4] * Chain [39,46]: 1 with precondition: [H=2,A=I,A=2*C+B+3,A=B+J+2,B>=0,A>=B+3] * Chain [39,45]: 1 with precondition: [H=3,A=2*C+B+3,C>=0,A>=2*C+3] #### Cost of chains of evalrealheapsortbb18in(A,B,C,D,H,I,J,K): * 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 Such that:aux(27) =< A/2 aux(28) =< A/2-B/2 aux(43) =< A-B it(47) =< aux(43) aux(40) =< aux(28)-1/2 aux(30) =< aux(27) aux(29) =< aux(28)+1 aux(37) =< aux(28) aux(34) =< aux(28)*2 s(71) =< it(47)*aux(28) s(70) =< it(47)*aux(27) s(86) =< it(47)*aux(40) s(74) =< it(47)*aux(30) s(72) =< it(47)*aux(29) s(82) =< it(47)*aux(37) s(78) =< it(47)*aux(34) s(84) =< s(72) s(84) =< s(86) s(84) =< s(74) s(80) =< s(72) s(80) =< s(82) s(80) =< s(74) s(76) =< s(72) s(76) =< s(78) s(76) =< s(74) s(73) =< s(72) s(73) =< s(74) s(69) =< s(72) s(69) =< s(71) s(69) =< s(70) with precondition: [H=3,B>=0,A>=B+4] * 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 Such that:aux(27) =< A/2 aux(28) =< A/2-B/2 aux(44) =< A-B it(47) =< aux(44) aux(40) =< aux(28)-1/2 aux(30) =< aux(27) aux(29) =< aux(28)+1 aux(37) =< aux(28) aux(34) =< aux(28)*2 s(71) =< it(47)*aux(28) s(70) =< it(47)*aux(27) s(86) =< it(47)*aux(40) s(74) =< it(47)*aux(30) s(72) =< it(47)*aux(29) s(82) =< it(47)*aux(37) s(78) =< it(47)*aux(34) s(84) =< s(72) s(84) =< s(86) s(84) =< s(74) s(80) =< s(72) s(80) =< s(82) s(80) =< s(74) s(76) =< s(72) s(76) =< s(78) s(76) =< s(74) s(73) =< s(72) s(73) =< s(74) s(69) =< s(72) s(69) =< s(71) s(69) =< s(70) with precondition: [H=3,B>=0,A>=B+4] * 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 Such that:aux(27) =< A/2 aux(28) =< A/2-B/2 aux(45) =< A-B it(47) =< aux(45) aux(40) =< aux(28)-1/2 aux(30) =< aux(27) aux(29) =< aux(28)+1 aux(37) =< aux(28) aux(34) =< aux(28)*2 s(71) =< it(47)*aux(28) s(70) =< it(47)*aux(27) s(86) =< it(47)*aux(40) s(74) =< it(47)*aux(30) s(72) =< it(47)*aux(29) s(82) =< it(47)*aux(37) s(78) =< it(47)*aux(34) s(84) =< s(72) s(84) =< s(86) s(84) =< s(74) s(80) =< s(72) s(80) =< s(82) s(80) =< s(74) s(76) =< s(72) s(76) =< s(78) s(76) =< s(74) s(73) =< s(72) s(73) =< s(74) s(69) =< s(72) s(69) =< s(71) s(69) =< s(70) with precondition: [H=3,B>=0,A>=B+4] * 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 Such that:aux(46) =< A-B aux(47) =< A/2 aux(48) =< A/2-B/2 s(89) =< aux(46) s(89) =< aux(48) s(91) =< s(89) s(91) =< aux(46) s(91) =< aux(47) it(47) =< aux(46) aux(40) =< aux(48)-1/2 aux(30) =< aux(47) aux(29) =< aux(48)+1 aux(37) =< aux(48) aux(34) =< aux(48)*2 s(71) =< it(47)*aux(48) s(70) =< it(47)*aux(47) s(86) =< it(47)*aux(40) s(74) =< it(47)*aux(30) s(72) =< it(47)*aux(29) s(82) =< it(47)*aux(37) s(78) =< it(47)*aux(34) s(84) =< s(72) s(84) =< s(86) s(84) =< s(74) s(80) =< s(72) s(80) =< s(82) s(80) =< s(74) s(76) =< s(72) s(76) =< s(78) s(76) =< s(74) s(73) =< s(72) s(73) =< s(74) s(69) =< s(72) s(69) =< s(71) s(69) =< s(70) with precondition: [H=3,B>=0,A>=B+5] * 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 Such that:aux(49) =< A-B aux(50) =< A/2 aux(51) =< A/2-B/2 s(92) =< aux(49) s(92) =< aux(51) s(94) =< s(92) s(94) =< aux(50) it(47) =< aux(49) aux(40) =< aux(51)-1/2 aux(30) =< aux(50) aux(29) =< aux(51)+1 aux(37) =< aux(51) aux(34) =< aux(51)*2 s(71) =< it(47)*aux(51) s(70) =< it(47)*aux(50) s(86) =< it(47)*aux(40) s(74) =< it(47)*aux(30) s(72) =< it(47)*aux(29) s(82) =< it(47)*aux(37) s(78) =< it(47)*aux(34) s(84) =< s(72) s(84) =< s(86) s(84) =< s(74) s(80) =< s(72) s(80) =< s(82) s(80) =< s(74) s(76) =< s(72) s(76) =< s(78) s(76) =< s(74) s(73) =< s(72) s(73) =< s(74) s(69) =< s(72) s(69) =< s(71) s(69) =< s(70) with precondition: [H=3,B>=0,A>=B+6] * 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 Such that:aux(52) =< A-B aux(53) =< A/2 aux(54) =< A/2-B/2 s(95) =< aux(52) s(95) =< aux(54) s(97) =< s(95) s(97) =< aux(53) it(47) =< aux(52) aux(40) =< aux(54)-1/2 aux(30) =< aux(53) aux(29) =< aux(54)+1 aux(37) =< aux(54) aux(34) =< aux(54)*2 s(71) =< it(47)*aux(54) s(70) =< it(47)*aux(53) s(86) =< it(47)*aux(40) s(74) =< it(47)*aux(30) s(72) =< it(47)*aux(29) s(82) =< it(47)*aux(37) s(78) =< it(47)*aux(34) s(84) =< s(72) s(84) =< s(86) s(84) =< s(74) s(80) =< s(72) s(80) =< s(82) s(80) =< s(74) s(76) =< s(72) s(76) =< s(78) s(76) =< s(74) s(73) =< s(72) s(73) =< s(74) s(69) =< s(72) s(69) =< s(71) s(69) =< s(70) with precondition: [H=3,B>=0,A>=B+7] * 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 Such that:aux(27) =< A/2 aux(28) =< A/2-B/2 aux(55) =< A-B it(47) =< aux(55) aux(40) =< aux(28)-1/2 aux(30) =< aux(27) aux(29) =< aux(28)+1 aux(37) =< aux(28) aux(34) =< aux(28)*2 s(71) =< it(47)*aux(28) s(70) =< it(47)*aux(27) s(86) =< it(47)*aux(40) s(74) =< it(47)*aux(30) s(72) =< it(47)*aux(29) s(82) =< it(47)*aux(37) s(78) =< it(47)*aux(34) s(84) =< s(72) s(84) =< s(86) s(84) =< s(74) s(80) =< s(72) s(80) =< s(82) s(80) =< s(74) s(76) =< s(72) s(76) =< s(78) s(76) =< s(74) s(73) =< s(72) s(73) =< s(74) s(69) =< s(72) s(69) =< s(71) s(69) =< s(70) with precondition: [H=3,B>=0,A>=B+4] * 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 Such that:aux(27) =< A/2 aux(28) =< A/2-B/2 aux(56) =< A-B it(47) =< aux(56) aux(40) =< aux(28)-1/2 aux(30) =< aux(27) aux(29) =< aux(28)+1 aux(37) =< aux(28) aux(34) =< aux(28)*2 s(71) =< it(47)*aux(28) s(70) =< it(47)*aux(27) s(86) =< it(47)*aux(40) s(74) =< it(47)*aux(30) s(72) =< it(47)*aux(29) s(82) =< it(47)*aux(37) s(78) =< it(47)*aux(34) s(84) =< s(72) s(84) =< s(86) s(84) =< s(74) s(80) =< s(72) s(80) =< s(82) s(80) =< s(74) s(76) =< s(72) s(76) =< s(78) s(76) =< s(74) s(73) =< s(72) s(73) =< s(74) s(69) =< s(72) s(69) =< s(71) s(69) =< s(70) with precondition: [H=3,B>=0,A>=B+4] * 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 Such that:aux(27) =< A/2 aux(28) =< A/2-B/2 aux(57) =< A-B it(47) =< aux(57) aux(40) =< aux(28)-1/2 aux(30) =< aux(27) aux(29) =< aux(28)+1 aux(37) =< aux(28) aux(34) =< aux(28)*2 s(71) =< it(47)*aux(28) s(70) =< it(47)*aux(27) s(86) =< it(47)*aux(40) s(74) =< it(47)*aux(30) s(72) =< it(47)*aux(29) s(82) =< it(47)*aux(37) s(78) =< it(47)*aux(34) s(84) =< s(72) s(84) =< s(86) s(84) =< s(74) s(80) =< s(72) s(80) =< s(82) s(80) =< s(74) s(76) =< s(72) s(76) =< s(78) s(76) =< s(74) s(73) =< s(72) s(73) =< s(74) s(69) =< s(72) s(69) =< s(71) s(69) =< s(70) with precondition: [H=3,B>=0,A>=B+4] * 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 Such that:aux(42) =< -B+I aux(41) =< -B+I+1 aux(28) =< -B/2+I/2+1/2 aux(27) =< I/2+1/2 it(47) =< aux(41) it(47) =< aux(42) aux(40) =< aux(28)-1/2 aux(30) =< aux(27) aux(29) =< aux(28)+1 aux(37) =< aux(28) aux(34) =< aux(28)*2 s(71) =< it(47)*aux(28) s(70) =< it(47)*aux(27) s(86) =< it(47)*aux(40) s(74) =< it(47)*aux(30) s(72) =< it(47)*aux(29) s(82) =< it(47)*aux(37) s(78) =< it(47)*aux(34) s(84) =< s(72) s(84) =< s(86) s(84) =< s(74) s(80) =< s(72) s(80) =< s(82) s(80) =< s(74) s(76) =< s(72) s(76) =< s(78) s(76) =< s(74) s(73) =< s(72) s(73) =< s(74) s(69) =< s(72) s(69) =< s(71) s(69) =< s(70) with precondition: [H=5,J=0,K=1,A=I+1,B>=0,A>=B+4] * 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 Such that:aux(27) =< A/2 aux(28) =< A/2-B/2 aux(58) =< A-B it(47) =< aux(58) aux(40) =< aux(28)-1/2 aux(30) =< aux(27) aux(29) =< aux(28)+1 aux(37) =< aux(28) aux(34) =< aux(28)*2 s(71) =< it(47)*aux(28) s(70) =< it(47)*aux(27) s(86) =< it(47)*aux(40) s(74) =< it(47)*aux(30) s(72) =< it(47)*aux(29) s(82) =< it(47)*aux(37) s(78) =< it(47)*aux(34) s(84) =< s(72) s(84) =< s(86) s(84) =< s(74) s(80) =< s(72) s(80) =< s(82) s(80) =< s(74) s(76) =< s(72) s(76) =< s(78) s(76) =< s(74) s(73) =< s(72) s(73) =< s(74) s(69) =< s(72) s(69) =< s(71) s(69) =< s(70) with precondition: [H=3,B>=0,A>=B+4] * 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 Such that:aux(27) =< A/2 aux(28) =< A/2-B/2 aux(59) =< A-B it(47) =< aux(59) aux(40) =< aux(28)-1/2 aux(30) =< aux(27) aux(29) =< aux(28)+1 aux(37) =< aux(28) aux(34) =< aux(28)*2 s(71) =< it(47)*aux(28) s(70) =< it(47)*aux(27) s(86) =< it(47)*aux(40) s(74) =< it(47)*aux(30) s(72) =< it(47)*aux(29) s(82) =< it(47)*aux(37) s(78) =< it(47)*aux(34) s(84) =< s(72) s(84) =< s(86) s(84) =< s(74) s(80) =< s(72) s(80) =< s(82) s(80) =< s(74) s(76) =< s(72) s(76) =< s(78) s(76) =< s(74) s(73) =< s(72) s(73) =< s(74) s(69) =< s(72) s(69) =< s(71) s(69) =< s(70) with precondition: [H=3,B>=0,A>=B+4] * 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 Such that:aux(27) =< A/2 aux(28) =< A/2-B/2 aux(60) =< A-B it(47) =< aux(60) aux(40) =< aux(28)-1/2 aux(30) =< aux(27) aux(29) =< aux(28)+1 aux(37) =< aux(28) aux(34) =< aux(28)*2 s(71) =< it(47)*aux(28) s(70) =< it(47)*aux(27) s(86) =< it(47)*aux(40) s(74) =< it(47)*aux(30) s(72) =< it(47)*aux(29) s(82) =< it(47)*aux(37) s(78) =< it(47)*aux(34) s(84) =< s(72) s(84) =< s(86) s(84) =< s(74) s(80) =< s(72) s(80) =< s(82) s(80) =< s(74) s(76) =< s(72) s(76) =< s(78) s(76) =< s(74) s(73) =< s(72) s(73) =< s(74) s(69) =< s(72) s(69) =< s(71) s(69) =< s(70) with precondition: [H=3,B>=0,A>=B+4] * 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 Such that:aux(42) =< -B+I aux(41) =< -B+I+1 aux(28) =< -B/2+I/2+1/2 aux(27) =< I/2+1/2 it(47) =< aux(41) it(47) =< aux(42) aux(40) =< aux(28)-1/2 aux(30) =< aux(27) aux(29) =< aux(28)+1 aux(37) =< aux(28) aux(34) =< aux(28)*2 s(71) =< it(47)*aux(28) s(70) =< it(47)*aux(27) s(86) =< it(47)*aux(40) s(74) =< it(47)*aux(30) s(72) =< it(47)*aux(29) s(82) =< it(47)*aux(37) s(78) =< it(47)*aux(34) s(84) =< s(72) s(84) =< s(86) s(84) =< s(74) s(80) =< s(72) s(80) =< s(82) s(80) =< s(74) s(76) =< s(72) s(76) =< s(78) s(76) =< s(74) s(73) =< s(72) s(73) =< s(74) s(69) =< s(72) s(69) =< s(71) s(69) =< s(70) with precondition: [H=5,J=0,K=1,A=I+1,B>=0,A>=B+4] * Chain [63]: 1 with precondition: [H=3,B+3=A,B>=0] * Chain [62]: 0 with precondition: [H=3,A>=3,B>=0,A>=B+1] * Chain [61]: 0 with precondition: [H=3,A>=3,B>=0,A>=B+2] * Chain [60]: 2*s(91)+1 Such that:s(88) =< A-B s(90) =< A/2 s(89) =< A/2-B/2 s(91) =< s(89) s(91) =< s(88) s(91) =< s(90) with precondition: [H=3,B>=0,A>=B+4] * Chain [59]: 4*s(94)+1 Such that:s(93) =< A/2 s(92) =< A/2-B/2 s(94) =< s(92) s(94) =< s(93) with precondition: [H=3,B>=0,A>=B+5] * Chain [58]: 4*s(97)+1 Such that:s(96) =< A/2 s(95) =< A/2-B/2 s(97) =< s(95) s(97) =< s(96) with precondition: [H=3,B>=0,A>=B+6] * Chain [55,62]: 2 with precondition: [H=3,A=B+3,A>=3] * Chain [55,61]: 2 with precondition: [H=3,A=B+3,A>=3] * Chain [55,56,62]: 3 with precondition: [H=3,A=B+3,A>=3] * Chain [55,56,57]: 3 with precondition: [H=5,J=0,K=1,A=B+3,A=I+1,A>=3] * Chain [54,62]: 2 with precondition: [H=3,A=B+3,A>=3] * Chain [54,61]: 2 with precondition: [H=3,A=B+3,A>=3] * Chain [54,56,62]: 3 with precondition: [H=3,A=B+3,A>=3] * Chain [54,56,57]: 3 with precondition: [H=5,J=0,K=1,A=B+3,A=I+1,A>=3] #### Cost of chains of evalrealheapsortbb18in_loop_cont(A,B,C,D,E,F): * Chain [65]: 0 with precondition: [A=3,B>=3] * Chain [64]: 0 with precondition: [A=5,B>=3] #### Cost of chains of evalrealheapsortbb7in(A,B,C,D,H): * Chain [71]: 3 with precondition: [A=3] * Chain [70]: 0 with precondition: [A>=3] * Chain [69]: 2*s(390)+143*s(391)+22*s(404)+44*s(405)+22*s(406)+22*s(408)+3 Such that:aux(75) =< A aux(76) =< A/2 s(391) =< aux(75) s(392) =< aux(76)-1/2 s(393) =< aux(76) s(394) =< aux(76)+1 s(396) =< aux(76)*2 s(397) =< s(391)*aux(76) s(399) =< s(391)*s(392) s(400) =< s(391)*s(393) s(401) =< s(391)*s(394) s(403) =< s(391)*s(396) s(404) =< s(401) s(404) =< s(399) s(404) =< s(400) s(405) =< s(401) s(405) =< s(400) s(406) =< s(401) s(406) =< s(403) s(406) =< s(400) s(408) =< s(401) s(408) =< s(397) s(390) =< aux(76) s(390) =< aux(75) with precondition: [A>=4] * Chain [68]: 2*s(435)+13*s(436)+2*s(449)+4*s(450)+2*s(451)+2*s(453)+4*s(454)+1 Such that:s(431) =< A aux(77) =< A/2 s(434) =< s(431) s(434) =< aux(77) s(435) =< s(434) s(435) =< s(431) s(435) =< aux(77) s(436) =< s(431) s(437) =< aux(77)-1/2 s(438) =< aux(77) s(439) =< aux(77)+1 s(441) =< aux(77)*2 s(442) =< s(436)*aux(77) s(444) =< s(436)*s(437) s(445) =< s(436)*s(438) s(446) =< s(436)*s(439) s(448) =< s(436)*s(441) s(449) =< s(446) s(449) =< s(444) s(449) =< s(445) s(450) =< s(446) s(450) =< s(445) s(451) =< s(446) s(451) =< s(448) s(451) =< s(445) s(453) =< s(446) s(453) =< s(442) s(454) =< aux(77) with precondition: [A>=5] * Chain [67]: 4*s(459)+13*s(460)+2*s(473)+4*s(474)+2*s(475)+2*s(477)+4*s(478)+1 Such that:s(455) =< A aux(78) =< A/2 s(458) =< s(455) s(458) =< aux(78) s(459) =< s(458) s(459) =< aux(78) s(460) =< s(455) s(461) =< aux(78)-1/2 s(462) =< aux(78) s(463) =< aux(78)+1 s(465) =< aux(78)*2 s(466) =< s(460)*aux(78) s(468) =< s(460)*s(461) s(469) =< s(460)*s(462) s(470) =< s(460)*s(463) s(472) =< s(460)*s(465) s(473) =< s(470) s(473) =< s(468) s(473) =< s(469) s(474) =< s(470) s(474) =< s(469) s(475) =< s(470) s(475) =< s(472) s(475) =< s(469) s(477) =< s(470) s(477) =< s(466) s(478) =< aux(78) with precondition: [A>=6] * Chain [66]: 4*s(483)+13*s(484)+2*s(497)+4*s(498)+2*s(499)+2*s(501)+1 Such that:s(479) =< A aux(79) =< A/2 s(482) =< s(479) s(482) =< aux(79) s(483) =< s(482) s(483) =< aux(79) s(484) =< s(479) s(485) =< aux(79)-1/2 s(486) =< aux(79) s(487) =< aux(79)+1 s(489) =< aux(79)*2 s(490) =< s(484)*aux(79) s(492) =< s(484)*s(485) s(493) =< s(484)*s(486) s(494) =< s(484)*s(487) s(496) =< s(484)*s(489) s(497) =< s(494) s(497) =< s(492) s(497) =< s(493) s(498) =< s(494) s(498) =< s(493) s(499) =< s(494) s(499) =< s(496) s(499) =< s(493) s(501) =< s(494) s(501) =< s(490) with precondition: [A>=7] #### Cost of chains of evalrealheapsortbb6in_loop_cont(A,B,C,D,E,F): * Chain [78]: 0 with precondition: [A=3,B>=3] * Chain [77]: 3 with precondition: [A=6,B=3] * Chain [76]: 0 with precondition: [A=6,B>=3] * Chain [75]: 143*s(504)+22*s(514)+44*s(515)+22*s(516)+22*s(517)+2*s(518)+3 Such that:s(502) =< B s(503) =< B/2 s(504) =< s(502) s(505) =< s(503)-1/2 s(506) =< s(503) s(507) =< s(503)+1 s(508) =< s(503)*2 s(509) =< s(504)*s(503) s(510) =< s(504)*s(505) s(511) =< s(504)*s(506) s(512) =< s(504)*s(507) s(513) =< s(504)*s(508) s(514) =< s(512) s(514) =< s(510) s(514) =< s(511) s(515) =< s(512) s(515) =< s(511) s(516) =< s(512) s(516) =< s(513) s(516) =< s(511) s(517) =< s(512) s(517) =< s(509) s(518) =< s(503) s(518) =< s(502) with precondition: [A=6,B>=4] * Chain [74]: 2*s(522)+13*s(523)+2*s(533)+4*s(534)+2*s(535)+2*s(536)+4*s(537)+1 Such that:s(519) =< B s(520) =< B/2 s(521) =< s(519) s(521) =< s(520) s(522) =< s(521) s(522) =< s(519) s(522) =< s(520) s(523) =< s(519) s(524) =< s(520)-1/2 s(525) =< s(520) s(526) =< s(520)+1 s(527) =< s(520)*2 s(528) =< s(523)*s(520) s(529) =< s(523)*s(524) s(530) =< s(523)*s(525) s(531) =< s(523)*s(526) s(532) =< s(523)*s(527) s(533) =< s(531) s(533) =< s(529) s(533) =< s(530) s(534) =< s(531) s(534) =< s(530) s(535) =< s(531) s(535) =< s(532) s(535) =< s(530) s(536) =< s(531) s(536) =< s(528) s(537) =< s(520) with precondition: [A=6,B>=5] * Chain [73]: 4*s(541)+13*s(542)+2*s(552)+4*s(553)+2*s(554)+2*s(555)+4*s(556)+1 Such that:s(538) =< B s(539) =< B/2 s(540) =< s(538) s(540) =< s(539) s(541) =< s(540) s(541) =< s(539) s(542) =< s(538) s(543) =< s(539)-1/2 s(544) =< s(539) s(545) =< s(539)+1 s(546) =< s(539)*2 s(547) =< s(542)*s(539) s(548) =< s(542)*s(543) s(549) =< s(542)*s(544) s(550) =< s(542)*s(545) s(551) =< s(542)*s(546) s(552) =< s(550) s(552) =< s(548) s(552) =< s(549) s(553) =< s(550) s(553) =< s(549) s(554) =< s(550) s(554) =< s(551) s(554) =< s(549) s(555) =< s(550) s(555) =< s(547) s(556) =< s(539) with precondition: [A=6,B>=6] * Chain [72]: 4*s(560)+13*s(561)+2*s(571)+4*s(572)+2*s(573)+2*s(574)+1 Such that:s(557) =< B s(558) =< B/2 s(559) =< s(557) s(559) =< s(558) s(560) =< s(559) s(560) =< s(558) s(561) =< s(557) s(562) =< s(558)-1/2 s(563) =< s(558) s(564) =< s(558)+1 s(565) =< s(558)*2 s(566) =< s(561)*s(558) s(567) =< s(561)*s(562) s(568) =< s(561)*s(563) s(569) =< s(561)*s(564) s(570) =< s(561)*s(565) s(571) =< s(569) s(571) =< s(567) s(571) =< s(568) s(572) =< s(569) s(572) =< s(568) s(573) =< s(569) s(573) =< s(570) s(573) =< s(568) s(574) =< s(569) s(574) =< s(566) with precondition: [A=6,B>=7] #### Cost of chains of evalrealheapsortentryin(A,B,C,D,H): * Chain [85]: 3*s(577)+1*s(579)+1*s(580)+3 Such that:s(576) =< 2 s(575) =< 3 s(577) =< s(576) s(578) =< s(575)+1 s(579) =< s(577)*s(575) s(580) =< s(577)*s(578) with precondition: [A=3] * Chain [84]: 0 with precondition: [2>=A] * Chain [83]: 1*s(583)+10*s(584)+3*s(586)+3*s(587)+0 Such that:s(583) =< 1 aux(83) =< A s(584) =< aux(83) s(585) =< aux(83)+1 s(586) =< s(584)*aux(83) s(587) =< s(584)*s(585) with precondition: [A>=3] * 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 Such that:s(608) =< A/2 aux(84) =< A s(603) =< aux(84) s(610) =< s(608)-1/2 s(611) =< s(608) s(612) =< s(608)+1 s(613) =< s(608)*2 s(614) =< s(603)*s(608) s(615) =< s(603)*s(610) s(616) =< s(603)*s(611) s(617) =< s(603)*s(612) s(618) =< s(603)*s(613) s(619) =< s(617) s(619) =< s(615) s(619) =< s(616) s(620) =< s(617) s(620) =< s(616) s(621) =< s(617) s(621) =< s(618) s(621) =< s(616) s(622) =< s(617) s(622) =< s(614) s(623) =< s(608) s(623) =< aux(84) s(604) =< aux(84)+1 s(605) =< s(603)*aux(84) s(606) =< s(603)*s(604) with precondition: [A>=4] * 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 Such that:s(631) =< A/2 aux(85) =< A s(632) =< aux(85) s(632) =< s(631) s(633) =< s(632) s(633) =< aux(85) s(633) =< s(631) s(626) =< aux(85) s(635) =< s(631)-1/2 s(636) =< s(631) s(637) =< s(631)+1 s(638) =< s(631)*2 s(639) =< s(626)*s(631) s(640) =< s(626)*s(635) s(641) =< s(626)*s(636) s(642) =< s(626)*s(637) s(643) =< s(626)*s(638) s(644) =< s(642) s(644) =< s(640) s(644) =< s(641) s(645) =< s(642) s(645) =< s(641) s(646) =< s(642) s(646) =< s(643) s(646) =< s(641) s(647) =< s(642) s(647) =< s(639) s(648) =< s(631) s(627) =< aux(85)+1 s(628) =< s(626)*aux(85) s(629) =< s(626)*s(627) with precondition: [A>=5] * 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 Such that:s(656) =< A/2 aux(86) =< A s(657) =< aux(86) s(657) =< s(656) s(658) =< s(657) s(658) =< s(656) s(651) =< aux(86) s(660) =< s(656)-1/2 s(661) =< s(656) s(662) =< s(656)+1 s(663) =< s(656)*2 s(664) =< s(651)*s(656) s(665) =< s(651)*s(660) s(666) =< s(651)*s(661) s(667) =< s(651)*s(662) s(668) =< s(651)*s(663) s(669) =< s(667) s(669) =< s(665) s(669) =< s(666) s(670) =< s(667) s(670) =< s(666) s(671) =< s(667) s(671) =< s(668) s(671) =< s(666) s(672) =< s(667) s(672) =< s(664) s(673) =< s(656) s(652) =< aux(86)+1 s(653) =< s(651)*aux(86) s(654) =< s(651)*s(652) with precondition: [A>=6] * 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 Such that:s(681) =< A/2 aux(87) =< A s(682) =< aux(87) s(682) =< s(681) s(683) =< s(682) s(683) =< s(681) s(676) =< aux(87) s(685) =< s(681)-1/2 s(686) =< s(681) s(687) =< s(681)+1 s(688) =< s(681)*2 s(689) =< s(676)*s(681) s(690) =< s(676)*s(685) s(691) =< s(676)*s(686) s(692) =< s(676)*s(687) s(693) =< s(676)*s(688) s(694) =< s(692) s(694) =< s(690) s(694) =< s(691) s(695) =< s(692) s(695) =< s(691) s(696) =< s(692) s(696) =< s(693) s(696) =< s(691) s(697) =< s(692) s(697) =< s(689) s(677) =< aux(87)+1 s(678) =< s(676)*aux(87) s(679) =< s(676)*s(677) with precondition: [A>=7] #### Cost of chains of evalrealheapsortstart(A,B,C,D,H): * Chain [92]: 3*s(700)+1*s(702)+1*s(703)+3 Such that:s(698) =< 2 s(699) =< 3 s(700) =< s(698) s(701) =< s(699)+1 s(702) =< s(700)*s(699) s(703) =< s(700)*s(701) with precondition: [A=3] * Chain [91]: 0 with precondition: [2>=A] * Chain [90]: 1*s(704)+10*s(706)+3*s(708)+3*s(709)+0 Such that:s(704) =< 1 s(705) =< A s(706) =< s(705) s(707) =< s(705)+1 s(708) =< s(706)*s(705) s(709) =< s(706)*s(707) with precondition: [A>=3] * 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 Such that:s(711) =< A s(710) =< A/2 s(712) =< s(711) s(713) =< s(710)-1/2 s(714) =< s(710) s(715) =< s(710)+1 s(716) =< s(710)*2 s(717) =< s(712)*s(710) s(718) =< s(712)*s(713) s(719) =< s(712)*s(714) s(720) =< s(712)*s(715) s(721) =< s(712)*s(716) s(722) =< s(720) s(722) =< s(718) s(722) =< s(719) s(723) =< s(720) s(723) =< s(719) s(724) =< s(720) s(724) =< s(721) s(724) =< s(719) s(725) =< s(720) s(725) =< s(717) s(726) =< s(710) s(726) =< s(711) s(727) =< s(711)+1 s(728) =< s(712)*s(711) s(729) =< s(712)*s(727) with precondition: [A>=4] * 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 Such that:s(731) =< A s(730) =< A/2 s(732) =< s(731) s(732) =< s(730) s(733) =< s(732) s(733) =< s(731) s(733) =< s(730) s(734) =< s(731) s(735) =< s(730)-1/2 s(736) =< s(730) s(737) =< s(730)+1 s(738) =< s(730)*2 s(739) =< s(734)*s(730) s(740) =< s(734)*s(735) s(741) =< s(734)*s(736) s(742) =< s(734)*s(737) s(743) =< s(734)*s(738) s(744) =< s(742) s(744) =< s(740) s(744) =< s(741) s(745) =< s(742) s(745) =< s(741) s(746) =< s(742) s(746) =< s(743) s(746) =< s(741) s(747) =< s(742) s(747) =< s(739) s(748) =< s(730) s(749) =< s(731)+1 s(750) =< s(734)*s(731) s(751) =< s(734)*s(749) with precondition: [A>=5] * 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 Such that:s(753) =< A s(752) =< A/2 s(754) =< s(753) s(754) =< s(752) s(755) =< s(754) s(755) =< s(752) s(756) =< s(753) s(757) =< s(752)-1/2 s(758) =< s(752) s(759) =< s(752)+1 s(760) =< s(752)*2 s(761) =< s(756)*s(752) s(762) =< s(756)*s(757) s(763) =< s(756)*s(758) s(764) =< s(756)*s(759) s(765) =< s(756)*s(760) s(766) =< s(764) s(766) =< s(762) s(766) =< s(763) s(767) =< s(764) s(767) =< s(763) s(768) =< s(764) s(768) =< s(765) s(768) =< s(763) s(769) =< s(764) s(769) =< s(761) s(770) =< s(752) s(771) =< s(753)+1 s(772) =< s(756)*s(753) s(773) =< s(756)*s(771) with precondition: [A>=6] * 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 Such that:s(775) =< A s(774) =< A/2 s(776) =< s(775) s(776) =< s(774) s(777) =< s(776) s(777) =< s(774) s(778) =< s(775) s(779) =< s(774)-1/2 s(780) =< s(774) s(781) =< s(774)+1 s(782) =< s(774)*2 s(783) =< s(778)*s(774) s(784) =< s(778)*s(779) s(785) =< s(778)*s(780) s(786) =< s(778)*s(781) s(787) =< s(778)*s(782) s(788) =< s(786) s(788) =< s(784) s(788) =< s(785) s(789) =< s(786) s(789) =< s(785) s(790) =< s(786) s(790) =< s(787) s(790) =< s(785) s(791) =< s(786) s(791) =< s(783) s(792) =< s(775)+1 s(793) =< s(778)*s(775) s(794) =< s(778)*s(792) with precondition: [A>=7] Closed-form bounds of evalrealheapsortstart(A,B,C,D,H): ------------------------------------- * Chain [92] with precondition: [A=3] - Upper bound: 23 - Complexity: constant * Chain [91] with precondition: [2>=A] - Upper bound: 0 - Complexity: constant * Chain [90] with precondition: [A>=3] - Upper bound: 13*A+1+6*A*A - Complexity: n^2 * Chain [89] with precondition: [A>=4] - Upper bound: 257*A+3+2*A*A+A/2*(110*A)+A - Complexity: n^2 * Chain [88] with precondition: [A>=5] - Upper bound: 29*A+1+2*A*A+A/2*(10*A)+2*A - Complexity: n^2 * Chain [87] with precondition: [A>=6] - Upper bound: 31*A+1+2*A*A+A/2*(10*A)+2*A - Complexity: n^2 * Chain [86] with precondition: [A>=7] - Upper bound: 31*A+1+2*A*A+A/2*(10*A) - Complexity: n^2 ### 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 Asymptotic class: n^2 * Total analysis performed in 2220 ms.