/export/starexec/sandbox/solver/bin/starexec_run_C /export/starexec/sandbox/benchmark/theBenchmark.c /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?,O(n^2)) Preprocessing Cost Relations ===================================== #### Computed strongly connected components 0. recursive : [eval_sipmamergesort_init_12/6,eval_sipmamergesort_init_13/7,eval_sipmamergesort_init_bb3_in/6,eval_sipmamergesort_init_bb4_in/6,eval_sipmamergesort_init_bb5_in/7,eval_sipmamergesort_init_bb6_in/7] 1. recursive : [eval_sipmamergesort_init_bb7_in/3,eval_sipmamergesort_init_bb8_in/3] 2. recursive : [eval_sipmamergesort_init_bb10_in/3,eval_sipmamergesort_init_bb9_in/3] 3. recursive : [eval_sipmamergesort_init_bb11_in/14,eval_sipmamergesort_init_bb2_in/9,eval_sipmamergesort_init_bb3_in_loop_cont/14,eval_sipmamergesort_init_bb7_in_loop_cont/15,eval_sipmamergesort_init_bb9_in_loop_cont/15] 4. recursive : [eval_sipmamergesort_init_bb12_in/11,eval_sipmamergesort_init_bb1_in/5,eval_sipmamergesort_init_bb2_in_loop_cont/12] 5. recursive : [eval_sipmamergesort_init_bb14_in/3,eval_sipmamergesort_init_bb15_in/3] 6. non_recursive : [eval_sipmamergesort_init_stop/1] 7. non_recursive : [eval_sipmamergesort_init_bb16_in/1] 8. non_recursive : [eval_sipmamergesort_init_bb14_in_loop_cont/2] 9. non_recursive : [eval_sipmamergesort_init_bb13_in/3] 10. non_recursive : [eval_sipmamergesort_init_bb1_in_loop_cont/4] 11. non_recursive : [eval_sipmamergesort_init_bb0_in/2] 12. non_recursive : [eval_sipmamergesort_init_start/2] #### Obtained direct recursion through partial evaluation 0. SCC is partially evaluated into eval_sipmamergesort_init_bb3_in/6 1. SCC is partially evaluated into eval_sipmamergesort_init_bb7_in/3 2. SCC is partially evaluated into eval_sipmamergesort_init_bb9_in/3 3. SCC is partially evaluated into eval_sipmamergesort_init_bb2_in/9 4. SCC is partially evaluated into eval_sipmamergesort_init_bb1_in/5 5. SCC is partially evaluated into eval_sipmamergesort_init_bb14_in/3 6. SCC is completely evaluated into other SCCs 7. SCC is completely evaluated into other SCCs 8. SCC is completely evaluated into other SCCs 9. SCC is partially evaluated into eval_sipmamergesort_init_bb13_in/3 10. SCC is completely evaluated into other SCCs 11. SCC is partially evaluated into eval_sipmamergesort_init_bb0_in/2 12. SCC is partially evaluated into eval_sipmamergesort_init_start/2 Control-Flow Refinement of Cost Relations ===================================== ### Specialization of cost equations eval_sipmamergesort_init_bb3_in/6 * CE 22 is refined into CE [28] * CE 23 is refined into CE [29] * CE 21 is refined into CE [30] * CE 20 is refined into CE [31] ### Cost equations --> "Loop" of eval_sipmamergesort_init_bb3_in/6 * CEs [30] --> Loop 28 * CEs [31] --> Loop 29 * CEs [28] --> Loop 30 * CEs [29] --> Loop 31 ### Ranking functions of CR eval_sipmamergesort_init_bb3_in(V_r_1,V_q_1,B,C,D,E) * RF of phase [28,29]: [V_r_1+V_q_1-1] #### Partial ranking functions of CR eval_sipmamergesort_init_bb3_in(V_r_1,V_q_1,B,C,D,E) * Partial RF of phase [28,29]: - RF of loop [28:1]: V_r_1 - RF of loop [29:1]: V_q_1 ### Specialization of cost equations eval_sipmamergesort_init_bb7_in/3 * CE 25 is refined into CE [32] * CE 24 is refined into CE [33] ### Cost equations --> "Loop" of eval_sipmamergesort_init_bb7_in/3 * CEs [33] --> Loop 32 * CEs [32] --> Loop 33 ### Ranking functions of CR eval_sipmamergesort_init_bb7_in(V_r_3,B,C) * RF of phase [32]: [V_r_3] #### Partial ranking functions of CR eval_sipmamergesort_init_bb7_in(V_r_3,B,C) * Partial RF of phase [32]: - RF of loop [32:1]: V_r_3 ### Specialization of cost equations eval_sipmamergesort_init_bb9_in/3 * CE 27 is refined into CE [34] * CE 26 is refined into CE [35] ### Cost equations --> "Loop" of eval_sipmamergesort_init_bb9_in/3 * CEs [35] --> Loop 34 * CEs [34] --> Loop 35 ### Ranking functions of CR eval_sipmamergesort_init_bb9_in(V_q_3,B,C) * RF of phase [34]: [V_q_3] #### Partial ranking functions of CR eval_sipmamergesort_init_bb9_in(V_q_3,B,C) * Partial RF of phase [34]: - RF of loop [34:1]: V_q_3 ### Specialization of cost equations eval_sipmamergesort_init_bb2_in/9 * CE 17 is refined into CE [36,37] * CE 16 is discarded (unfeasible) * CE 14 is refined into CE [38,39,40] * CE 12 is refined into CE [41,42,43] * CE 15 is refined into CE [44,45] * CE 13 is discarded (unfeasible) ### Cost equations --> "Loop" of eval_sipmamergesort_init_bb2_in/9 * CEs [40] --> Loop 36 * CEs [45] --> Loop 37 * CEs [42,43] --> Loop 38 * CEs [41] --> Loop 39 * CEs [44] --> Loop 40 * CEs [39] --> Loop 41 * CEs [38] --> Loop 42 * CEs [36,37] --> Loop 43 ### Ranking functions of CR eval_sipmamergesort_init_bb2_in(V_p_0,V_m_0,B,C,D,E,F,G,H) * RF of phase [43]: [V_m_0/2-1,-V_p_0+V_m_0/2] #### Partial ranking functions of CR eval_sipmamergesort_init_bb2_in(V_p_0,V_m_0,B,C,D,E,F,G,H) * Partial RF of phase [43]: - RF of loop [43:1]: V_m_0/2-1 -V_p_0+V_m_0/2 ### Specialization of cost equations eval_sipmamergesort_init_bb1_in/5 * CE 7 is refined into CE [46,47,48,49,50,51] * CE 8 is discarded (unfeasible) * CE 6 is refined into CE [52,53,54,55,56,57] * CE 4 is refined into CE [58,59,60,61,62,63,64] * CE 5 is discarded (unfeasible) * CE 3 is refined into CE [65,66,67,68,69,70,71] ### Cost equations --> "Loop" of eval_sipmamergesort_init_bb1_in/5 * CEs [59,64] --> Loop 44 * CEs [61] --> Loop 45 * CEs [62] --> Loop 46 * CEs [58] --> Loop 47 * CEs [60,63] --> Loop 48 * CEs [66,71] --> Loop 49 * CEs [68] --> Loop 50 * CEs [69] --> Loop 51 * CEs [65] --> Loop 52 * CEs [67,70] --> Loop 53 * CEs [46] --> Loop 54 * CEs [48] --> Loop 55 * CEs [49,51] --> Loop 56 * CEs [47,50] --> Loop 57 * CEs [52] --> Loop 58 * CEs [54] --> Loop 59 * CEs [53,56] --> Loop 60 * CEs [55,57] --> Loop 61 ### Ranking functions of CR eval_sipmamergesort_init_bb1_in(V_n,V_up_0,V_p_0,B,C) * RF of phase [54,55,56,57,58,59,60,61]: [V_n/2-V_p_0,V_n/2+V_up_0/3-2/3*V_p_0-1,V_n/3+V_up_0/3-2/3*V_p_0] #### Partial ranking functions of CR eval_sipmamergesort_init_bb1_in(V_n,V_up_0,V_p_0,B,C) * Partial RF of phase [54,55,56,57,58,59,60,61]: - RF of loop [54:1]: V_n/3-V_p_0+1/3 - RF of loop [54:1,55:1,56:1,57:1]: V_up_0 depends on loops [58:1,59:1,60:1,61:1] - RF of loop [55:1,59:1]: V_n/4-V_p_0/2 - RF of loop [56:1,61:1]: V_n/6-V_p_0/2 - RF of loop [57:1]: V_n/4-V_p_0+1/4 - RF of loop [58:1]: V_n/6-V_p_0/2+1/6 - RF of loop [58:1,59:1,60:1,61:1]: -V_up_0+1 depends on loops [54:1,55:1,56:1,57:1] - RF of loop [60:1]: V_n/8-V_p_0/2+1/8 ### Specialization of cost equations eval_sipmamergesort_init_bb14_in/3 * CE 19 is refined into CE [72] * CE 18 is refined into CE [73] ### Cost equations --> "Loop" of eval_sipmamergesort_init_bb14_in/3 * CEs [73] --> Loop 62 * CEs [72] --> Loop 63 ### Ranking functions of CR eval_sipmamergesort_init_bb14_in(V_n,V_i_5,B) * RF of phase [62]: [V_n-V_i_5+1] #### Partial ranking functions of CR eval_sipmamergesort_init_bb14_in(V_n,V_i_5,B) * Partial RF of phase [62]: - RF of loop [62:1]: V_n-V_i_5+1 ### Specialization of cost equations eval_sipmamergesort_init_bb13_in/3 * CE 10 is refined into CE [74] * CE 9 is refined into CE [75] * CE 11 is refined into CE [76,77] ### Cost equations --> "Loop" of eval_sipmamergesort_init_bb13_in/3 * CEs [74] --> Loop 64 * CEs [75] --> Loop 65 * CEs [77] --> Loop 66 * CEs [76] --> Loop 67 ### Ranking functions of CR eval_sipmamergesort_init_bb13_in(V_n,V_26,B) #### Partial ranking functions of CR eval_sipmamergesort_init_bb13_in(V_n,V_26,B) ### Specialization of cost equations eval_sipmamergesort_init_bb0_in/2 * CE 2 is refined into CE [78,79,80,81,82,83,84] ### Cost equations --> "Loop" of eval_sipmamergesort_init_bb0_in/2 * CEs [81] --> Loop 68 * CEs [82] --> Loop 69 * CEs [83] --> Loop 70 * CEs [84] --> Loop 71 * CEs [79] --> Loop 72 * CEs [80] --> Loop 73 * CEs [78] --> Loop 74 ### Ranking functions of CR eval_sipmamergesort_init_bb0_in(V_n,B) #### Partial ranking functions of CR eval_sipmamergesort_init_bb0_in(V_n,B) ### Specialization of cost equations eval_sipmamergesort_init_start/2 * CE 1 is refined into CE [85,86,87,88,89,90,91] ### Cost equations --> "Loop" of eval_sipmamergesort_init_start/2 * CEs [91] --> Loop 75 * CEs [90] --> Loop 76 * CEs [89] --> Loop 77 * CEs [88] --> Loop 78 * CEs [87] --> Loop 79 * CEs [86] --> Loop 80 * CEs [85] --> Loop 81 ### Ranking functions of CR eval_sipmamergesort_init_start(V_n,B) #### Partial ranking functions of CR eval_sipmamergesort_init_start(V_n,B) Computing Bounds ===================================== #### Cost of chains of eval_sipmamergesort_init_bb3_in(V_r_1,V_q_1,B,C,D,E): * Chain [[28,29],31]: 1*it(28)+1*it(29)+0 Such that:it(28) =< V_r_1 aux(1) =< V_r_1+V_q_1 aux(2) =< V_r_1+V_q_1-D it(29) =< V_q_1-D it(28) =< aux(1) it(29) =< aux(1) it(28) =< aux(2) it(29) =< aux(2) with precondition: [B=4,C=0,E=0,V_r_1>=1,D>=1,V_q_1>=D] * Chain [[28,29],30]: 1*it(28)+1*it(29)+0 Such that:aux(1) =< V_r_1+V_q_1 aux(2) =< V_r_1+V_q_1-E it(28) =< V_r_1-E it(29) =< V_q_1 it(28) =< aux(1) it(29) =< aux(1) it(28) =< aux(2) it(29) =< aux(2) with precondition: [B=4,D=0,C=E,V_q_1>=1,C>=1,V_r_1>=C] * Chain [31]: 0 with precondition: [V_r_1=0,B=4,C=0,E=0,D=V_q_1] * Chain [30]: 0 with precondition: [B=4,V_r_1=C,V_q_1=D,V_r_1=E,0>=V_q_1,V_r_1>=0] #### Cost of chains of eval_sipmamergesort_init_bb7_in(V_r_3,B,C): * Chain [[32],33]: 1*it(32)+0 Such that:it(32) =< V_r_3 with precondition: [B=3,C=0,V_r_3>=1] * Chain [33]: 0 with precondition: [B=3,V_r_3=C,0>=V_r_3] #### Cost of chains of eval_sipmamergesort_init_bb9_in(V_q_3,B,C): * Chain [[34],35]: 1*it(34)+0 Such that:it(34) =< V_q_3 with precondition: [B=2,C=0,V_q_3>=1] * Chain [35]: 0 with precondition: [B=2,V_q_3=C,0>=V_q_3] #### Cost of chains of eval_sipmamergesort_init_bb2_in(V_p_0,V_m_0,B,C,D,E,F,G,H): * Chain [[43],42]: 1*it(43)+1*s(1)+6*s(15)+0 Such that:aux(10) =< V_m_0/2 it(43) =< V_m_0/2-F aux(11) =< V_m_0/2-F/2 s(1) =< F aux(9) =< aux(10) it(43) =< aux(10) aux(9) =< aux(11) it(43) =< aux(11) s(16) =< aux(9)*2 s(15) =< aux(9) s(15) =< s(16) with precondition: [B=5,D=0,E=0,G=0,H=0,V_p_0=C,V_p_0=F,V_p_0>=1,V_m_0>=3*V_p_0] * Chain [[43],41]: 1*it(43)+6*s(15)+1*s(18)+2*s(21)+0 Such that:it(43) =< -V_p_0+V_m_0/2 s(18) =< -V_p_0+C aux(12) =< V_p_0 aux(10) =< V_m_0/2 aux(11) =< V_m_0/2-C/2 aux(13) =< C s(21) =< aux(12) s(21) =< aux(13) s(18) =< aux(13) aux(9) =< aux(10) it(43) =< aux(10) aux(9) =< aux(11) it(43) =< aux(11) s(16) =< aux(9)*2 s(15) =< aux(9) s(15) =< s(16) with precondition: [B=5,D=0,E=0,G=0,H=0,F>=1,C>=V_p_0+1,2*V_p_0>=C+1,V_p_0>=F,V_m_0>=2*V_p_0+C] * Chain [[43],40]: 1*it(43)+6*s(15)+3*s(23)+0 Such that:aux(15) =< V_p_0 aux(14) =< 2*V_p_0 aux(10) =< V_m_0/2 aux(16) =< -V_p_0+V_m_0/2 it(43) =< aux(16) s(23) =< aux(14) s(23) =< aux(15) aux(9) =< aux(10) it(43) =< aux(10) aux(9) =< aux(16) s(16) =< aux(9)*2 s(15) =< aux(9) s(15) =< s(16) with precondition: [B=5,D=0,E=0,G=0,H=0,2*V_p_0=C,F>=1,V_m_0>=4*V_p_0,V_p_0>=F] * Chain [[43],39]: 1*it(43)+6*s(15)+1*s(28)+0 Such that:it(43) =< -V_p_0+V_m_0/2 aux(10) =< V_m_0/2 aux(11) =< V_m_0/2-F/2 s(28) =< F aux(9) =< aux(10) it(43) =< aux(10) aux(9) =< aux(11) it(43) =< aux(11) s(16) =< aux(9)*2 s(15) =< aux(9) s(15) =< s(16) with precondition: [B=5,D=0,E=0,G=0,H=0,C=F,C>=1,V_p_0>=C+1,V_m_0>=2*V_p_0+C] * Chain [[43],37]: 1*it(43)+6*s(15)+3*s(31)+0 Such that:aux(18) =< V_p_0 aux(17) =< 2*V_p_0 aux(10) =< V_m_0/2 aux(19) =< -V_p_0+V_m_0/2 it(43) =< aux(19) s(31) =< aux(17) s(31) =< aux(18) aux(9) =< aux(10) it(43) =< aux(10) aux(9) =< aux(19) s(16) =< aux(9)*2 s(15) =< aux(9) s(15) =< s(16) with precondition: [B=5,D=0,F=0,G=0,H=0,2*V_p_0=C,E>=1,V_m_0>=4*V_p_0,V_p_0>=E] * Chain [[43],36]: 1*it(43)+6*s(15)+2*s(36)+1*s(37)+0 Such that:it(43) =< -V_p_0+V_m_0/2 aux(20) =< -V_p_0+C s(37) =< V_p_0 aux(10) =< V_m_0/2 aux(11) =< V_m_0/2-C/2 aux(21) =< C s(36) =< aux(20) s(36) =< aux(21) s(37) =< aux(21) aux(9) =< aux(10) it(43) =< aux(10) aux(9) =< aux(11) it(43) =< aux(11) s(16) =< aux(9)*2 s(15) =< aux(9) s(15) =< s(16) with precondition: [B=5,D=0,F=0,G=0,H=0,E>=1,2*V_p_0>=C+1,V_m_0>=2*V_p_0+C,C>=V_p_0+E] * Chain [42]: 1*s(1)+0 Such that:s(1) =< V_m_0 with precondition: [B=5,D=0,E=0,G=0,H=0,V_p_0=V_m_0,V_p_0=C,V_p_0=F,V_p_0>=1] * Chain [41]: 1*s(18)+2*s(21)+0 Such that:s(18) =< -V_p_0+V_m_0 aux(12) =< V_p_0 aux(13) =< V_m_0 s(21) =< aux(12) s(21) =< aux(13) s(18) =< aux(13) with precondition: [B=5,D=0,E=0,G=0,H=0,C=V_m_0,F>=1,C>=V_p_0+1,2*V_p_0>=C+1,V_p_0>=F] * Chain [40]: 3*s(23)+0 Such that:aux(14) =< V_m_0 aux(15) =< V_m_0/2 s(23) =< aux(14) s(23) =< aux(15) with precondition: [B=5,D=0,E=0,G=0,H=0,2*V_p_0=V_m_0,2*V_p_0=C,F>=1,V_p_0>=F] * Chain [39]: 1*s(28)+0 Such that:s(28) =< V_m_0 with precondition: [B=5,D=0,E=0,G=0,H=0,V_m_0=C,V_m_0=F,V_m_0>=1,V_p_0>=V_m_0+1] * Chain [38]: 0 with precondition: [B=5,D=0,E=0,G=0,V_m_0=C,V_m_0=F,V_m_0=H,0>=V_m_0,V_p_0>=1] * Chain [37]: 3*s(31)+0 Such that:aux(17) =< V_m_0 aux(18) =< V_m_0/2 s(31) =< aux(17) s(31) =< aux(18) with precondition: [B=5,D=0,F=0,G=0,H=0,2*V_p_0=V_m_0,2*V_p_0=C,E>=1,V_p_0>=E] * Chain [36]: 2*s(36)+1*s(37)+0 Such that:s(37) =< V_p_0 aux(20) =< -V_p_0+V_m_0 aux(21) =< V_m_0 s(36) =< aux(20) s(36) =< aux(21) s(37) =< aux(21) with precondition: [B=5,D=0,F=0,G=0,H=0,V_m_0=C,E>=1,2*V_p_0>=V_m_0+1,V_m_0>=V_p_0+E] #### Cost of chains of eval_sipmamergesort_init_bb1_in(V_n,V_up_0,V_p_0,B,C): * Chain [[54,55,56,57,58,59,60,61],53]: 1*it(54)+1*it(55)+1*it(56)+1*it(57)+1*it(58)+1*it(59)+1*it(60)+1*it(61)+6*s(41)+1*s(229)+2*s(230)+6*s(231)+1*s(236)+1*s(237)+6*s(238)+2*s(244)+1*s(245)+3*s(246)+12*s(247)+2*s(248)+2*s(260)+12*s(261)+12*s(262)+1*s(269)+6*s(271)+1*s(276)+1*s(277)+6*s(278)+2*s(284)+12*s(286)+2*s(293)+1*s(294)+3*s(295)+12*s(296)+2*s(297)+0 Such that:aux(23) =< V_n aux(106) =< V_n-V_p_0 aux(108) =< V_n/2+V_up_0/3-2/3*V_p_0 aux(64) =< V_n/2-V_p_0/2 aux(114) =< V_n/3-V_p_0+1/3 it(57) =< V_n/4-V_p_0+1/4 aux(119) =< V_n/6-V_p_0/2 it(58) =< V_n/6-V_p_0/2+1/6 it(60) =< V_n/8-V_p_0/2+1/8 aux(122) =< 2/3*V_n-V_p_0 aux(124) =< 4/3*V_n-2*V_p_0 aux(130) =< V_n-2*V_p_0 aux(131) =< V_n/2 aux(132) =< V_n/2-V_p_0 aux(133) =< V_n/3+V_up_0/3-2/3*V_p_0 aux(134) =< V_n/4-V_p_0/2 s(41) =< aux(23) s(41) =< aux(131) it(58) =< aux(130) it(59) =< aux(130) it(60) =< aux(130) it(61) =< aux(130) it(56) =< aux(106) it(57) =< aux(106) it(58) =< aux(106) it(59) =< aux(106) it(60) =< aux(106) it(61) =< aux(106) s(237) =< aux(106) s(277) =< aux(106) it(56) =< aux(132) it(57) =< aux(132) it(58) =< aux(132) it(59) =< aux(132) it(60) =< aux(132) it(61) =< aux(132) s(237) =< aux(132) s(277) =< aux(132) it(54) =< aux(108) it(55) =< aux(108) it(56) =< aux(108) it(57) =< aux(108) it(58) =< aux(108) it(59) =< aux(108) it(60) =< aux(108) it(61) =< aux(108) it(54) =< aux(133) it(55) =< aux(133) it(56) =< aux(133) it(57) =< aux(133) it(58) =< aux(133) it(59) =< aux(133) it(60) =< aux(133) it(61) =< aux(133) it(54) =< aux(132) it(55) =< aux(132) it(54) =< aux(114) it(60) =< aux(114) it(55) =< aux(134) it(59) =< aux(134) it(60) =< aux(134) it(56) =< aux(134) it(58) =< aux(134) it(61) =< aux(134) it(56) =< aux(119) it(61) =< aux(119) it(55) =< aux(122) it(56) =< aux(122) it(57) =< aux(122) it(58) =< aux(122) it(59) =< aux(122) it(60) =< aux(122) it(61) =< aux(122) s(230) =< aux(122) s(230) =< aux(132) aux(76) =< aux(124) it(57) =< aux(124) it(58) =< aux(124) it(59) =< aux(124) it(60) =< aux(124) it(61) =< aux(124) aux(76) =< aux(130) it(57) =< aux(130) aux(69) =< aux(132) aux(73) =< aux(64)*2 aux(67) =< aux(131)*2 aux(79) =< aux(131) aux(86) =< aux(64) s(251) =< aux(76)*(1/2) s(267) =< aux(130)*(1/2) s(308) =< it(61)*aux(69) aux(101) =< it(61)*aux(67) s(301) =< it(61)*aux(73) s(289) =< it(60)*aux(69) s(290) =< it(60)*aux(79) s(276) =< it(59)*aux(69) aux(90) =< it(59)*aux(67) s(274) =< it(58)*aux(86) s(269) =< it(58)*aux(69) s(275) =< it(58)*aux(79) s(265) =< it(57)*aux(69) s(266) =< it(57)*aux(79) s(259) =< it(56)*aux(69) aux(74) =< it(56)*aux(67) s(252) =< it(56)*aux(73) s(236) =< it(55)*aux(69) aux(68) =< it(55)*aux(67) s(234) =< it(54)*aux(64) s(229) =< it(54)*aux(132) s(235) =< it(54)*aux(131) s(305) =< aux(101)*(1/2) s(282) =< aux(90)*(1/2) s(256) =< aux(74)*(1/2) s(242) =< aux(68)*(1/2) s(293) =< s(308) s(298) =< aux(76) s(304) =< aux(101) s(298) =< aux(101) s(294) =< s(301) s(304) =< s(301) s(294) =< s(251) s(295) =< s(251) s(295) =< s(298) s(294) =< s(298) s(303) =< s(305) s(293) =< s(305) s(303) =< s(304) s(293) =< s(304) s(302) =< s(303)*2 s(296) =< s(303) s(296) =< s(302) s(299) =< s(301) s(299) =< s(251) s(297) =< s(299) s(297) =< s(298) s(284) =< s(289) s(261) =< aux(130) s(261) =< s(267) s(288) =< s(290) s(284) =< s(290) s(288) =< s(289) s(287) =< s(288)*2 s(286) =< s(288) s(286) =< s(287) s(281) =< aux(90) s(277) =< aux(90) s(281) =< s(282) s(280) =< s(282) s(276) =< s(282) s(280) =< s(281) s(276) =< s(281) s(279) =< s(280)*2 s(278) =< s(280) s(278) =< s(279) s(273) =< s(275) s(269) =< s(275) s(273) =< s(274) s(269) =< s(274) s(272) =< s(273)*2 s(271) =< s(273) s(271) =< s(272) s(260) =< s(265) s(264) =< s(266) s(260) =< s(266) s(264) =< s(265) s(263) =< s(264)*2 s(262) =< s(264) s(262) =< s(263) s(244) =< s(259) s(249) =< aux(76) s(255) =< aux(74) s(249) =< aux(74) s(245) =< s(252) s(255) =< s(252) s(245) =< s(251) s(246) =< s(251) s(246) =< s(249) s(245) =< s(249) s(254) =< s(256) s(244) =< s(256) s(254) =< s(255) s(244) =< s(255) s(253) =< s(254)*2 s(247) =< s(254) s(247) =< s(253) s(250) =< s(252) s(250) =< s(251) s(248) =< s(250) s(248) =< s(249) s(241) =< aux(68) s(237) =< aux(68) s(241) =< s(242) s(240) =< s(242) s(236) =< s(242) s(240) =< s(241) s(236) =< s(241) s(239) =< s(240)*2 s(238) =< s(240) s(238) =< s(239) s(233) =< s(235) s(229) =< s(235) s(233) =< s(234) s(229) =< s(234) s(232) =< s(233)*2 s(231) =< s(233) s(231) =< s(232) with precondition: [B=7,C=1,1>=V_up_0,V_up_0>=0,V_p_0+V_up_0>=2,V_n+8*V_up_0>=4*V_p_0+8] * Chain [[54,55,56,57,58,59,60,61],49]: 1*it(54)+1*it(55)+1*it(56)+1*it(57)+1*it(58)+1*it(59)+1*it(60)+1*it(61)+1*s(229)+2*s(230)+6*s(231)+1*s(236)+1*s(237)+6*s(238)+2*s(244)+1*s(245)+3*s(246)+12*s(247)+2*s(248)+2*s(260)+12*s(261)+12*s(262)+1*s(269)+6*s(271)+1*s(276)+1*s(277)+6*s(278)+2*s(284)+12*s(286)+2*s(293)+1*s(294)+3*s(295)+12*s(296)+2*s(297)+3*s(309)+3*s(312)+0 Such that:aux(104) =< V_n-2*V_p_0 aux(62) =< V_n/2 aux(108) =< V_n/2+V_up_0/3-2/3*V_p_0 aux(110) =< V_n/2-V_p_0 aux(112) =< V_n/3+V_up_0/3-2/3*V_p_0 aux(114) =< V_n/3-V_p_0+1/3 it(57) =< V_n/4-V_p_0+1/4 aux(117) =< V_n/4-V_p_0/2 aux(119) =< V_n/6-V_p_0/2 it(58) =< V_n/6-V_p_0/2+1/6 it(60) =< V_n/8-V_p_0/2+1/8 aux(122) =< 2/3*V_n-V_p_0 aux(124) =< 4/3*V_n-2*V_p_0 aux(138) =< V_n aux(139) =< V_n-V_p_0 aux(140) =< 2*V_n+V_up_0-2*V_p_0 aux(141) =< 2*V_n-2*V_p_0 aux(142) =< V_n/2-V_p_0/2 aux(143) =< 2/3*V_n+V_up_0/3-2/3*V_p_0 aux(136) =< aux(138) aux(118) =< aux(139) aux(109) =< aux(140) aux(136) =< aux(141) aux(118) =< aux(142) aux(109) =< aux(143) s(309) =< aux(136) s(312) =< aux(138) s(309) =< aux(138) aux(81) =< aux(104) it(58) =< aux(104) it(59) =< aux(104) it(60) =< aux(104) it(61) =< aux(104) aux(81) =< aux(141) it(58) =< aux(141) it(59) =< aux(141) it(60) =< aux(141) it(61) =< aux(141) it(56) =< aux(139) it(57) =< aux(139) it(58) =< aux(139) it(59) =< aux(139) it(60) =< aux(139) it(61) =< aux(139) s(237) =< aux(139) s(277) =< aux(139) it(54) =< aux(108) it(55) =< aux(108) it(56) =< aux(108) it(57) =< aux(108) it(58) =< aux(108) it(59) =< aux(108) it(60) =< aux(108) it(61) =< aux(108) it(54) =< aux(109) it(55) =< aux(109) it(56) =< aux(109) it(57) =< aux(109) it(58) =< aux(109) it(59) =< aux(109) it(60) =< aux(109) it(61) =< aux(109) it(54) =< aux(110) it(55) =< aux(110) it(56) =< aux(110) it(57) =< aux(110) it(58) =< aux(110) it(59) =< aux(110) it(60) =< aux(110) it(61) =< aux(110) it(54) =< aux(139) it(55) =< aux(139) it(54) =< aux(112) it(55) =< aux(112) it(56) =< aux(112) it(57) =< aux(112) it(58) =< aux(112) it(59) =< aux(112) it(60) =< aux(112) it(61) =< aux(112) it(54) =< aux(114) it(60) =< aux(114) it(55) =< aux(117) it(59) =< aux(117) it(60) =< aux(117) it(55) =< aux(118) it(56) =< aux(118) it(58) =< aux(118) it(59) =< aux(118) it(60) =< aux(118) it(61) =< aux(118) it(56) =< aux(119) it(61) =< aux(119) it(55) =< aux(122) it(56) =< aux(122) it(57) =< aux(122) it(58) =< aux(122) it(59) =< aux(122) it(60) =< aux(122) it(61) =< aux(122) s(230) =< aux(122) s(230) =< aux(139) aux(76) =< aux(124) it(57) =< aux(124) it(58) =< aux(124) it(59) =< aux(124) it(60) =< aux(124) it(61) =< aux(124) aux(76) =< aux(141) it(57) =< aux(141) aux(69) =< aux(110) aux(73) =< aux(142)*2 aux(67) =< aux(62)*2 aux(79) =< aux(62) aux(86) =< aux(142) s(251) =< aux(76)*(1/2) s(267) =< aux(81)*(1/2) s(308) =< it(61)*aux(69) aux(101) =< it(61)*aux(67) s(301) =< it(61)*aux(73) s(289) =< it(60)*aux(69) s(290) =< it(60)*aux(79) s(276) =< it(59)*aux(69) aux(90) =< it(59)*aux(67) s(274) =< it(58)*aux(86) s(269) =< it(58)*aux(69) s(275) =< it(58)*aux(79) s(265) =< it(57)*aux(69) s(266) =< it(57)*aux(79) s(259) =< it(56)*aux(69) aux(74) =< it(56)*aux(67) s(252) =< it(56)*aux(73) s(236) =< it(55)*aux(69) aux(68) =< it(55)*aux(67) s(234) =< it(54)*aux(142) s(229) =< it(54)*aux(110) s(235) =< it(54)*aux(62) s(305) =< aux(101)*(1/2) s(282) =< aux(90)*(1/2) s(256) =< aux(74)*(1/2) s(242) =< aux(68)*(1/2) s(293) =< s(308) s(298) =< aux(76) s(304) =< aux(101) s(298) =< aux(101) s(294) =< s(301) s(304) =< s(301) s(294) =< s(251) s(295) =< s(251) s(295) =< s(298) s(294) =< s(298) s(303) =< s(305) s(293) =< s(305) s(303) =< s(304) s(293) =< s(304) s(302) =< s(303)*2 s(296) =< s(303) s(296) =< s(302) s(299) =< s(301) s(299) =< s(251) s(297) =< s(299) s(297) =< s(298) s(284) =< s(289) s(261) =< aux(81) s(261) =< s(267) s(288) =< s(290) s(284) =< s(290) s(288) =< s(289) s(287) =< s(288)*2 s(286) =< s(288) s(286) =< s(287) s(281) =< aux(90) s(277) =< aux(90) s(281) =< s(282) s(280) =< s(282) s(276) =< s(282) s(280) =< s(281) s(276) =< s(281) s(279) =< s(280)*2 s(278) =< s(280) s(278) =< s(279) s(273) =< s(275) s(269) =< s(275) s(273) =< s(274) s(269) =< s(274) s(272) =< s(273)*2 s(271) =< s(273) s(271) =< s(272) s(260) =< s(265) s(264) =< s(266) s(260) =< s(266) s(264) =< s(265) s(263) =< s(264)*2 s(262) =< s(264) s(262) =< s(263) s(244) =< s(259) s(249) =< aux(76) s(255) =< aux(74) s(249) =< aux(74) s(245) =< s(252) s(255) =< s(252) s(245) =< s(251) s(246) =< s(251) s(246) =< s(249) s(245) =< s(249) s(254) =< s(256) s(244) =< s(256) s(254) =< s(255) s(244) =< s(255) s(253) =< s(254)*2 s(247) =< s(254) s(247) =< s(253) s(250) =< s(252) s(250) =< s(251) s(248) =< s(250) s(248) =< s(249) s(241) =< aux(68) s(237) =< aux(68) s(241) =< s(242) s(240) =< s(242) s(236) =< s(242) s(240) =< s(241) s(236) =< s(241) s(239) =< s(240)*2 s(238) =< s(240) s(238) =< s(239) s(233) =< s(235) s(229) =< s(235) s(233) =< s(234) s(229) =< s(234) s(232) =< s(233)*2 s(231) =< s(233) s(231) =< s(232) with precondition: [B=7,C=1,1>=V_up_0,V_up_0>=0,V_p_0+V_up_0>=2,V_n+4*V_up_0>=2*V_p_0+5] * Chain [[54,55,56,57,58,59,60,61],48]: 1*it(54)+1*it(55)+1*it(56)+1*it(57)+1*it(58)+1*it(59)+1*it(60)+1*it(61)+1*s(229)+2*s(230)+6*s(231)+1*s(236)+1*s(237)+6*s(238)+2*s(244)+1*s(245)+3*s(246)+12*s(247)+2*s(248)+2*s(260)+12*s(261)+12*s(262)+1*s(269)+6*s(271)+1*s(276)+1*s(277)+6*s(278)+2*s(284)+12*s(286)+2*s(293)+1*s(294)+3*s(295)+12*s(296)+2*s(297)+6*s(319)+0 Such that:aux(145) =< V_n aux(106) =< V_n-V_p_0 aux(108) =< V_n/2+V_up_0/3-2/3*V_p_0 aux(64) =< V_n/2-V_p_0/2 aux(114) =< V_n/3-V_p_0+1/3 it(57) =< V_n/4-V_p_0+1/4 aux(119) =< V_n/6-V_p_0/2 it(58) =< V_n/6-V_p_0/2+1/6 it(60) =< V_n/8-V_p_0/2+1/8 aux(122) =< 2/3*V_n-V_p_0 aux(124) =< 4/3*V_n-2*V_p_0 aux(146) =< V_n-2*V_p_0 aux(147) =< V_n/2 aux(148) =< V_n/2-V_p_0 aux(149) =< V_n/3+V_up_0/3-2/3*V_p_0 aux(150) =< V_n/4-V_p_0/2 s(319) =< aux(145) s(319) =< aux(147) it(58) =< aux(146) it(59) =< aux(146) it(60) =< aux(146) it(61) =< aux(146) it(56) =< aux(106) it(57) =< aux(106) it(58) =< aux(106) it(59) =< aux(106) it(60) =< aux(106) it(61) =< aux(106) s(237) =< aux(106) s(277) =< aux(106) it(56) =< aux(148) it(57) =< aux(148) it(58) =< aux(148) it(59) =< aux(148) it(60) =< aux(148) it(61) =< aux(148) s(237) =< aux(148) s(277) =< aux(148) it(54) =< aux(108) it(55) =< aux(108) it(56) =< aux(108) it(57) =< aux(108) it(58) =< aux(108) it(59) =< aux(108) it(60) =< aux(108) it(61) =< aux(108) it(54) =< aux(149) it(55) =< aux(149) it(56) =< aux(149) it(57) =< aux(149) it(58) =< aux(149) it(59) =< aux(149) it(60) =< aux(149) it(61) =< aux(149) it(54) =< aux(148) it(55) =< aux(148) it(54) =< aux(114) it(60) =< aux(114) it(55) =< aux(150) it(59) =< aux(150) it(60) =< aux(150) it(56) =< aux(150) it(58) =< aux(150) it(61) =< aux(150) it(56) =< aux(119) it(61) =< aux(119) it(55) =< aux(122) it(56) =< aux(122) it(57) =< aux(122) it(58) =< aux(122) it(59) =< aux(122) it(60) =< aux(122) it(61) =< aux(122) s(230) =< aux(122) s(230) =< aux(148) aux(76) =< aux(124) it(57) =< aux(124) it(58) =< aux(124) it(59) =< aux(124) it(60) =< aux(124) it(61) =< aux(124) aux(76) =< aux(146) it(57) =< aux(146) aux(69) =< aux(148) aux(73) =< aux(64)*2 aux(67) =< aux(147)*2 aux(79) =< aux(147) aux(86) =< aux(64) s(251) =< aux(76)*(1/2) s(267) =< aux(146)*(1/2) s(308) =< it(61)*aux(69) aux(101) =< it(61)*aux(67) s(301) =< it(61)*aux(73) s(289) =< it(60)*aux(69) s(290) =< it(60)*aux(79) s(276) =< it(59)*aux(69) aux(90) =< it(59)*aux(67) s(274) =< it(58)*aux(86) s(269) =< it(58)*aux(69) s(275) =< it(58)*aux(79) s(265) =< it(57)*aux(69) s(266) =< it(57)*aux(79) s(259) =< it(56)*aux(69) aux(74) =< it(56)*aux(67) s(252) =< it(56)*aux(73) s(236) =< it(55)*aux(69) aux(68) =< it(55)*aux(67) s(234) =< it(54)*aux(64) s(229) =< it(54)*aux(148) s(235) =< it(54)*aux(147) s(305) =< aux(101)*(1/2) s(282) =< aux(90)*(1/2) s(256) =< aux(74)*(1/2) s(242) =< aux(68)*(1/2) s(293) =< s(308) s(298) =< aux(76) s(304) =< aux(101) s(298) =< aux(101) s(294) =< s(301) s(304) =< s(301) s(294) =< s(251) s(295) =< s(251) s(295) =< s(298) s(294) =< s(298) s(303) =< s(305) s(293) =< s(305) s(303) =< s(304) s(293) =< s(304) s(302) =< s(303)*2 s(296) =< s(303) s(296) =< s(302) s(299) =< s(301) s(299) =< s(251) s(297) =< s(299) s(297) =< s(298) s(284) =< s(289) s(261) =< aux(146) s(261) =< s(267) s(288) =< s(290) s(284) =< s(290) s(288) =< s(289) s(287) =< s(288)*2 s(286) =< s(288) s(286) =< s(287) s(281) =< aux(90) s(277) =< aux(90) s(281) =< s(282) s(280) =< s(282) s(276) =< s(282) s(280) =< s(281) s(276) =< s(281) s(279) =< s(280)*2 s(278) =< s(280) s(278) =< s(279) s(273) =< s(275) s(269) =< s(275) s(273) =< s(274) s(269) =< s(274) s(272) =< s(273)*2 s(271) =< s(273) s(271) =< s(272) s(260) =< s(265) s(264) =< s(266) s(260) =< s(266) s(264) =< s(265) s(263) =< s(264)*2 s(262) =< s(264) s(262) =< s(263) s(244) =< s(259) s(249) =< aux(76) s(255) =< aux(74) s(249) =< aux(74) s(245) =< s(252) s(255) =< s(252) s(245) =< s(251) s(246) =< s(251) s(246) =< s(249) s(245) =< s(249) s(254) =< s(256) s(244) =< s(256) s(254) =< s(255) s(244) =< s(255) s(253) =< s(254)*2 s(247) =< s(254) s(247) =< s(253) s(250) =< s(252) s(250) =< s(251) s(248) =< s(250) s(248) =< s(249) s(241) =< aux(68) s(237) =< aux(68) s(241) =< s(242) s(240) =< s(242) s(236) =< s(242) s(240) =< s(241) s(236) =< s(241) s(239) =< s(240)*2 s(238) =< s(240) s(238) =< s(239) s(233) =< s(235) s(229) =< s(235) s(233) =< s(234) s(229) =< s(234) s(232) =< s(233)*2 s(231) =< s(233) s(231) =< s(232) with precondition: [B=7,C=0,1>=V_up_0,V_up_0>=0,V_p_0+V_up_0>=2,V_n>=4*V_p_0+4*V_up_0] * Chain [[54,55,56,57,58,59,60,61],44]: 1*it(54)+1*it(55)+1*it(56)+1*it(57)+1*it(58)+1*it(59)+1*it(60)+1*it(61)+1*s(229)+2*s(230)+6*s(231)+1*s(236)+1*s(237)+6*s(238)+2*s(244)+1*s(245)+3*s(246)+12*s(247)+2*s(248)+2*s(260)+12*s(261)+12*s(262)+1*s(269)+6*s(271)+1*s(276)+1*s(277)+6*s(278)+2*s(284)+12*s(286)+2*s(293)+1*s(294)+3*s(295)+12*s(296)+2*s(297)+3*s(323)+3*s(326)+0 Such that:aux(104) =< V_n-2*V_p_0 aux(62) =< V_n/2 aux(108) =< V_n/2+V_up_0/3-2/3*V_p_0 aux(110) =< V_n/2-V_p_0 aux(112) =< V_n/3+V_up_0/3-2/3*V_p_0 aux(114) =< V_n/3-V_p_0+1/3 it(57) =< V_n/4-V_p_0+1/4 aux(117) =< V_n/4-V_p_0/2 aux(119) =< V_n/6-V_p_0/2 it(58) =< V_n/6-V_p_0/2+1/6 it(60) =< V_n/8-V_p_0/2+1/8 aux(122) =< 2/3*V_n-V_p_0 aux(124) =< 4/3*V_n-2*V_p_0 aux(154) =< V_n aux(155) =< V_n-V_p_0 aux(156) =< 2*V_n+V_up_0-2*V_p_0 aux(157) =< 2*V_n-2*V_p_0 aux(158) =< V_n/2-V_p_0/2 aux(159) =< 2/3*V_n+V_up_0/3-2/3*V_p_0 aux(152) =< aux(154) aux(118) =< aux(155) aux(109) =< aux(156) aux(152) =< aux(157) aux(118) =< aux(158) aux(109) =< aux(159) s(323) =< aux(152) s(326) =< aux(154) s(323) =< aux(154) aux(81) =< aux(104) it(58) =< aux(104) it(59) =< aux(104) it(60) =< aux(104) it(61) =< aux(104) aux(81) =< aux(157) it(58) =< aux(157) it(59) =< aux(157) it(60) =< aux(157) it(61) =< aux(157) it(56) =< aux(155) it(57) =< aux(155) it(58) =< aux(155) it(59) =< aux(155) it(60) =< aux(155) it(61) =< aux(155) s(237) =< aux(155) s(277) =< aux(155) it(54) =< aux(108) it(55) =< aux(108) it(56) =< aux(108) it(57) =< aux(108) it(58) =< aux(108) it(59) =< aux(108) it(60) =< aux(108) it(61) =< aux(108) it(54) =< aux(109) it(55) =< aux(109) it(56) =< aux(109) it(57) =< aux(109) it(58) =< aux(109) it(59) =< aux(109) it(60) =< aux(109) it(61) =< aux(109) it(54) =< aux(110) it(55) =< aux(110) it(56) =< aux(110) it(57) =< aux(110) it(58) =< aux(110) it(59) =< aux(110) it(60) =< aux(110) it(61) =< aux(110) it(54) =< aux(155) it(55) =< aux(155) it(54) =< aux(112) it(55) =< aux(112) it(56) =< aux(112) it(57) =< aux(112) it(58) =< aux(112) it(59) =< aux(112) it(60) =< aux(112) it(61) =< aux(112) it(54) =< aux(114) it(60) =< aux(114) it(55) =< aux(117) it(59) =< aux(117) it(60) =< aux(117) it(55) =< aux(118) it(56) =< aux(118) it(58) =< aux(118) it(59) =< aux(118) it(60) =< aux(118) it(61) =< aux(118) it(56) =< aux(119) it(61) =< aux(119) it(55) =< aux(122) it(56) =< aux(122) it(57) =< aux(122) it(58) =< aux(122) it(59) =< aux(122) it(60) =< aux(122) it(61) =< aux(122) s(230) =< aux(122) s(230) =< aux(155) aux(76) =< aux(124) it(57) =< aux(124) it(58) =< aux(124) it(59) =< aux(124) it(60) =< aux(124) it(61) =< aux(124) aux(76) =< aux(157) it(57) =< aux(157) aux(69) =< aux(110) aux(73) =< aux(158)*2 aux(67) =< aux(62)*2 aux(79) =< aux(62) aux(86) =< aux(158) s(251) =< aux(76)*(1/2) s(267) =< aux(81)*(1/2) s(308) =< it(61)*aux(69) aux(101) =< it(61)*aux(67) s(301) =< it(61)*aux(73) s(289) =< it(60)*aux(69) s(290) =< it(60)*aux(79) s(276) =< it(59)*aux(69) aux(90) =< it(59)*aux(67) s(274) =< it(58)*aux(86) s(269) =< it(58)*aux(69) s(275) =< it(58)*aux(79) s(265) =< it(57)*aux(69) s(266) =< it(57)*aux(79) s(259) =< it(56)*aux(69) aux(74) =< it(56)*aux(67) s(252) =< it(56)*aux(73) s(236) =< it(55)*aux(69) aux(68) =< it(55)*aux(67) s(234) =< it(54)*aux(158) s(229) =< it(54)*aux(110) s(235) =< it(54)*aux(62) s(305) =< aux(101)*(1/2) s(282) =< aux(90)*(1/2) s(256) =< aux(74)*(1/2) s(242) =< aux(68)*(1/2) s(293) =< s(308) s(298) =< aux(76) s(304) =< aux(101) s(298) =< aux(101) s(294) =< s(301) s(304) =< s(301) s(294) =< s(251) s(295) =< s(251) s(295) =< s(298) s(294) =< s(298) s(303) =< s(305) s(293) =< s(305) s(303) =< s(304) s(293) =< s(304) s(302) =< s(303)*2 s(296) =< s(303) s(296) =< s(302) s(299) =< s(301) s(299) =< s(251) s(297) =< s(299) s(297) =< s(298) s(284) =< s(289) s(261) =< aux(81) s(261) =< s(267) s(288) =< s(290) s(284) =< s(290) s(288) =< s(289) s(287) =< s(288)*2 s(286) =< s(288) s(286) =< s(287) s(281) =< aux(90) s(277) =< aux(90) s(281) =< s(282) s(280) =< s(282) s(276) =< s(282) s(280) =< s(281) s(276) =< s(281) s(279) =< s(280)*2 s(278) =< s(280) s(278) =< s(279) s(273) =< s(275) s(269) =< s(275) s(273) =< s(274) s(269) =< s(274) s(272) =< s(273)*2 s(271) =< s(273) s(271) =< s(272) s(260) =< s(265) s(264) =< s(266) s(260) =< s(266) s(264) =< s(265) s(263) =< s(264)*2 s(262) =< s(264) s(262) =< s(263) s(244) =< s(259) s(249) =< aux(76) s(255) =< aux(74) s(249) =< aux(74) s(245) =< s(252) s(255) =< s(252) s(245) =< s(251) s(246) =< s(251) s(246) =< s(249) s(245) =< s(249) s(254) =< s(256) s(244) =< s(256) s(254) =< s(255) s(244) =< s(255) s(253) =< s(254)*2 s(247) =< s(254) s(247) =< s(253) s(250) =< s(252) s(250) =< s(251) s(248) =< s(250) s(248) =< s(249) s(241) =< aux(68) s(237) =< aux(68) s(241) =< s(242) s(240) =< s(242) s(236) =< s(242) s(240) =< s(241) s(236) =< s(241) s(239) =< s(240)*2 s(238) =< s(240) s(238) =< s(239) s(233) =< s(235) s(229) =< s(235) s(233) =< s(234) s(229) =< s(234) s(232) =< s(233)*2 s(231) =< s(233) s(231) =< s(232) with precondition: [B=7,C=0,1>=V_up_0,V_up_0>=0,V_p_0+V_up_0>=2,V_n>=2*V_p_0+2*V_up_0+1] * Chain [48]: 6*s(319)+0 Such that:aux(144) =< V_p_0 aux(145) =< 2*V_p_0 s(319) =< aux(145) s(319) =< aux(144) with precondition: [V_up_0=1,B=7,C=0,2*V_p_0=V_n,V_p_0>=1] * Chain [47]: 1*s(331)+0 Such that:s(331) =< 1 with precondition: [V_n=1,V_up_0=1,V_p_0=1,B=7,C=0] * Chain [46]: 0 with precondition: [V_up_0=1,V_p_0=1,B=7,C=0,0>=V_n] #### Cost of chains of eval_sipmamergesort_init_bb14_in(V_n,V_i_5,B): * Chain [[62],63]: 1*it(62)+0 Such that:it(62) =< V_n-V_i_5+1 with precondition: [B=6,V_i_5>=1,V_n>=V_i_5] * Chain [63]: 0 with precondition: [B=6,V_i_5>=1,V_i_5>=V_n+1] #### Cost of chains of eval_sipmamergesort_init_bb13_in(V_n,V_26,B): * Chain [67]: 0 with precondition: [V_26=0,0>=V_n] * Chain [66]: 1*s(332)+0 Such that:s(332) =< V_n with precondition: [V_26=0,V_n>=1] * Chain [65]: 0 with precondition: [0>=V_26+1] * Chain [64]: 0 with precondition: [V_26>=1] #### Cost of chains of eval_sipmamergesort_init_bb0_in(V_n,B): * Chain [74]: 2*s(333)+0 Such that:aux(160) =< 1 s(333) =< aux(160) with precondition: [V_n=1] * Chain [73]: 6*s(337)+1*s(338)+0 Such that:s(335) =< 1 aux(161) =< 2 s(338) =< aux(161) s(337) =< aux(161) s(337) =< s(335) with precondition: [V_n=2] * Chain [72]: 0 with precondition: [0>=V_n] * Chain [71]: 1*s(345)+2*s(348)+1*s(349)+3*s(361)+3*s(362)+1*s(364)+1*s(366)+1*s(367)+1*s(368)+1*s(369)+1*s(370)+2*s(371)+1*s(385)+1*s(388)+1*s(395)+1*s(398)+2*s(404)+1*s(407)+3*s(408)+12*s(411)+2*s(413)+2*s(414)+12*s(415)+12*s(418)+6*s(422)+6*s(425)+2*s(426)+12*s(429)+2*s(430)+1*s(433)+3*s(434)+12*s(437)+2*s(439)+6*s(443)+6*s(446)+0 Such that:s(349) =< V_n/8 s(351) =< 4/3*V_n aux(162) =< V_n aux(163) =< 2*V_n aux(164) =< V_n/2 aux(165) =< V_n/3 aux(166) =< V_n/4 aux(167) =< V_n/6 aux(168) =< 2/3*V_n s(345) =< aux(166) s(348) =< aux(167) s(358) =< aux(162) s(359) =< aux(162) s(360) =< aux(163) s(358) =< aux(163) s(359) =< aux(164) s(360) =< aux(168) s(361) =< s(358) s(362) =< aux(162) s(361) =< aux(162) s(348) =< aux(162) s(364) =< aux(162) s(349) =< aux(162) s(348) =< aux(163) s(364) =< aux(163) s(349) =< aux(163) s(366) =< aux(162) s(345) =< aux(162) s(367) =< aux(162) s(368) =< aux(162) s(369) =< aux(164) s(370) =< aux(164) s(366) =< aux(164) s(345) =< aux(164) s(348) =< aux(164) s(364) =< aux(164) s(349) =< aux(164) s(369) =< s(360) s(370) =< s(360) s(366) =< s(360) s(345) =< s(360) s(348) =< s(360) s(364) =< s(360) s(349) =< s(360) s(369) =< aux(162) s(370) =< aux(162) s(369) =< aux(165) s(370) =< aux(165) s(366) =< aux(165) s(345) =< aux(165) s(348) =< aux(165) s(364) =< aux(165) s(349) =< aux(165) s(370) =< aux(166) s(364) =< aux(166) s(349) =< aux(166) s(370) =< s(359) s(366) =< s(359) s(348) =< s(359) s(364) =< s(359) s(349) =< s(359) s(366) =< aux(167) s(370) =< aux(168) s(366) =< aux(168) s(345) =< aux(168) s(348) =< aux(168) s(364) =< aux(168) s(349) =< aux(168) s(371) =< aux(168) s(371) =< aux(162) s(372) =< s(351) s(345) =< s(351) s(348) =< s(351) s(364) =< s(351) s(349) =< s(351) s(372) =< aux(163) s(345) =< aux(163) s(373) =< aux(164) s(374) =< aux(164)*2 s(378) =< s(372)*(1/2) s(379) =< s(358)*(1/2) s(380) =< s(348)*s(373) s(381) =< s(348)*s(374) s(383) =< s(349)*s(373) s(385) =< s(364)*s(373) s(386) =< s(364)*s(374) s(388) =< s(348)*s(373) s(390) =< s(345)*s(373) s(392) =< s(366)*s(373) s(393) =< s(366)*s(374) s(395) =< s(370)*s(373) s(396) =< s(370)*s(374) s(397) =< s(369)*aux(164) s(398) =< s(369)*aux(164) s(400) =< s(381)*(1/2) s(401) =< s(386)*(1/2) s(402) =< s(393)*(1/2) s(403) =< s(396)*(1/2) s(404) =< s(380) s(405) =< s(372) s(405) =< s(381) s(407) =< s(381) s(407) =< s(378) s(408) =< s(378) s(408) =< s(405) s(407) =< s(405) s(409) =< s(400) s(404) =< s(400) s(409) =< s(381) s(404) =< s(381) s(410) =< s(409)*2 s(411) =< s(409) s(411) =< s(410) s(412) =< s(381) s(412) =< s(378) s(413) =< s(412) s(413) =< s(405) s(414) =< s(383) s(415) =< s(358) s(415) =< s(379) s(417) =< s(383)*2 s(418) =< s(383) s(418) =< s(417) s(419) =< s(386) s(368) =< s(386) s(419) =< s(401) s(420) =< s(401) s(385) =< s(401) s(420) =< s(419) s(385) =< s(419) s(421) =< s(420)*2 s(422) =< s(420) s(422) =< s(421) s(388) =< s(380) s(424) =< s(380)*2 s(425) =< s(380) s(425) =< s(424) s(426) =< s(390) s(428) =< s(390)*2 s(429) =< s(390) s(429) =< s(428) s(430) =< s(392) s(431) =< s(372) s(431) =< s(393) s(433) =< s(393) s(433) =< s(378) s(434) =< s(378) s(434) =< s(431) s(433) =< s(431) s(435) =< s(402) s(430) =< s(402) s(435) =< s(393) s(430) =< s(393) s(436) =< s(435)*2 s(437) =< s(435) s(437) =< s(436) s(438) =< s(393) s(438) =< s(378) s(439) =< s(438) s(439) =< s(431) s(440) =< s(396) s(367) =< s(396) s(440) =< s(403) s(441) =< s(403) s(395) =< s(403) s(441) =< s(440) s(395) =< s(440) s(442) =< s(441)*2 s(443) =< s(441) s(443) =< s(442) s(398) =< s(397) s(445) =< s(397)*2 s(446) =< s(397) s(446) =< s(445) with precondition: [V_n>=3] * Chain [70]: 2*s(452)+2*s(454)+1*s(455)+6*s(463)+1*s(466)+1*s(467)+1*s(468)+1*s(469)+1*s(470)+2*s(471)+1*s(485)+1*s(488)+1*s(495)+1*s(498)+2*s(504)+1*s(507)+3*s(508)+12*s(511)+2*s(513)+2*s(514)+12*s(515)+12*s(518)+6*s(522)+6*s(525)+2*s(526)+12*s(529)+2*s(530)+1*s(533)+3*s(534)+12*s(537)+2*s(539)+6*s(543)+6*s(546)+0 Such that:s(455) =< V_n/8 s(456) =< 2/3*V_n s(457) =< 4/3*V_n aux(169) =< V_n aux(170) =< V_n/2 aux(171) =< V_n/3 aux(172) =< V_n/4 aux(173) =< V_n/6 s(452) =< aux(172) s(454) =< aux(173) s(463) =< aux(169) s(463) =< aux(170) s(454) =< aux(169) s(452) =< aux(169) s(455) =< aux(169) s(466) =< aux(169) s(467) =< aux(169) s(468) =< aux(169) s(466) =< aux(170) s(452) =< aux(170) s(454) =< aux(170) s(455) =< aux(170) s(467) =< aux(170) s(468) =< aux(170) s(469) =< aux(170) s(470) =< aux(170) s(469) =< aux(171) s(470) =< aux(171) s(466) =< aux(171) s(452) =< aux(171) s(454) =< aux(171) s(455) =< aux(171) s(470) =< aux(172) s(455) =< aux(172) s(466) =< aux(172) s(454) =< aux(172) s(466) =< aux(173) s(470) =< s(456) s(466) =< s(456) s(452) =< s(456) s(454) =< s(456) s(455) =< s(456) s(471) =< s(456) s(471) =< aux(170) s(472) =< s(457) s(452) =< s(457) s(454) =< s(457) s(455) =< s(457) s(472) =< aux(169) s(473) =< aux(170) s(474) =< aux(170)*2 s(478) =< s(472)*(1/2) s(479) =< aux(169)*(1/2) s(480) =< s(454)*s(473) s(481) =< s(454)*s(474) s(483) =< s(455)*s(473) s(485) =< s(452)*s(473) s(486) =< s(452)*s(474) s(488) =< s(454)*s(473) s(490) =< s(452)*s(473) s(492) =< s(466)*s(473) s(493) =< s(466)*s(474) s(495) =< s(470)*s(473) s(496) =< s(470)*s(474) s(497) =< s(469)*aux(170) s(498) =< s(469)*aux(170) s(500) =< s(481)*(1/2) s(501) =< s(486)*(1/2) s(502) =< s(493)*(1/2) s(503) =< s(496)*(1/2) s(504) =< s(480) s(505) =< s(472) s(505) =< s(481) s(507) =< s(481) s(507) =< s(478) s(508) =< s(478) s(508) =< s(505) s(507) =< s(505) s(509) =< s(500) s(504) =< s(500) s(509) =< s(481) s(504) =< s(481) s(510) =< s(509)*2 s(511) =< s(509) s(511) =< s(510) s(512) =< s(481) s(512) =< s(478) s(513) =< s(512) s(513) =< s(505) s(514) =< s(483) s(515) =< aux(169) s(515) =< s(479) s(517) =< s(483)*2 s(518) =< s(483) s(518) =< s(517) s(519) =< s(486) s(468) =< s(486) s(519) =< s(501) s(520) =< s(501) s(485) =< s(501) s(520) =< s(519) s(485) =< s(519) s(521) =< s(520)*2 s(522) =< s(520) s(522) =< s(521) s(488) =< s(480) s(524) =< s(480)*2 s(525) =< s(480) s(525) =< s(524) s(526) =< s(490) s(528) =< s(490)*2 s(529) =< s(490) s(529) =< s(528) s(530) =< s(492) s(531) =< s(472) s(531) =< s(493) s(533) =< s(493) s(533) =< s(478) s(534) =< s(478) s(534) =< s(531) s(533) =< s(531) s(535) =< s(502) s(530) =< s(502) s(535) =< s(493) s(530) =< s(493) s(536) =< s(535)*2 s(537) =< s(535) s(537) =< s(536) s(538) =< s(493) s(538) =< s(478) s(539) =< s(538) s(539) =< s(531) s(540) =< s(496) s(467) =< s(496) s(540) =< s(503) s(541) =< s(503) s(495) =< s(503) s(541) =< s(540) s(495) =< s(540) s(542) =< s(541)*2 s(543) =< s(541) s(543) =< s(542) s(498) =< s(497) s(545) =< s(497)*2 s(546) =< s(497) s(546) =< s(545) with precondition: [V_n>=4] * Chain [69]: 1*s(553)+2*s(556)+1*s(557)+3*s(569)+4*s(570)+1*s(572)+1*s(574)+1*s(575)+1*s(576)+1*s(577)+1*s(578)+2*s(579)+1*s(593)+1*s(596)+1*s(603)+1*s(606)+2*s(612)+1*s(615)+3*s(616)+12*s(619)+2*s(621)+2*s(622)+12*s(623)+12*s(626)+6*s(630)+6*s(633)+2*s(634)+12*s(637)+2*s(638)+1*s(641)+3*s(642)+12*s(645)+2*s(647)+6*s(651)+6*s(654)+0 Such that:s(557) =< V_n/8 s(559) =< 4/3*V_n aux(174) =< V_n aux(175) =< 2*V_n aux(176) =< V_n/2 aux(177) =< V_n/3 aux(178) =< V_n/4 aux(179) =< V_n/6 aux(180) =< 2/3*V_n s(570) =< aux(174) s(553) =< aux(178) s(556) =< aux(179) s(566) =< aux(174) s(567) =< aux(174) s(568) =< aux(175) s(566) =< aux(175) s(567) =< aux(176) s(568) =< aux(180) s(569) =< s(566) s(569) =< aux(174) s(556) =< aux(174) s(572) =< aux(174) s(557) =< aux(174) s(556) =< aux(175) s(572) =< aux(175) s(557) =< aux(175) s(574) =< aux(174) s(553) =< aux(174) s(575) =< aux(174) s(576) =< aux(174) s(577) =< aux(176) s(578) =< aux(176) s(574) =< aux(176) s(553) =< aux(176) s(556) =< aux(176) s(572) =< aux(176) s(557) =< aux(176) s(577) =< s(568) s(578) =< s(568) s(574) =< s(568) s(553) =< s(568) s(556) =< s(568) s(572) =< s(568) s(557) =< s(568) s(577) =< aux(174) s(578) =< aux(174) s(577) =< aux(177) s(578) =< aux(177) s(574) =< aux(177) s(553) =< aux(177) s(556) =< aux(177) s(572) =< aux(177) s(557) =< aux(177) s(578) =< aux(178) s(572) =< aux(178) s(557) =< aux(178) s(578) =< s(567) s(574) =< s(567) s(556) =< s(567) s(572) =< s(567) s(557) =< s(567) s(574) =< aux(179) s(578) =< aux(180) s(574) =< aux(180) s(553) =< aux(180) s(556) =< aux(180) s(572) =< aux(180) s(557) =< aux(180) s(579) =< aux(180) s(579) =< aux(174) s(580) =< s(559) s(553) =< s(559) s(556) =< s(559) s(572) =< s(559) s(557) =< s(559) s(580) =< aux(175) s(553) =< aux(175) s(581) =< aux(176) s(582) =< aux(176)*2 s(586) =< s(580)*(1/2) s(587) =< s(566)*(1/2) s(588) =< s(556)*s(581) s(589) =< s(556)*s(582) s(591) =< s(557)*s(581) s(593) =< s(572)*s(581) s(594) =< s(572)*s(582) s(596) =< s(556)*s(581) s(598) =< s(553)*s(581) s(600) =< s(574)*s(581) s(601) =< s(574)*s(582) s(603) =< s(578)*s(581) s(604) =< s(578)*s(582) s(605) =< s(577)*aux(176) s(606) =< s(577)*aux(176) s(608) =< s(589)*(1/2) s(609) =< s(594)*(1/2) s(610) =< s(601)*(1/2) s(611) =< s(604)*(1/2) s(612) =< s(588) s(613) =< s(580) s(613) =< s(589) s(615) =< s(589) s(615) =< s(586) s(616) =< s(586) s(616) =< s(613) s(615) =< s(613) s(617) =< s(608) s(612) =< s(608) s(617) =< s(589) s(612) =< s(589) s(618) =< s(617)*2 s(619) =< s(617) s(619) =< s(618) s(620) =< s(589) s(620) =< s(586) s(621) =< s(620) s(621) =< s(613) s(622) =< s(591) s(623) =< s(566) s(623) =< s(587) s(625) =< s(591)*2 s(626) =< s(591) s(626) =< s(625) s(627) =< s(594) s(576) =< s(594) s(627) =< s(609) s(628) =< s(609) s(593) =< s(609) s(628) =< s(627) s(593) =< s(627) s(629) =< s(628)*2 s(630) =< s(628) s(630) =< s(629) s(596) =< s(588) s(632) =< s(588)*2 s(633) =< s(588) s(633) =< s(632) s(634) =< s(598) s(636) =< s(598)*2 s(637) =< s(598) s(637) =< s(636) s(638) =< s(600) s(639) =< s(580) s(639) =< s(601) s(641) =< s(601) s(641) =< s(586) s(642) =< s(586) s(642) =< s(639) s(641) =< s(639) s(643) =< s(610) s(638) =< s(610) s(643) =< s(601) s(638) =< s(601) s(644) =< s(643)*2 s(645) =< s(643) s(645) =< s(644) s(646) =< s(601) s(646) =< s(586) s(647) =< s(646) s(647) =< s(639) s(648) =< s(604) s(575) =< s(604) s(648) =< s(611) s(649) =< s(611) s(603) =< s(611) s(649) =< s(648) s(603) =< s(648) s(650) =< s(649)*2 s(651) =< s(649) s(651) =< s(650) s(606) =< s(605) s(653) =< s(605)*2 s(654) =< s(605) s(654) =< s(653) with precondition: [V_n>=5] * Chain [68]: 2*s(661)+2*s(663)+1*s(664)+6*s(672)+1*s(675)+1*s(676)+1*s(677)+1*s(678)+1*s(679)+2*s(680)+1*s(694)+1*s(697)+1*s(704)+1*s(707)+2*s(713)+1*s(716)+3*s(717)+12*s(720)+2*s(722)+2*s(723)+12*s(724)+12*s(727)+6*s(731)+6*s(734)+2*s(735)+12*s(738)+2*s(739)+1*s(742)+3*s(743)+12*s(746)+2*s(748)+6*s(752)+6*s(755)+1*s(756)+0 Such that:s(664) =< V_n/8 s(665) =< 2/3*V_n s(666) =< 4/3*V_n aux(181) =< V_n aux(182) =< V_n/2 aux(183) =< V_n/3 aux(184) =< V_n/4 aux(185) =< V_n/6 s(756) =< aux(181) s(661) =< aux(184) s(663) =< aux(185) s(672) =< aux(181) s(672) =< aux(182) s(663) =< aux(181) s(661) =< aux(181) s(664) =< aux(181) s(675) =< aux(181) s(676) =< aux(181) s(677) =< aux(181) s(675) =< aux(182) s(661) =< aux(182) s(663) =< aux(182) s(664) =< aux(182) s(676) =< aux(182) s(677) =< aux(182) s(678) =< aux(182) s(679) =< aux(182) s(678) =< aux(183) s(679) =< aux(183) s(675) =< aux(183) s(661) =< aux(183) s(663) =< aux(183) s(664) =< aux(183) s(679) =< aux(184) s(664) =< aux(184) s(675) =< aux(184) s(663) =< aux(184) s(675) =< aux(185) s(679) =< s(665) s(675) =< s(665) s(661) =< s(665) s(663) =< s(665) s(664) =< s(665) s(680) =< s(665) s(680) =< aux(182) s(681) =< s(666) s(661) =< s(666) s(663) =< s(666) s(664) =< s(666) s(681) =< aux(181) s(682) =< aux(182) s(683) =< aux(182)*2 s(687) =< s(681)*(1/2) s(688) =< aux(181)*(1/2) s(689) =< s(663)*s(682) s(690) =< s(663)*s(683) s(692) =< s(664)*s(682) s(694) =< s(661)*s(682) s(695) =< s(661)*s(683) s(697) =< s(663)*s(682) s(699) =< s(661)*s(682) s(701) =< s(675)*s(682) s(702) =< s(675)*s(683) s(704) =< s(679)*s(682) s(705) =< s(679)*s(683) s(706) =< s(678)*aux(182) s(707) =< s(678)*aux(182) s(709) =< s(690)*(1/2) s(710) =< s(695)*(1/2) s(711) =< s(702)*(1/2) s(712) =< s(705)*(1/2) s(713) =< s(689) s(714) =< s(681) s(714) =< s(690) s(716) =< s(690) s(716) =< s(687) s(717) =< s(687) s(717) =< s(714) s(716) =< s(714) s(718) =< s(709) s(713) =< s(709) s(718) =< s(690) s(713) =< s(690) s(719) =< s(718)*2 s(720) =< s(718) s(720) =< s(719) s(721) =< s(690) s(721) =< s(687) s(722) =< s(721) s(722) =< s(714) s(723) =< s(692) s(724) =< aux(181) s(724) =< s(688) s(726) =< s(692)*2 s(727) =< s(692) s(727) =< s(726) s(728) =< s(695) s(677) =< s(695) s(728) =< s(710) s(729) =< s(710) s(694) =< s(710) s(729) =< s(728) s(694) =< s(728) s(730) =< s(729)*2 s(731) =< s(729) s(731) =< s(730) s(697) =< s(689) s(733) =< s(689)*2 s(734) =< s(689) s(734) =< s(733) s(735) =< s(699) s(737) =< s(699)*2 s(738) =< s(699) s(738) =< s(737) s(739) =< s(701) s(740) =< s(681) s(740) =< s(702) s(742) =< s(702) s(742) =< s(687) s(743) =< s(687) s(743) =< s(740) s(742) =< s(740) s(744) =< s(711) s(739) =< s(711) s(744) =< s(702) s(739) =< s(702) s(745) =< s(744)*2 s(746) =< s(744) s(746) =< s(745) s(747) =< s(702) s(747) =< s(687) s(748) =< s(747) s(748) =< s(740) s(749) =< s(705) s(676) =< s(705) s(749) =< s(712) s(750) =< s(712) s(704) =< s(712) s(750) =< s(749) s(704) =< s(749) s(751) =< s(750)*2 s(752) =< s(750) s(752) =< s(751) s(707) =< s(706) s(754) =< s(706)*2 s(755) =< s(706) s(755) =< s(754) with precondition: [V_n>=8] #### Cost of chains of eval_sipmamergesort_init_start(V_n,B): * Chain [81]: 2*s(758)+0 Such that:s(757) =< 1 s(758) =< s(757) with precondition: [V_n=1] * Chain [80]: 1*s(761)+6*s(762)+0 Such that:s(759) =< 1 s(760) =< 2 s(761) =< s(760) s(762) =< s(760) s(762) =< s(759) with precondition: [V_n=2] * Chain [79]: 0 with precondition: [0>=V_n] * Chain [78]: 1*s(763)+1*s(772)+2*s(773)+3*s(777)+3*s(778)+1*s(779)+1*s(780)+1*s(781)+1*s(782)+1*s(783)+1*s(784)+2*s(785)+1*s(794)+1*s(796)+1*s(800)+1*s(803)+2*s(808)+1*s(810)+3*s(811)+12*s(814)+2*s(816)+2*s(817)+12*s(818)+12*s(820)+6*s(824)+6*s(826)+2*s(827)+12*s(829)+2*s(830)+1*s(832)+3*s(833)+12*s(836)+2*s(838)+6*s(842)+6*s(844)+0 Such that:s(765) =< V_n s(766) =< 2*V_n s(767) =< V_n/2 s(768) =< V_n/3 s(769) =< V_n/4 s(770) =< V_n/6 s(763) =< V_n/8 s(771) =< 2/3*V_n s(764) =< 4/3*V_n s(772) =< s(769) s(773) =< s(770) s(774) =< s(765) s(775) =< s(765) s(776) =< s(766) s(774) =< s(766) s(775) =< s(767) s(776) =< s(771) s(777) =< s(774) s(778) =< s(765) s(777) =< s(765) s(773) =< s(765) s(779) =< s(765) s(763) =< s(765) s(773) =< s(766) s(779) =< s(766) s(763) =< s(766) s(780) =< s(765) s(772) =< s(765) s(781) =< s(765) s(782) =< s(765) s(783) =< s(767) s(784) =< s(767) s(780) =< s(767) s(772) =< s(767) s(773) =< s(767) s(779) =< s(767) s(763) =< s(767) s(783) =< s(776) s(784) =< s(776) s(780) =< s(776) s(772) =< s(776) s(773) =< s(776) s(779) =< s(776) s(763) =< s(776) s(783) =< s(765) s(784) =< s(765) s(783) =< s(768) s(784) =< s(768) s(780) =< s(768) s(772) =< s(768) s(773) =< s(768) s(779) =< s(768) s(763) =< s(768) s(784) =< s(769) s(779) =< s(769) s(763) =< s(769) s(784) =< s(775) s(780) =< s(775) s(773) =< s(775) s(779) =< s(775) s(763) =< s(775) s(780) =< s(770) s(784) =< s(771) s(780) =< s(771) s(772) =< s(771) s(773) =< s(771) s(779) =< s(771) s(763) =< s(771) s(785) =< s(771) s(785) =< s(765) s(786) =< s(764) s(772) =< s(764) s(773) =< s(764) s(779) =< s(764) s(763) =< s(764) s(786) =< s(766) s(772) =< s(766) s(787) =< s(767) s(788) =< s(767)*2 s(789) =< s(786)*(1/2) s(790) =< s(774)*(1/2) s(791) =< s(773)*s(787) s(792) =< s(773)*s(788) s(793) =< s(763)*s(787) s(794) =< s(779)*s(787) s(795) =< s(779)*s(788) s(796) =< s(773)*s(787) s(797) =< s(772)*s(787) s(798) =< s(780)*s(787) s(799) =< s(780)*s(788) s(800) =< s(784)*s(787) s(801) =< s(784)*s(788) s(802) =< s(783)*s(767) s(803) =< s(783)*s(767) s(804) =< s(792)*(1/2) s(805) =< s(795)*(1/2) s(806) =< s(799)*(1/2) s(807) =< s(801)*(1/2) s(808) =< s(791) s(809) =< s(786) s(809) =< s(792) s(810) =< s(792) s(810) =< s(789) s(811) =< s(789) s(811) =< s(809) s(810) =< s(809) s(812) =< s(804) s(808) =< s(804) s(812) =< s(792) s(808) =< s(792) s(813) =< s(812)*2 s(814) =< s(812) s(814) =< s(813) s(815) =< s(792) s(815) =< s(789) s(816) =< s(815) s(816) =< s(809) s(817) =< s(793) s(818) =< s(774) s(818) =< s(790) s(819) =< s(793)*2 s(820) =< s(793) s(820) =< s(819) s(821) =< s(795) s(782) =< s(795) s(821) =< s(805) s(822) =< s(805) s(794) =< s(805) s(822) =< s(821) s(794) =< s(821) s(823) =< s(822)*2 s(824) =< s(822) s(824) =< s(823) s(796) =< s(791) s(825) =< s(791)*2 s(826) =< s(791) s(826) =< s(825) s(827) =< s(797) s(828) =< s(797)*2 s(829) =< s(797) s(829) =< s(828) s(830) =< s(798) s(831) =< s(786) s(831) =< s(799) s(832) =< s(799) s(832) =< s(789) s(833) =< s(789) s(833) =< s(831) s(832) =< s(831) s(834) =< s(806) s(830) =< s(806) s(834) =< s(799) s(830) =< s(799) s(835) =< s(834)*2 s(836) =< s(834) s(836) =< s(835) s(837) =< s(799) s(837) =< s(789) s(838) =< s(837) s(838) =< s(831) s(839) =< s(801) s(781) =< s(801) s(839) =< s(807) s(840) =< s(807) s(800) =< s(807) s(840) =< s(839) s(800) =< s(839) s(841) =< s(840)*2 s(842) =< s(840) s(842) =< s(841) s(803) =< s(802) s(843) =< s(802)*2 s(844) =< s(802) s(844) =< s(843) with precondition: [V_n>=3] * Chain [77]: 1*s(845)+2*s(853)+2*s(854)+6*s(855)+1*s(856)+1*s(857)+1*s(858)+1*s(859)+1*s(860)+2*s(861)+1*s(870)+1*s(872)+1*s(876)+1*s(879)+2*s(884)+1*s(886)+3*s(887)+12*s(890)+2*s(892)+2*s(893)+12*s(894)+12*s(896)+6*s(900)+6*s(902)+2*s(903)+12*s(905)+2*s(906)+1*s(908)+3*s(909)+12*s(912)+2*s(914)+6*s(918)+6*s(920)+0 Such that:s(848) =< V_n s(849) =< V_n/2 s(850) =< V_n/3 s(851) =< V_n/4 s(852) =< V_n/6 s(845) =< V_n/8 s(846) =< 2/3*V_n s(847) =< 4/3*V_n s(853) =< s(851) s(854) =< s(852) s(855) =< s(848) s(855) =< s(849) s(854) =< s(848) s(853) =< s(848) s(845) =< s(848) s(856) =< s(848) s(857) =< s(848) s(858) =< s(848) s(856) =< s(849) s(853) =< s(849) s(854) =< s(849) s(845) =< s(849) s(857) =< s(849) s(858) =< s(849) s(859) =< s(849) s(860) =< s(849) s(859) =< s(850) s(860) =< s(850) s(856) =< s(850) s(853) =< s(850) s(854) =< s(850) s(845) =< s(850) s(860) =< s(851) s(845) =< s(851) s(856) =< s(851) s(854) =< s(851) s(856) =< s(852) s(860) =< s(846) s(856) =< s(846) s(853) =< s(846) s(854) =< s(846) s(845) =< s(846) s(861) =< s(846) s(861) =< s(849) s(862) =< s(847) s(853) =< s(847) s(854) =< s(847) s(845) =< s(847) s(862) =< s(848) s(863) =< s(849) s(864) =< s(849)*2 s(865) =< s(862)*(1/2) s(866) =< s(848)*(1/2) s(867) =< s(854)*s(863) s(868) =< s(854)*s(864) s(869) =< s(845)*s(863) s(870) =< s(853)*s(863) s(871) =< s(853)*s(864) s(872) =< s(854)*s(863) s(873) =< s(853)*s(863) s(874) =< s(856)*s(863) s(875) =< s(856)*s(864) s(876) =< s(860)*s(863) s(877) =< s(860)*s(864) s(878) =< s(859)*s(849) s(879) =< s(859)*s(849) s(880) =< s(868)*(1/2) s(881) =< s(871)*(1/2) s(882) =< s(875)*(1/2) s(883) =< s(877)*(1/2) s(884) =< s(867) s(885) =< s(862) s(885) =< s(868) s(886) =< s(868) s(886) =< s(865) s(887) =< s(865) s(887) =< s(885) s(886) =< s(885) s(888) =< s(880) s(884) =< s(880) s(888) =< s(868) s(884) =< s(868) s(889) =< s(888)*2 s(890) =< s(888) s(890) =< s(889) s(891) =< s(868) s(891) =< s(865) s(892) =< s(891) s(892) =< s(885) s(893) =< s(869) s(894) =< s(848) s(894) =< s(866) s(895) =< s(869)*2 s(896) =< s(869) s(896) =< s(895) s(897) =< s(871) s(858) =< s(871) s(897) =< s(881) s(898) =< s(881) s(870) =< s(881) s(898) =< s(897) s(870) =< s(897) s(899) =< s(898)*2 s(900) =< s(898) s(900) =< s(899) s(872) =< s(867) s(901) =< s(867)*2 s(902) =< s(867) s(902) =< s(901) s(903) =< s(873) s(904) =< s(873)*2 s(905) =< s(873) s(905) =< s(904) s(906) =< s(874) s(907) =< s(862) s(907) =< s(875) s(908) =< s(875) s(908) =< s(865) s(909) =< s(865) s(909) =< s(907) s(908) =< s(907) s(910) =< s(882) s(906) =< s(882) s(910) =< s(875) s(906) =< s(875) s(911) =< s(910)*2 s(912) =< s(910) s(912) =< s(911) s(913) =< s(875) s(913) =< s(865) s(914) =< s(913) s(914) =< s(907) s(915) =< s(877) s(857) =< s(877) s(915) =< s(883) s(916) =< s(883) s(876) =< s(883) s(916) =< s(915) s(876) =< s(915) s(917) =< s(916)*2 s(918) =< s(916) s(918) =< s(917) s(879) =< s(878) s(919) =< s(878)*2 s(920) =< s(878) s(920) =< s(919) with precondition: [V_n>=4] * Chain [76]: 1*s(921)+4*s(930)+1*s(931)+2*s(932)+3*s(936)+1*s(937)+1*s(938)+1*s(939)+1*s(940)+1*s(941)+1*s(942)+2*s(943)+1*s(952)+1*s(954)+1*s(958)+1*s(961)+2*s(966)+1*s(968)+3*s(969)+12*s(972)+2*s(974)+2*s(975)+12*s(976)+12*s(978)+6*s(982)+6*s(984)+2*s(985)+12*s(987)+2*s(988)+1*s(990)+3*s(991)+12*s(994)+2*s(996)+6*s(1000)+6*s(1002)+0 Such that:s(923) =< V_n s(924) =< 2*V_n s(925) =< V_n/2 s(926) =< V_n/3 s(927) =< V_n/4 s(928) =< V_n/6 s(921) =< V_n/8 s(929) =< 2/3*V_n s(922) =< 4/3*V_n s(930) =< s(923) s(931) =< s(927) s(932) =< s(928) s(933) =< s(923) s(934) =< s(923) s(935) =< s(924) s(933) =< s(924) s(934) =< s(925) s(935) =< s(929) s(936) =< s(933) s(936) =< s(923) s(932) =< s(923) s(937) =< s(923) s(921) =< s(923) s(932) =< s(924) s(937) =< s(924) s(921) =< s(924) s(938) =< s(923) s(931) =< s(923) s(939) =< s(923) s(940) =< s(923) s(941) =< s(925) s(942) =< s(925) s(938) =< s(925) s(931) =< s(925) s(932) =< s(925) s(937) =< s(925) s(921) =< s(925) s(941) =< s(935) s(942) =< s(935) s(938) =< s(935) s(931) =< s(935) s(932) =< s(935) s(937) =< s(935) s(921) =< s(935) s(941) =< s(923) s(942) =< s(923) s(941) =< s(926) s(942) =< s(926) s(938) =< s(926) s(931) =< s(926) s(932) =< s(926) s(937) =< s(926) s(921) =< s(926) s(942) =< s(927) s(937) =< s(927) s(921) =< s(927) s(942) =< s(934) s(938) =< s(934) s(932) =< s(934) s(937) =< s(934) s(921) =< s(934) s(938) =< s(928) s(942) =< s(929) s(938) =< s(929) s(931) =< s(929) s(932) =< s(929) s(937) =< s(929) s(921) =< s(929) s(943) =< s(929) s(943) =< s(923) s(944) =< s(922) s(931) =< s(922) s(932) =< s(922) s(937) =< s(922) s(921) =< s(922) s(944) =< s(924) s(931) =< s(924) s(945) =< s(925) s(946) =< s(925)*2 s(947) =< s(944)*(1/2) s(948) =< s(933)*(1/2) s(949) =< s(932)*s(945) s(950) =< s(932)*s(946) s(951) =< s(921)*s(945) s(952) =< s(937)*s(945) s(953) =< s(937)*s(946) s(954) =< s(932)*s(945) s(955) =< s(931)*s(945) s(956) =< s(938)*s(945) s(957) =< s(938)*s(946) s(958) =< s(942)*s(945) s(959) =< s(942)*s(946) s(960) =< s(941)*s(925) s(961) =< s(941)*s(925) s(962) =< s(950)*(1/2) s(963) =< s(953)*(1/2) s(964) =< s(957)*(1/2) s(965) =< s(959)*(1/2) s(966) =< s(949) s(967) =< s(944) s(967) =< s(950) s(968) =< s(950) s(968) =< s(947) s(969) =< s(947) s(969) =< s(967) s(968) =< s(967) s(970) =< s(962) s(966) =< s(962) s(970) =< s(950) s(966) =< s(950) s(971) =< s(970)*2 s(972) =< s(970) s(972) =< s(971) s(973) =< s(950) s(973) =< s(947) s(974) =< s(973) s(974) =< s(967) s(975) =< s(951) s(976) =< s(933) s(976) =< s(948) s(977) =< s(951)*2 s(978) =< s(951) s(978) =< s(977) s(979) =< s(953) s(940) =< s(953) s(979) =< s(963) s(980) =< s(963) s(952) =< s(963) s(980) =< s(979) s(952) =< s(979) s(981) =< s(980)*2 s(982) =< s(980) s(982) =< s(981) s(954) =< s(949) s(983) =< s(949)*2 s(984) =< s(949) s(984) =< s(983) s(985) =< s(955) s(986) =< s(955)*2 s(987) =< s(955) s(987) =< s(986) s(988) =< s(956) s(989) =< s(944) s(989) =< s(957) s(990) =< s(957) s(990) =< s(947) s(991) =< s(947) s(991) =< s(989) s(990) =< s(989) s(992) =< s(964) s(988) =< s(964) s(992) =< s(957) s(988) =< s(957) s(993) =< s(992)*2 s(994) =< s(992) s(994) =< s(993) s(995) =< s(957) s(995) =< s(947) s(996) =< s(995) s(996) =< s(989) s(997) =< s(959) s(939) =< s(959) s(997) =< s(965) s(998) =< s(965) s(958) =< s(965) s(998) =< s(997) s(958) =< s(997) s(999) =< s(998)*2 s(1000) =< s(998) s(1000) =< s(999) s(961) =< s(960) s(1001) =< s(960)*2 s(1002) =< s(960) s(1002) =< s(1001) with precondition: [V_n>=5] * Chain [75]: 1*s(1003)+1*s(1011)+2*s(1012)+2*s(1013)+6*s(1014)+1*s(1015)+1*s(1016)+1*s(1017)+1*s(1018)+1*s(1019)+2*s(1020)+1*s(1029)+1*s(1031)+1*s(1035)+1*s(1038)+2*s(1043)+1*s(1045)+3*s(1046)+12*s(1049)+2*s(1051)+2*s(1052)+12*s(1053)+12*s(1055)+6*s(1059)+6*s(1061)+2*s(1062)+12*s(1064)+2*s(1065)+1*s(1067)+3*s(1068)+12*s(1071)+2*s(1073)+6*s(1077)+6*s(1079)+0 Such that:s(1006) =< V_n s(1007) =< V_n/2 s(1008) =< V_n/3 s(1009) =< V_n/4 s(1010) =< V_n/6 s(1003) =< V_n/8 s(1004) =< 2/3*V_n s(1005) =< 4/3*V_n s(1011) =< s(1006) s(1012) =< s(1009) s(1013) =< s(1010) s(1014) =< s(1006) s(1014) =< s(1007) s(1013) =< s(1006) s(1012) =< s(1006) s(1003) =< s(1006) s(1015) =< s(1006) s(1016) =< s(1006) s(1017) =< s(1006) s(1015) =< s(1007) s(1012) =< s(1007) s(1013) =< s(1007) s(1003) =< s(1007) s(1016) =< s(1007) s(1017) =< s(1007) s(1018) =< s(1007) s(1019) =< s(1007) s(1018) =< s(1008) s(1019) =< s(1008) s(1015) =< s(1008) s(1012) =< s(1008) s(1013) =< s(1008) s(1003) =< s(1008) s(1019) =< s(1009) s(1003) =< s(1009) s(1015) =< s(1009) s(1013) =< s(1009) s(1015) =< s(1010) s(1019) =< s(1004) s(1015) =< s(1004) s(1012) =< s(1004) s(1013) =< s(1004) s(1003) =< s(1004) s(1020) =< s(1004) s(1020) =< s(1007) s(1021) =< s(1005) s(1012) =< s(1005) s(1013) =< s(1005) s(1003) =< s(1005) s(1021) =< s(1006) s(1022) =< s(1007) s(1023) =< s(1007)*2 s(1024) =< s(1021)*(1/2) s(1025) =< s(1006)*(1/2) s(1026) =< s(1013)*s(1022) s(1027) =< s(1013)*s(1023) s(1028) =< s(1003)*s(1022) s(1029) =< s(1012)*s(1022) s(1030) =< s(1012)*s(1023) s(1031) =< s(1013)*s(1022) s(1032) =< s(1012)*s(1022) s(1033) =< s(1015)*s(1022) s(1034) =< s(1015)*s(1023) s(1035) =< s(1019)*s(1022) s(1036) =< s(1019)*s(1023) s(1037) =< s(1018)*s(1007) s(1038) =< s(1018)*s(1007) s(1039) =< s(1027)*(1/2) s(1040) =< s(1030)*(1/2) s(1041) =< s(1034)*(1/2) s(1042) =< s(1036)*(1/2) s(1043) =< s(1026) s(1044) =< s(1021) s(1044) =< s(1027) s(1045) =< s(1027) s(1045) =< s(1024) s(1046) =< s(1024) s(1046) =< s(1044) s(1045) =< s(1044) s(1047) =< s(1039) s(1043) =< s(1039) s(1047) =< s(1027) s(1043) =< s(1027) s(1048) =< s(1047)*2 s(1049) =< s(1047) s(1049) =< s(1048) s(1050) =< s(1027) s(1050) =< s(1024) s(1051) =< s(1050) s(1051) =< s(1044) s(1052) =< s(1028) s(1053) =< s(1006) s(1053) =< s(1025) s(1054) =< s(1028)*2 s(1055) =< s(1028) s(1055) =< s(1054) s(1056) =< s(1030) s(1017) =< s(1030) s(1056) =< s(1040) s(1057) =< s(1040) s(1029) =< s(1040) s(1057) =< s(1056) s(1029) =< s(1056) s(1058) =< s(1057)*2 s(1059) =< s(1057) s(1059) =< s(1058) s(1031) =< s(1026) s(1060) =< s(1026)*2 s(1061) =< s(1026) s(1061) =< s(1060) s(1062) =< s(1032) s(1063) =< s(1032)*2 s(1064) =< s(1032) s(1064) =< s(1063) s(1065) =< s(1033) s(1066) =< s(1021) s(1066) =< s(1034) s(1067) =< s(1034) s(1067) =< s(1024) s(1068) =< s(1024) s(1068) =< s(1066) s(1067) =< s(1066) s(1069) =< s(1041) s(1065) =< s(1041) s(1069) =< s(1034) s(1065) =< s(1034) s(1070) =< s(1069)*2 s(1071) =< s(1069) s(1071) =< s(1070) s(1072) =< s(1034) s(1072) =< s(1024) s(1073) =< s(1072) s(1073) =< s(1066) s(1074) =< s(1036) s(1016) =< s(1036) s(1074) =< s(1042) s(1075) =< s(1042) s(1035) =< s(1042) s(1075) =< s(1074) s(1035) =< s(1074) s(1076) =< s(1075)*2 s(1077) =< s(1075) s(1077) =< s(1076) s(1038) =< s(1037) s(1078) =< s(1037)*2 s(1079) =< s(1037) s(1079) =< s(1078) with precondition: [V_n>=8] Closed-form bounds of eval_sipmamergesort_init_start(V_n,B): ------------------------------------- * Chain [81] with precondition: [V_n=1] - Upper bound: 2 - Complexity: constant * Chain [80] with precondition: [V_n=2] - Upper bound: 14 - Complexity: constant * Chain [79] with precondition: [0>=V_n] - Upper bound: 0 - Complexity: constant * Chain [78] with precondition: [V_n>=3] - Upper bound: V_n/8+(V_n/3+(V_n/4+(V_n/2*(21*V_n)+22*V_n+4/3*V_n+8*V_n+V_n+V_n/2*(7*V_n)+V_n/4*(7*V_n)+V_n/6*(21/2*V_n)+V_n/8*(7*V_n)))) - Complexity: n^2 * Chain [77] with precondition: [V_n>=4] - Upper bound: V_n/8+(V_n/3+(V_n/2+(V_n/2*(14*V_n)+21*V_n+4/3*V_n+8*V_n+V_n+V_n/2*(7*V_n)+V_n/4*(21/2*V_n)+V_n/6*(21/2*V_n)+V_n/8*(7*V_n)))) - Complexity: n^2 * Chain [76] with precondition: [V_n>=5] - Upper bound: V_n/8+(V_n/3+(V_n/4+(V_n/2*(21*V_n)+23*V_n+4/3*V_n+8*V_n+V_n+V_n/2*(7*V_n)+V_n/4*(7*V_n)+V_n/6*(21/2*V_n)+V_n/8*(7*V_n)))) - Complexity: n^2 * Chain [75] with precondition: [V_n>=8] - Upper bound: V_n/8+(V_n/3+(V_n/2+(V_n/2*(14*V_n)+22*V_n+4/3*V_n+8*V_n+V_n+V_n/2*(7*V_n)+V_n/4*(21/2*V_n)+V_n/6*(21/2*V_n)+V_n/8*(7*V_n)))) - Complexity: n^2 ### Maximum cost of eval_sipmamergesort_init_start(V_n,B): max([14,nat(V_n)*14*nat(V_n/2)+nat(V_n)*21+nat(2/3*V_n)*2+nat(4/3*V_n)*6+nat(V_n/2)*2+nat(V_n/2)*14*nat(V_n/2)+nat(V_n/2)*14*nat(V_n/4)+nat(V_n/2)*21*nat(V_n/6)+nat(V_n/2)*14*nat(V_n/8)+nat(V_n/4)+nat(V_n/6)*2+nat(V_n/8)+max([nat(V_n)+max([nat(V_n)*7*nat(V_n/2)+nat(V_n),nat(V_n/2)*7*nat(V_n/4)+nat(V_n/4)]),nat(V_n/2)*7*nat(V_n/4)+nat(V_n/4)])]) Asymptotic class: n^2 * Total analysis performed in 3172 ms.