9.23/9.23 WORST_CASE(?,O(n^1)) 9.23/9.23 9.23/9.23 Preprocessing Cost Relations 9.23/9.23 ===================================== 9.23/9.23 9.23/9.23 #### Computed strongly connected components 9.23/9.23 0. recursive : [eval_bin_search_StepSize2_16/22,eval_bin_search_StepSize2_17/22,eval_bin_search_StepSize2_bb10_in/22,eval_bin_search_StepSize2_bb11_in/22,eval_bin_search_StepSize2_bb1_in/22,eval_bin_search_StepSize2_bb2_in/22,eval_bin_search_StepSize2_bb3_in/22,eval_bin_search_StepSize2_bb4_in/22,eval_bin_search_StepSize2_bb5_in/22,eval_bin_search_StepSize2_bb6_in/22,eval_bin_search_StepSize2_bb7_in/22,eval_bin_search_StepSize2_bb8_in/22,eval_bin_search_StepSize2_bb9_in/22] 9.23/9.23 1. non_recursive : [eval_bin_search_StepSize2_stop/13] 9.23/9.23 2. non_recursive : [eval_bin_search_StepSize2_bb12_in/13] 9.23/9.23 3. non_recursive : [exit_location/1] 9.23/9.23 4. non_recursive : [eval_bin_search_StepSize2_bb1_in_loop_cont/14] 9.23/9.23 5. non_recursive : [eval_bin_search_StepSize2_15/13] 9.23/9.23 6. non_recursive : [eval_bin_search_StepSize2_14/13] 9.23/9.23 7. non_recursive : [eval_bin_search_StepSize2_13/13] 9.23/9.23 8. non_recursive : [eval_bin_search_StepSize2_12/13] 9.23/9.23 9. non_recursive : [eval_bin_search_StepSize2_11/13] 9.23/9.23 10. non_recursive : [eval_bin_search_StepSize2_10/13] 9.23/9.23 11. non_recursive : [eval_bin_search_StepSize2_9/13] 9.23/9.23 12. non_recursive : [eval_bin_search_StepSize2_8/13] 9.23/9.23 13. non_recursive : [eval_bin_search_StepSize2_7/13] 9.23/9.23 14. non_recursive : [eval_bin_search_StepSize2_6/13] 9.23/9.23 15. non_recursive : [eval_bin_search_StepSize2_5/13] 9.23/9.23 16. non_recursive : [eval_bin_search_StepSize2_4/13] 9.23/9.23 17. non_recursive : [eval_bin_search_StepSize2_3/13] 9.23/9.23 18. non_recursive : [eval_bin_search_StepSize2_2/13] 9.23/9.23 19. non_recursive : [eval_bin_search_StepSize2_1/13] 9.23/9.23 20. non_recursive : [eval_bin_search_StepSize2_0/13] 9.23/9.23 21. non_recursive : [eval_bin_search_StepSize2_bb0_in/13] 9.23/9.23 22. non_recursive : [eval_bin_search_StepSize2_start/13] 9.23/9.23 9.23/9.23 #### Obtained direct recursion through partial evaluation 9.23/9.23 0. SCC is partially evaluated into eval_bin_search_StepSize2_bb1_in/22 9.23/9.23 1. SCC is completely evaluated into other SCCs 9.23/9.23 2. SCC is completely evaluated into other SCCs 9.23/9.23 3. SCC is completely evaluated into other SCCs 9.23/9.23 4. SCC is partially evaluated into eval_bin_search_StepSize2_bb1_in_loop_cont/14 9.23/9.23 5. SCC is partially evaluated into eval_bin_search_StepSize2_15/13 9.23/9.23 6. SCC is completely evaluated into other SCCs 9.23/9.23 7. SCC is completely evaluated into other SCCs 9.23/9.23 8. SCC is completely evaluated into other SCCs 9.23/9.23 9. SCC is completely evaluated into other SCCs 9.23/9.23 10. SCC is completely evaluated into other SCCs 9.23/9.23 11. SCC is completely evaluated into other SCCs 9.23/9.23 12. SCC is completely evaluated into other SCCs 9.23/9.23 13. SCC is completely evaluated into other SCCs 9.23/9.23 14. SCC is completely evaluated into other SCCs 9.23/9.23 15. SCC is completely evaluated into other SCCs 9.23/9.23 16. SCC is completely evaluated into other SCCs 9.23/9.23 17. SCC is completely evaluated into other SCCs 9.23/9.23 18. SCC is completely evaluated into other SCCs 9.23/9.23 19. SCC is completely evaluated into other SCCs 9.23/9.23 20. SCC is completely evaluated into other SCCs 9.23/9.23 21. SCC is completely evaluated into other SCCs 9.23/9.23 22. SCC is partially evaluated into eval_bin_search_StepSize2_start/13 9.23/9.23 9.23/9.23 Control-Flow Refinement of Cost Relations 9.23/9.23 ===================================== 9.23/9.23 9.23/9.23 ### Specialization of cost equations eval_bin_search_StepSize2_bb1_in/22 9.23/9.23 * CE 64 is refined into CE [67] 9.23/9.23 * CE 8 is refined into CE [68] 9.23/9.23 * CE 10 is discarded (unfeasible) 9.23/9.23 * CE 4 is discarded (unfeasible) 9.23/9.23 * CE 6 is discarded (unfeasible) 9.23/9.23 * CE 34 is refined into CE [69] 9.23/9.23 * CE 36 is discarded (unfeasible) 9.23/9.23 * CE 30 is discarded (unfeasible) 9.23/9.23 * CE 32 is discarded (unfeasible) 9.23/9.23 * CE 57 is refined into CE [70] 9.23/9.23 * CE 58 is discarded (unfeasible) 9.23/9.23 * CE 55 is discarded (unfeasible) 9.23/9.23 * CE 56 is discarded (unfeasible) 9.23/9.23 * CE 61 is refined into CE [71] 9.23/9.23 * CE 62 is discarded (unfeasible) 9.23/9.23 * CE 45 is discarded (unfeasible) 9.23/9.23 * CE 46 is refined into CE [72] 9.23/9.23 * CE 53 is discarded (unfeasible) 9.23/9.23 * CE 54 is discarded (unfeasible) 9.23/9.23 * CE 19 is refined into CE [73] 9.23/9.23 * CE 20 is refined into CE [74] 9.23/9.23 * CE 27 is discarded (unfeasible) 9.23/9.23 * CE 28 is discarded (unfeasible) 9.23/9.23 * CE 41 is refined into CE [75] 9.23/9.23 * CE 48 is discarded (unfeasible) 9.23/9.23 * CE 15 is refined into CE [76] 9.23/9.23 * CE 22 is discarded (unfeasible) 9.23/9.23 * CE 63 is refined into CE [77] 9.23/9.23 * CE 59 is discarded (unfeasible) 9.23/9.23 * CE 60 is discarded (unfeasible) 9.23/9.23 * CE 38 is discarded (unfeasible) 9.23/9.23 * CE 40 is discarded (unfeasible) 9.23/9.23 * CE 12 is discarded (unfeasible) 9.23/9.23 * CE 14 is discarded (unfeasible) 9.23/9.23 * CE 47 is discarded (unfeasible) 9.23/9.23 * CE 21 is discarded (unfeasible) 9.23/9.23 * CE 7 is refined into CE [78] 9.23/9.23 * CE 9 is discarded (unfeasible) 9.23/9.23 * CE 3 is discarded (unfeasible) 9.23/9.23 * CE 5 is discarded (unfeasible) 9.23/9.23 * CE 33 is refined into CE [79] 9.23/9.23 * CE 35 is discarded (unfeasible) 9.23/9.23 * CE 29 is discarded (unfeasible) 9.23/9.23 * CE 31 is discarded (unfeasible) 9.23/9.23 * CE 17 is refined into CE [80] 9.23/9.23 * CE 18 is refined into CE [81] 9.23/9.23 * CE 25 is discarded (unfeasible) 9.23/9.23 * CE 26 is discarded (unfeasible) 9.23/9.23 * CE 43 is discarded (unfeasible) 9.23/9.23 * CE 44 is refined into CE [82] 9.23/9.23 * CE 51 is discarded (unfeasible) 9.23/9.23 * CE 52 is discarded (unfeasible) 9.23/9.23 * CE 42 is refined into CE [83] 9.23/9.23 * CE 50 is discarded (unfeasible) 9.23/9.23 * CE 16 is refined into CE [84] 9.23/9.23 * CE 24 is discarded (unfeasible) 9.23/9.23 * CE 37 is discarded (unfeasible) 9.23/9.23 * CE 39 is discarded (unfeasible) 9.23/9.23 * CE 11 is discarded (unfeasible) 9.23/9.23 * CE 13 is discarded (unfeasible) 9.23/9.23 * CE 49 is discarded (unfeasible) 9.23/9.23 * CE 23 is discarded (unfeasible) 9.23/9.23 9.23/9.23 9.23/9.23 ### Cost equations --> "Loop" of eval_bin_search_StepSize2_bb1_in/22 9.23/9.23 * CEs [82] --> Loop 67 9.23/9.23 * CEs [84] --> Loop 68 9.23/9.23 * CEs [81] --> Loop 69 9.23/9.23 * CEs [83] --> Loop 70 9.23/9.23 * CEs [80] --> Loop 71 9.23/9.23 * CEs [78] --> Loop 72 9.23/9.23 * CEs [79] --> Loop 73 9.23/9.23 * CEs [67] --> Loop 74 9.23/9.23 * CEs [71] --> Loop 75 9.23/9.23 * CEs [72] --> Loop 76 9.23/9.23 * CEs [76] --> Loop 77 9.23/9.23 * CEs [74] --> Loop 78 9.23/9.23 * CEs [73] --> Loop 79 9.23/9.23 * CEs [75] --> Loop 80 9.23/9.23 * CEs [70] --> Loop 81 9.23/9.23 * CEs [69] --> Loop 82 9.23/9.23 * CEs [77] --> Loop 83 9.23/9.23 * CEs [68] --> Loop 84 9.23/9.23 9.23/9.23 ### Ranking functions of CR eval_bin_search_StepSize2_bb1_in(V__0,V_0,V_c_0,V_c_1,V_c_2,V_c_3,V_d_0,V_f_0,V_f_1,V_f_2,V_r,B,C,D,E,F,G,H,I,J,K,L) 9.23/9.23 * RF of phase [67]: [V__0/4-3/4] 9.23/9.23 * RF of phase [71]: [-V__0/4+63] 9.23/9.23 9.23/9.23 #### Partial ranking functions of CR eval_bin_search_StepSize2_bb1_in(V__0,V_0,V_c_0,V_c_1,V_c_2,V_c_3,V_d_0,V_f_0,V_f_1,V_f_2,V_r,B,C,D,E,F,G,H,I,J,K,L) 9.23/9.23 * Partial RF of phase [67]: 9.23/9.23 - RF of loop [67:1]: 9.23/9.23 V__0/4-3/4 9.23/9.23 * Partial RF of phase [71]: 9.23/9.23 - RF of loop [71:1]: 9.23/9.23 -V__0/4+63 9.23/9.23 9.23/9.23 9.23/9.23 ### Specialization of cost equations eval_bin_search_StepSize2_bb1_in_loop_cont/14 9.23/9.23 * CE 66 is refined into CE [85] 9.23/9.23 * CE 65 is refined into CE [86] 9.23/9.23 9.23/9.23 9.23/9.23 ### Cost equations --> "Loop" of eval_bin_search_StepSize2_bb1_in_loop_cont/14 9.23/9.23 * CEs [85] --> Loop 85 9.23/9.23 * CEs [86] --> Loop 86 9.23/9.23 9.23/9.23 ### Ranking functions of CR eval_bin_search_StepSize2_bb1_in_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N) 9.23/9.23 9.23/9.23 #### Partial ranking functions of CR eval_bin_search_StepSize2_bb1_in_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N) 9.23/9.23 9.23/9.23 9.23/9.23 ### Specialization of cost equations eval_bin_search_StepSize2_15/13 9.23/9.23 * CE 2 is refined into CE [87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117] 9.23/9.23 9.23/9.23 9.23/9.23 ### Cost equations --> "Loop" of eval_bin_search_StepSize2_15/13 9.23/9.23 * CEs [111] --> Loop 87 9.23/9.23 * CEs [107] --> Loop 88 9.23/9.23 * CEs [95] --> Loop 89 9.23/9.23 * CEs [108,109,110,112,113,116] --> Loop 90 9.23/9.23 * CEs [97] --> Loop 91 9.23/9.23 * CEs [88] --> Loop 92 9.23/9.23 * CEs [96] --> Loop 93 9.23/9.23 * CEs [114] --> Loop 94 9.23/9.23 * CEs [90,92,94,100,101,106] --> Loop 95 9.23/9.23 * CEs [105] --> Loop 96 9.23/9.23 * CEs [104] --> Loop 97 9.23/9.23 * CEs [98] --> Loop 98 9.23/9.23 * CEs [91] --> Loop 99 9.23/9.23 * CEs [89,93,103] --> Loop 100 9.23/9.23 * CEs [99,102] --> Loop 101 9.23/9.23 * CEs [87] --> Loop 102 9.23/9.23 * CEs [115,117] --> Loop 103 9.23/9.23 9.23/9.23 ### Ranking functions of CR eval_bin_search_StepSize2_15(V__0,V_0,V_c_0,V_c_1,V_c_2,V_c_3,V_d_0,V_f_0,V_f_1,V_f_2,V_r,V_s,B) 9.23/9.23 9.23/9.23 #### Partial ranking functions of CR eval_bin_search_StepSize2_15(V__0,V_0,V_c_0,V_c_1,V_c_2,V_c_3,V_d_0,V_f_0,V_f_1,V_f_2,V_r,V_s,B) 9.23/9.23 9.23/9.23 9.23/9.23 ### Specialization of cost equations eval_bin_search_StepSize2_start/13 9.23/9.23 * CE 1 is refined into CE [118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134] 9.23/9.23 9.23/9.23 9.23/9.23 ### Cost equations --> "Loop" of eval_bin_search_StepSize2_start/13 9.23/9.23 * CEs [134] --> Loop 104 9.23/9.23 * CEs [133] --> Loop 105 9.23/9.23 * CEs [132] --> Loop 106 9.23/9.23 * CEs [131] --> Loop 107 9.23/9.23 * CEs [130] --> Loop 108 9.23/9.23 * CEs [129] --> Loop 109 9.23/9.23 * CEs [128] --> Loop 110 9.23/9.23 * CEs [127] --> Loop 111 9.23/9.23 * CEs [126] --> Loop 112 9.23/9.23 * CEs [125] --> Loop 113 9.23/9.23 * CEs [124] --> Loop 114 9.23/9.23 * CEs [123] --> Loop 115 9.23/9.23 * CEs [122] --> Loop 116 9.23/9.23 * CEs [121] --> Loop 117 9.23/9.23 * CEs [120] --> Loop 118 9.23/9.23 * CEs [119] --> Loop 119 9.23/9.23 * CEs [118] --> Loop 120 9.23/9.23 9.23/9.23 ### Ranking functions of CR eval_bin_search_StepSize2_start(V__0,V_0,V_c_0,V_c_1,V_c_2,V_c_3,V_d_0,V_f_0,V_f_1,V_f_2,V_r,V_s,B) 9.23/9.23 9.23/9.23 #### Partial ranking functions of CR eval_bin_search_StepSize2_start(V__0,V_0,V_c_0,V_c_1,V_c_2,V_c_3,V_d_0,V_f_0,V_f_1,V_f_2,V_r,V_s,B) 9.23/9.23 9.23/9.23 9.23/9.23 Computing Bounds 9.23/9.23 ===================================== 9.23/9.23 9.23/9.23 #### Cost of chains of eval_bin_search_StepSize2_bb1_in(V__0,V_0,V_c_0,V_c_1,V_c_2,V_c_3,V_d_0,V_f_0,V_f_1,V_f_2,V_r,B,C,D,E,F,G,H,I,J,K,L): 9.23/9.23 * Chain [[67],77]: 1*it(67)+0 9.23/9.23 Such that:it(67) =< V__0/4-C/4 9.23/9.23 9.23/9.23 with precondition: [V_c_0=4,V_f_0=0,B=2,E=4,F=4,H=4,I=1,J=0,K=1,L=0,1>=V_d_0,2>=G,V_d_0>=0,2*G>=3,D>=V_r+1,V__0>=C+4,C+G>=256] 9.23/9.23 9.23/9.23 * Chain [[67],76]: 1*it(67)+0 9.23/9.23 Such that:it(67) =< V__0/4-C/4 9.23/9.23 9.23/9.23 with precondition: [V_c_0=4,V_f_0=0,B=2,E=4,F=4,H=4,I=1,J=0,L=0,V_c_2=G,V_f_1=K,1>=V_d_0,3>=C,V_d_0>=0,C>=0,V__0>=C+4,V_r>=D+1] 9.23/9.23 9.23/9.23 * Chain [[67],75]: 1*it(67)+0 9.23/9.23 Such that:it(67) =< V__0/4-C/4 9.23/9.23 9.23/9.23 with precondition: [V_c_0=4,V_f_0=0,B=2,E=4,F=4,H=4,I=1,J=0,L=0,V_r=D,V_c_2=G,V_f_1=K,1>=V_d_0,V_d_0>=0,C>=0,V__0>=C+4] 9.23/9.23 9.23/9.23 * Chain [[67],74]: 1*it(67)+0 9.23/9.23 Such that:it(67) =< V__0/4 9.23/9.23 9.23/9.23 with precondition: [V_c_0=4,V_f_0=0,B=3,1>=V_d_0,V__0>=4,V_d_0>=0] 9.23/9.23 9.23/9.23 * Chain [[67],68,84]: 1*it(67)+1 9.23/9.23 Such that:it(67) =< V__0/4 9.23/9.23 9.23/9.23 with precondition: [V_c_0=4,V_f_0=0,B=2,C=255,E=2,F=1,G=1,H=4,I=2,J=1,K=1,L=0,1>=V_d_0,V__0>=257,V_d_0>=0,D>=V_r+1] 9.23/9.23 9.23/9.23 * Chain [[67],68,81]: 1*it(67)+1 9.23/9.23 Such that:it(67) =< V__0/4-C/4+1/2 9.23/9.23 9.23/9.23 with precondition: [V_c_0=4,V_f_0=0,B=2,E=2,G=2,H=4,I=2,J=1,K=1,L=0,V_r=D,1>=V_d_0,255>=C,1>=F,V_d_0>=0,C>=2,2*F>=1,V__0>=C+2] 9.23/9.23 9.23/9.23 * Chain [[67],68,74]: 1*it(67)+1 9.23/9.23 Such that:it(67) =< V__0/4 9.23/9.23 9.23/9.23 with precondition: [V_c_0=4,V_f_0=0,B=3,1>=V_d_0,V__0>=4,V_d_0>=0] 9.23/9.23 9.23/9.23 * Chain [[67],68,73,83]: 1*it(67)+2 9.23/9.23 Such that:it(67) =< V__0/4-C/4+1/4 9.23/9.23 9.23/9.23 with precondition: [V_c_0=4,V_f_0=0,B=2,E=1,F=1,G=2,H=1,I=1,J=1,K=1,L=1,1>=V_d_0,254>=C,V_d_0>=0,C>=1,V__0>=C+3] 9.23/9.23 9.23/9.23 * Chain [[67],68,73,74]: 1*it(67)+2 9.23/9.23 Such that:it(67) =< V__0/4 9.23/9.24 9.23/9.24 with precondition: [V_c_0=4,V_f_0=0,B=3,1>=V_d_0,V__0>=4,V_d_0>=0] 9.23/9.24 9.23/9.24 * Chain [[67],68,72,83]: 1*it(67)+2 9.23/9.24 Such that:it(67) =< V__0/4-C/4+3/4 9.23/9.24 9.23/9.24 with precondition: [V_c_0=4,V_f_0=0,B=2,E=1,F=1,G=1,H=4,I=2,J=1,K=1,L=0,1>=V_d_0,255>=C,V_d_0>=0,C>=3,V__0>=C+1] 9.23/9.24 9.23/9.24 * Chain [[67],68,72,74]: 1*it(67)+2 9.23/9.24 Such that:it(67) =< V__0/4 9.23/9.24 9.23/9.24 with precondition: [V_c_0=4,V_f_0=0,B=3,1>=V_d_0,V__0>=4,V_d_0>=0] 9.23/9.24 9.23/9.24 * Chain [78]: 0 9.23/9.24 with precondition: [V_c_0=4,V_d_0=0,V_f_0=0,B=2,E=4,F=4,G=4,I=0,J=0,K=0,H=V_c_3,L=V_f_2,V__0=C,V__0>=252,D>=V_r+1] 9.23/9.24 9.23/9.24 * Chain [76]: 0 9.23/9.24 with precondition: [V_c_0=4,V_f_0=0,B=2,E=4,F=4,H=4,J=0,L=0,G=V_c_2,K=V_f_1,V__0=C,V_d_0=I,3>=V__0,1>=V_d_0,V_d_0>=0,V_r>=D+1] 9.23/9.24 9.23/9.24 * Chain [75]: 0 9.23/9.24 with precondition: [V_c_0=4,V_f_0=0,B=2,E=4,F=4,J=0,C=V__0,G=V_c_2,H=V_c_3,K=V_f_1,L=V_f_2,D=V_r,V_d_0=I,2>=V_d_0,V_d_0>=0] 9.23/9.24 9.23/9.24 * Chain [74]: 0 9.23/9.24 with precondition: [B=3,2>=V_d_0,1>=V_f_0,4>=2*V_f_0+V_c_0,V_d_0>=V_f_0,2*V_c_0+7*V_f_0>=8] 9.23/9.24 9.23/9.24 * Chain [69,[71],80]: 1*it(71)+1 9.23/9.24 Such that:it(71) =< -V__0/4+C/4 9.23/9.24 9.23/9.24 with precondition: [V_c_0=4,V_d_0=0,V_f_0=0,B=2,E=4,F=4,G=4,I=2,J=0,K=0,L=1,2>=H,2*H>=3,C>=V__0+8,H>=C+1,V_r>=D+1] 9.23/9.24 9.23/9.24 * Chain [69,[71],79]: 1*it(71)+1 9.23/9.24 Such that:it(71) =< -V__0/4+62 9.23/9.24 9.23/9.24 with precondition: [V_c_0=4,V_d_0=0,V_f_0=0,B=2,E=4,F=4,G=4,I=2,J=0,K=0,V_c_3=H,V_f_2=L,255>=C,C>=252,C>=V__0+8,D>=V_r+1] 9.23/9.24 9.23/9.24 * Chain [69,[71],75]: 1*it(71)+1 9.23/9.24 Such that:it(71) =< -V__0/4+62 9.23/9.24 it(71) =< -V__0/4+C/4 9.23/9.24 9.23/9.24 with precondition: [V_c_0=4,V_d_0=0,V_f_0=0,B=2,E=4,F=4,G=4,I=2,J=0,K=0,V_r=D,V_c_3=H,V_f_2=L,255>=C,C>=V__0+8] 9.23/9.24 9.23/9.24 * Chain [69,[71],74]: 1*it(71)+1 9.23/9.24 Such that:it(71) =< -V__0/4+62 9.23/9.24 9.23/9.24 with precondition: [V_c_0=4,V_d_0=0,V_f_0=0,B=3,247>=V__0] 9.23/9.24 9.23/9.24 * Chain [69,[71],70,82]: 1*it(71)+2 9.23/9.24 Such that:it(71) =< -V__0/4 9.23/9.24 9.23/9.24 with precondition: [V_c_0=4,V_d_0=0,V_f_0=0,B=2,C=0,E=2,F=1,G=4,H=1,I=1,J=1,K=0,L=1,0>=V__0+6,V_r>=D+1] 9.23/9.24 9.23/9.24 * Chain [69,[71],70,81]: 1*it(71)+2 9.23/9.24 Such that:it(71) =< -V__0/4+62 9.23/9.24 it(71) =< -V__0/4+C/4 9.23/9.24 9.23/9.24 with precondition: [V_c_0=4,V_d_0=0,V_f_0=0,B=2,E=2,G=4,H=2,I=1,J=1,K=0,L=1,V_r=D,253>=C,1>=F,C>=0,2*F>=1,C>=V__0+6] 9.23/9.24 9.23/9.24 * Chain [69,[71],70,74]: 1*it(71)+2 9.23/9.24 Such that:it(71) =< -V__0/4+62 9.23/9.24 9.23/9.24 with precondition: [V_c_0=4,V_d_0=0,V_f_0=0,B=3,247>=V__0] 9.23/9.24 9.23/9.24 * Chain [69,[71],70,73,83]: 1*it(71)+3 9.23/9.24 Such that:it(71) =< -V__0/4+62 9.23/9.24 it(71) =< -V__0/4+C/4 9.23/9.24 9.23/9.24 with precondition: [V_c_0=4,V_d_0=0,V_f_0=0,B=2,E=1,F=1,G=4,H=1,I=1,J=1,K=0,L=1,252>=C,C>=0,C>=V__0+5] 9.23/9.24 9.23/9.24 * Chain [69,[71],70,73,74]: 1*it(71)+3 9.23/9.24 Such that:it(71) =< -V__0/4+62 9.23/9.24 9.23/9.24 with precondition: [V_c_0=4,V_d_0=0,V_f_0=0,B=3,247>=V__0] 9.23/9.24 9.23/9.24 * Chain [69,[71],70,72,83]: 1*it(71)+3 9.23/9.24 Such that:it(71) =< -V__0/4+62 9.23/9.24 it(71) =< -V__0/4+C/4 9.23/9.24 9.23/9.24 with precondition: [V_c_0=4,V_d_0=0,V_f_0=0,B=2,E=1,F=1,G=1,H=2,I=2,J=1,K=1,L=1,254>=C,C>=1,C>=V__0+7] 9.23/9.24 9.23/9.24 * Chain [69,[71],70,72,74]: 1*it(71)+3 9.23/9.24 Such that:it(71) =< -V__0/4+62 9.23/9.24 9.23/9.24 with precondition: [V_c_0=4,V_d_0=0,V_f_0=0,B=3,247>=V__0] 9.23/9.24 9.23/9.24 * Chain [69,80]: 1 9.23/9.24 with precondition: [V_c_0=4,V_d_0=0,V_f_0=0,B=2,E=4,F=4,G=4,I=2,J=0,K=0,L=1,C=V__0+4,2>=H,2*H>=3,H>=C+1,V_r>=D+1] 9.23/9.24 9.23/9.24 * Chain [69,79]: 1 9.23/9.24 with precondition: [V_c_0=4,V_d_0=0,V_f_0=0,B=2,E=4,F=4,G=4,I=2,J=0,K=0,C=V__0+4,V_c_3=H,V_f_2=L,255>=C,C>=252,D>=V_r+1] 9.23/9.24 9.23/9.24 * Chain [69,75]: 1 9.23/9.24 with precondition: [V_c_0=4,V_d_0=0,V_f_0=0,B=2,E=4,F=4,G=4,I=2,J=0,K=0,V__0+4=C,V_r=D,V_c_3=H,V_f_2=L,251>=V__0] 9.23/9.24 9.23/9.24 * Chain [69,74]: 1 9.23/9.24 with precondition: [V_c_0=4,V_d_0=0,V_f_0=0,B=3,251>=V__0] 9.23/9.24 9.23/9.24 * Chain [69,70,82]: 2 9.23/9.24 with precondition: [V__0+2=0,V_c_0=4,V_d_0=0,V_f_0=0,B=2,C=0,E=2,F=1,G=4,H=1,I=1,J=1,K=0,L=1,V_r>=D+1] 9.23/9.24 9.23/9.24 * Chain [69,70,81]: 2 9.23/9.24 with precondition: [V_c_0=4,V_d_0=0,V_f_0=0,B=2,E=2,G=4,H=2,I=1,J=1,K=0,L=1,C=V__0+2,V_r=D,253>=C,1>=F,C>=0,2*F>=1] 9.23/9.24 9.23/9.24 * Chain [69,70,74]: 2 9.23/9.24 with precondition: [V_c_0=4,V_d_0=0,V_f_0=0,B=3,251>=V__0,2*V__0+5>=0] 9.23/9.24 9.23/9.24 * Chain [69,70,73,83]: 3 9.23/9.24 with precondition: [V_c_0=4,V_d_0=0,V_f_0=0,B=2,E=1,F=1,G=4,H=1,I=1,J=1,K=0,L=1,C=V__0+1,252>=C,C>=0] 9.23/9.24 9.23/9.24 * Chain [69,70,73,74]: 3 9.23/9.24 with precondition: [V_c_0=4,V_d_0=0,V_f_0=0,B=3,251>=V__0,2*V__0+3>=0] 9.23/9.24 9.23/9.24 * Chain [69,70,72,83]: 3 9.23/9.24 with precondition: [V_c_0=4,V_d_0=0,V_f_0=0,B=2,E=1,F=1,G=1,H=2,I=2,J=1,K=1,L=1,C=V__0+3,254>=C,C>=1] 9.23/9.24 9.23/9.24 * Chain [69,70,72,74]: 3 9.23/9.24 with precondition: [V_c_0=4,V_d_0=0,V_f_0=0,B=3,251>=V__0,V__0+2>=0] 9.23/9.24 9.23/9.24 9.23/9.24 #### Cost of chains of eval_bin_search_StepSize2_bb1_in_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N): 9.23/9.24 * Chain [86]: 0 9.23/9.24 with precondition: [A=2] 9.23/9.24 9.23/9.24 * Chain [85]: 0 9.23/9.24 with precondition: [A=3] 9.23/9.24 9.23/9.24 9.23/9.24 #### Cost of chains of eval_bin_search_StepSize2_15(V__0,V_0,V_c_0,V_c_1,V_c_2,V_c_3,V_d_0,V_f_0,V_f_1,V_f_2,V_r,V_s,B): 9.23/9.24 * Chain [103]: 0 9.23/9.24 with precondition: [] 9.23/9.24 9.23/9.24 * Chain [102]: 2 9.23/9.24 with precondition: [V_s+2=0] 9.23/9.24 9.23/9.24 * Chain [101]: 1 9.23/9.24 with precondition: [251>=V_s] 9.23/9.24 9.23/9.24 * Chain [100]: 3 9.23/9.24 with precondition: [251>=V_s,V_s+2>=0] 9.23/9.24 9.23/9.24 * Chain [99]: 3 9.23/9.24 with precondition: [251>=V_s,V_s+1>=0] 9.23/9.24 9.23/9.24 * Chain [98]: 1 9.23/9.24 with precondition: [251>=V_s,V_s>=248] 9.23/9.24 9.23/9.24 * Chain [97]: 2 9.23/9.24 with precondition: [251>=V_s,2*V_s+5>=0] 9.23/9.24 9.23/9.24 * Chain [96]: 3 9.23/9.24 with precondition: [251>=V_s,2*V_s+3>=0] 9.23/9.24 9.23/9.24 * Chain [95]: 9*s(9)+3 9.23/9.24 Such that:aux(3) =< -V_s/4+62 9.23/9.24 s(9) =< aux(3) 9.23/9.24 9.23/9.24 with precondition: [247>=V_s] 9.23/9.24 9.23/9.24 * Chain [94]: 0 9.23/9.24 with precondition: [3>=V_s] 9.23/9.24 9.23/9.24 * Chain [93]: 1 9.23/9.24 with precondition: [0>=V_s+3] 9.23/9.24 9.23/9.24 * Chain [92]: 1*s(16)+2 9.23/9.24 Such that:s(16) =< -V_s/4 9.23/9.24 9.23/9.24 with precondition: [0>=V_s+6] 9.23/9.24 9.23/9.24 * Chain [91]: 1*s(17)+1 9.23/9.24 Such that:s(17) =< -V_s/4+1/4 9.23/9.24 9.23/9.24 with precondition: [0>=V_s+7] 9.23/9.24 9.23/9.24 * Chain [90]: 9*s(18)+2 9.23/9.24 Such that:aux(4) =< V_s/4 9.23/9.24 s(18) =< aux(4) 9.23/9.24 9.23/9.24 with precondition: [V_s>=4] 9.23/9.24 9.23/9.24 * Chain [89]: 0 9.23/9.24 with precondition: [V_s>=252] 9.23/9.24 9.23/9.24 * Chain [88]: 1*s(25)+1 9.23/9.24 Such that:s(25) =< V_s/4 9.23/9.24 9.23/9.24 with precondition: [V_s>=257] 9.23/9.24 9.23/9.24 * Chain [87]: 1*s(26)+0 9.23/9.24 Such that:s(26) =< V_s/4 9.23/9.24 9.23/9.24 with precondition: [V_s>=258] 9.23/9.24 9.23/9.24 9.23/9.24 #### Cost of chains of eval_bin_search_StepSize2_start(V__0,V_0,V_c_0,V_c_1,V_c_2,V_c_3,V_d_0,V_f_0,V_f_1,V_f_2,V_r,V_s,B): 9.23/9.24 * Chain [120]: 0 9.23/9.24 with precondition: [] 9.23/9.24 9.23/9.24 * Chain [119]: 2 9.23/9.24 with precondition: [V_s+2=0] 9.23/9.24 9.23/9.24 * Chain [118]: 1 9.23/9.24 with precondition: [251>=V_s] 9.23/9.24 9.23/9.24 * Chain [117]: 3 9.23/9.24 with precondition: [251>=V_s,V_s+2>=0] 9.23/9.24 9.23/9.24 * Chain [116]: 3 9.23/9.24 with precondition: [251>=V_s,V_s+1>=0] 9.23/9.24 9.23/9.24 * Chain [115]: 1 9.23/9.24 with precondition: [251>=V_s,V_s>=248] 9.23/9.24 9.23/9.24 * Chain [114]: 2 9.23/9.24 with precondition: [251>=V_s,2*V_s+5>=0] 9.23/9.24 9.23/9.24 * Chain [113]: 3 9.23/9.24 with precondition: [251>=V_s,2*V_s+3>=0] 9.23/9.24 9.23/9.24 * Chain [112]: 9*s(28)+3 9.23/9.24 Such that:s(27) =< -V_s/4+62 9.23/9.24 s(28) =< s(27) 9.23/9.24 9.23/9.24 with precondition: [247>=V_s] 9.23/9.24 9.23/9.24 * Chain [111]: 0 9.23/9.24 with precondition: [3>=V_s] 9.23/9.24 9.23/9.24 * Chain [110]: 1 9.23/9.24 with precondition: [0>=V_s+3] 9.23/9.24 9.23/9.24 * Chain [109]: 1*s(29)+2 9.23/9.24 Such that:s(29) =< -V_s/4 9.23/9.24 9.23/9.24 with precondition: [0>=V_s+6] 9.23/9.24 9.23/9.24 * Chain [108]: 1*s(30)+1 9.23/9.24 Such that:s(30) =< -V_s/4+1/4 9.23/9.24 9.23/9.24 with precondition: [0>=V_s+7] 9.23/9.24 9.23/9.24 * Chain [107]: 9*s(32)+2 9.23/9.24 Such that:s(31) =< V_s/4 9.23/9.24 s(32) =< s(31) 9.23/9.24 9.23/9.24 with precondition: [V_s>=4] 9.23/9.24 9.23/9.24 * Chain [106]: 0 9.23/9.24 with precondition: [V_s>=252] 9.23/9.24 9.23/9.24 * Chain [105]: 1*s(33)+1 9.23/9.24 Such that:s(33) =< V_s/4 9.23/9.24 9.23/9.24 with precondition: [V_s>=257] 9.23/9.24 9.23/9.24 * Chain [104]: 1*s(34)+0 9.23/9.24 Such that:s(34) =< V_s/4 9.23/9.24 9.23/9.24 with precondition: [V_s>=258] 9.23/9.24 9.23/9.24 9.23/9.24 Closed-form bounds of eval_bin_search_StepSize2_start(V__0,V_0,V_c_0,V_c_1,V_c_2,V_c_3,V_d_0,V_f_0,V_f_1,V_f_2,V_r,V_s,B): 9.23/9.24 ------------------------------------- 9.23/9.24 * Chain [120] with precondition: [] 9.23/9.24 - Upper bound: 0 9.23/9.24 - Complexity: constant 9.23/9.24 * Chain [119] with precondition: [V_s+2=0] 9.23/9.24 - Upper bound: 2 9.23/9.24 - Complexity: constant 9.23/9.24 * Chain [118] with precondition: [251>=V_s] 9.23/9.24 - Upper bound: 1 9.23/9.24 - Complexity: constant 9.23/9.24 * Chain [117] with precondition: [251>=V_s,V_s+2>=0] 9.23/9.24 - Upper bound: 3 9.23/9.24 - Complexity: constant 9.23/9.24 * Chain [116] with precondition: [251>=V_s,V_s+1>=0] 9.23/9.24 - Upper bound: 3 9.23/9.24 - Complexity: constant 9.23/9.24 * Chain [115] with precondition: [251>=V_s,V_s>=248] 9.23/9.24 - Upper bound: 1 9.23/9.24 - Complexity: constant 9.23/9.24 * Chain [114] with precondition: [251>=V_s,2*V_s+5>=0] 9.23/9.24 - Upper bound: 2 9.23/9.24 - Complexity: constant 9.23/9.24 * Chain [113] with precondition: [251>=V_s,2*V_s+3>=0] 9.23/9.24 - Upper bound: 3 9.23/9.24 - Complexity: constant 9.23/9.24 * Chain [112] with precondition: [247>=V_s] 9.23/9.24 - Upper bound: -9/4*V_s+561 9.23/9.24 - Complexity: n 9.23/9.24 * Chain [111] with precondition: [3>=V_s] 9.23/9.24 - Upper bound: 0 9.23/9.24 - Complexity: constant 9.23/9.24 * Chain [110] with precondition: [0>=V_s+3] 9.23/9.24 - Upper bound: 1 9.23/9.24 - Complexity: constant 9.23/9.24 * Chain [109] with precondition: [0>=V_s+6] 9.23/9.24 - Upper bound: -V_s/4+2 9.23/9.24 - Complexity: n 9.23/9.24 * Chain [108] with precondition: [0>=V_s+7] 9.23/9.24 - Upper bound: -V_s/4+5/4 9.23/9.24 - Complexity: n 9.23/9.24 * Chain [107] with precondition: [V_s>=4] 9.23/9.24 - Upper bound: 9/4*V_s+2 9.23/9.24 - Complexity: n 9.23/9.24 * Chain [106] with precondition: [V_s>=252] 9.23/9.24 - Upper bound: 0 9.23/9.24 - Complexity: constant 9.23/9.24 * Chain [105] with precondition: [V_s>=257] 9.23/9.24 - Upper bound: V_s/4+1 9.23/9.24 - Complexity: n 9.23/9.24 * Chain [104] with precondition: [V_s>=258] 9.23/9.24 - Upper bound: V_s/4 9.23/9.24 - Complexity: n 9.23/9.24 9.23/9.24 ### Maximum cost of eval_bin_search_StepSize2_start(V__0,V_0,V_c_0,V_c_1,V_c_2,V_c_3,V_d_0,V_f_0,V_f_1,V_f_2,V_r,V_s,B): max([max([3,nat(-V_s/4+1/4)+1,nat(-V_s/4)+2,nat(-V_s/4+62)*9+3]),nat(V_s/4)+max([1,nat(V_s/4)*8+2])]) 9.23/9.24 Asymptotic class: n 9.23/9.24 * Total analysis performed in 8867 ms. 9.23/9.24 9.25/9.34 EOF