2.31/2.33 WORST_CASE(?,O(n^2)) 2.31/2.33 2.31/2.33 Preprocessing Cost Relations 2.31/2.33 ===================================== 2.31/2.33 2.31/2.33 #### Computed strongly connected components 2.31/2.33 0. recursive : [eval_nestedLoop_10/9,eval_nestedLoop_11/9,eval_nestedLoop_bb4_in/9,eval_nestedLoop_bb5_in/9] 2.31/2.33 1. recursive : [eval_nestedLoop_6/15,eval_nestedLoop_7/15,eval_nestedLoop_bb2_in/15,eval_nestedLoop_bb3_in/15,eval_nestedLoop_bb4_in_loop_cont/16] 2.31/2.33 2. recursive : [eval_nestedLoop_15/22,eval_nestedLoop_16/22,eval_nestedLoop_4/22,eval_nestedLoop_5/22,eval_nestedLoop_bb1_in/22,eval_nestedLoop_bb2_in_loop_cont/23,eval_nestedLoop_bb6_in/22] 2.31/2.33 3. non_recursive : [eval_nestedLoop_stop/13] 2.31/2.33 4. non_recursive : [eval_nestedLoop_bb7_in/13] 2.31/2.33 5. non_recursive : [exit_location/1] 2.31/2.33 6. non_recursive : [eval_nestedLoop_bb1_in_loop_cont/14] 2.31/2.33 7. non_recursive : [eval_nestedLoop_3/13] 2.31/2.33 8. non_recursive : [eval_nestedLoop_2/13] 2.31/2.33 9. non_recursive : [eval_nestedLoop_1/13] 2.31/2.33 10. non_recursive : [eval_nestedLoop_0/13] 2.31/2.33 11. non_recursive : [eval_nestedLoop_bb0_in/13] 2.31/2.33 12. non_recursive : [eval_nestedLoop_start/13] 2.31/2.33 2.31/2.33 #### Obtained direct recursion through partial evaluation 2.31/2.33 0. SCC is partially evaluated into eval_nestedLoop_bb4_in/9 2.31/2.33 1. SCC is partially evaluated into eval_nestedLoop_bb2_in/15 2.31/2.33 2. SCC is partially evaluated into eval_nestedLoop_bb1_in/22 2.31/2.33 3. SCC is completely evaluated into other SCCs 2.31/2.33 4. SCC is completely evaluated into other SCCs 2.31/2.33 5. SCC is completely evaluated into other SCCs 2.31/2.33 6. SCC is partially evaluated into eval_nestedLoop_bb1_in_loop_cont/14 2.31/2.33 7. SCC is partially evaluated into eval_nestedLoop_3/13 2.31/2.33 8. SCC is completely evaluated into other SCCs 2.31/2.33 9. SCC is completely evaluated into other SCCs 2.31/2.33 10. SCC is completely evaluated into other SCCs 2.31/2.33 11. SCC is completely evaluated into other SCCs 2.31/2.33 12. SCC is partially evaluated into eval_nestedLoop_start/13 2.31/2.33 2.31/2.33 Control-Flow Refinement of Cost Relations 2.31/2.33 ===================================== 2.31/2.33 2.31/2.33 ### Specialization of cost equations eval_nestedLoop_bb4_in/9 2.31/2.33 * CE 21 is refined into CE [22] 2.31/2.33 * CE 18 is refined into CE [23] 2.31/2.33 * CE 19 is refined into CE [24] 2.31/2.33 * CE 20 is refined into CE [25] 2.31/2.33 2.31/2.33 2.31/2.33 ### Cost equations --> "Loop" of eval_nestedLoop_bb4_in/9 2.31/2.33 * CEs [25] --> Loop 22 2.31/2.33 * CEs [22] --> Loop 23 2.31/2.33 * CEs [23] --> Loop 24 2.31/2.33 * CEs [24] --> Loop 25 2.31/2.33 2.31/2.33 ### Ranking functions of CR eval_nestedLoop_bb4_in(V_10,V_N,V_i_1,V_j_0,V_k_0,B,C,D,E) 2.31/2.33 * RF of phase [22]: [V_N-V_k_0] 2.31/2.33 2.31/2.33 #### Partial ranking functions of CR eval_nestedLoop_bb4_in(V_10,V_N,V_i_1,V_j_0,V_k_0,B,C,D,E) 2.31/2.33 * Partial RF of phase [22]: 2.31/2.33 - RF of loop [22:1]: 2.31/2.33 V_N-V_k_0 2.31/2.33 2.31/2.33 2.31/2.33 ### Specialization of cost equations eval_nestedLoop_bb2_in/15 2.31/2.33 * CE 13 is refined into CE [26] 2.31/2.33 * CE 14 is refined into CE [27] 2.31/2.33 * CE 16 is refined into CE [28,29] 2.31/2.33 * CE 17 is refined into CE [30] 2.31/2.33 * CE 15 is refined into CE [31,32,33,34] 2.31/2.33 2.31/2.33 2.31/2.33 ### Cost equations --> "Loop" of eval_nestedLoop_bb2_in/15 2.31/2.33 * CEs [34] --> Loop 26 2.31/2.33 * CEs [33] --> Loop 27 2.31/2.33 * CEs [32] --> Loop 28 2.31/2.33 * CEs [31] --> Loop 29 2.31/2.33 * CEs [27] --> Loop 30 2.31/2.33 * CEs [26] --> Loop 31 2.31/2.33 * CEs [28] --> Loop 32 2.31/2.33 * CEs [30] --> Loop 33 2.31/2.33 * CEs [29] --> Loop 34 2.31/2.33 2.31/2.33 ### Ranking functions of CR eval_nestedLoop_bb2_in(V_10,V_6,V_9,V_N,V_i_1,V_j_0,V_k_0,V_m,B,C,D,E,F,G,H) 2.31/2.33 * RF of phase [26,27,28,29]: [-V_j_0+V_m] 2.31/2.33 2.31/2.33 #### Partial ranking functions of CR eval_nestedLoop_bb2_in(V_10,V_6,V_9,V_N,V_i_1,V_j_0,V_k_0,V_m,B,C,D,E,F,G,H) 2.31/2.33 * Partial RF of phase [26,27,28,29]: 2.31/2.33 - RF of loop [26:1,27:1,28:1,29:1]: 2.31/2.33 -V_j_0+V_m 2.31/2.33 - RF of loop [26:1,29:1]: 2.31/2.33 V_N-V_i_1 2.31/2.33 2.31/2.33 2.31/2.33 ### Specialization of cost equations eval_nestedLoop_bb1_in/22 2.31/2.33 * CE 6 is refined into CE [35] 2.31/2.33 * CE 7 is refined into CE [36] 2.31/2.33 * CE 9 is refined into CE [37,38,39,40,41] 2.31/2.33 * CE 10 is refined into CE [42] 2.31/2.33 * CE 8 is refined into CE [43,44,45,46] 2.31/2.33 2.31/2.33 2.31/2.33 ### Cost equations --> "Loop" of eval_nestedLoop_bb1_in/22 2.31/2.33 * CEs [46] --> Loop 35 2.31/2.33 * CEs [45] --> Loop 36 2.31/2.33 * CEs [44] --> Loop 37 2.31/2.33 * CEs [43] --> Loop 38 2.31/2.33 * CEs [35] --> Loop 39 2.31/2.33 * CEs [36] --> Loop 40 2.31/2.33 * CEs [41] --> Loop 41 2.31/2.33 * CEs [38] --> Loop 42 2.31/2.33 * CEs [40] --> Loop 43 2.31/2.33 * CEs [37] --> Loop 44 2.31/2.33 * CEs [39] --> Loop 45 2.31/2.33 * CEs [42] --> Loop 46 2.31/2.33 2.31/2.33 ### Ranking functions of CR eval_nestedLoop_bb1_in(V_10,V_14,V_3,V_6,V_9,V_N,V_i_0,V_i_1,V_j_0,V_k_0,V_m,V_n,B,C,D,E,F,G,H,I,J,K) 2.31/2.33 * RF of phase [35,36,37,38]: [-V_i_0+V_n] 2.31/2.33 2.31/2.33 #### Partial ranking functions of CR eval_nestedLoop_bb1_in(V_10,V_14,V_3,V_6,V_9,V_N,V_i_0,V_i_1,V_j_0,V_k_0,V_m,V_n,B,C,D,E,F,G,H,I,J,K) 2.31/2.33 * Partial RF of phase [35,36,37,38]: 2.31/2.33 - RF of loop [35:1,36:1,37:1,38:1]: 2.31/2.33 -V_i_0+V_n 2.31/2.33 2.31/2.33 2.31/2.33 ### Specialization of cost equations eval_nestedLoop_bb1_in_loop_cont/14 2.31/2.33 * CE 11 is refined into CE [47] 2.31/2.33 * CE 12 is refined into CE [48] 2.31/2.33 2.31/2.33 2.31/2.33 ### Cost equations --> "Loop" of eval_nestedLoop_bb1_in_loop_cont/14 2.31/2.33 * CEs [47] --> Loop 47 2.31/2.33 * CEs [48] --> Loop 48 2.31/2.33 2.31/2.33 ### Ranking functions of CR eval_nestedLoop_bb1_in_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N) 2.31/2.33 2.31/2.33 #### Partial ranking functions of CR eval_nestedLoop_bb1_in_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N) 2.31/2.33 2.31/2.33 2.31/2.33 ### Specialization of cost equations eval_nestedLoop_3/13 2.31/2.33 * CE 5 is refined into CE [49,50,51,52,53,54,55,56,57,58,59,60,61,62,63] 2.31/2.33 * CE 2 is refined into CE [64] 2.31/2.33 * CE 3 is refined into CE [65] 2.31/2.33 * CE 4 is refined into CE [66] 2.31/2.33 2.31/2.33 2.31/2.33 ### Cost equations --> "Loop" of eval_nestedLoop_3/13 2.31/2.33 * CEs [59] --> Loop 49 2.31/2.33 * CEs [57] --> Loop 50 2.31/2.33 * CEs [58] --> Loop 51 2.31/2.33 * CEs [56] --> Loop 52 2.31/2.33 * CEs [55] --> Loop 53 2.31/2.33 * CEs [54] --> Loop 54 2.31/2.33 * CEs [53] --> Loop 55 2.31/2.33 * CEs [52] --> Loop 56 2.31/2.33 * CEs [51] --> Loop 57 2.31/2.33 * CEs [50,62,63] --> Loop 58 2.31/2.33 * CEs [49,60] --> Loop 59 2.31/2.33 * CEs [64] --> Loop 60 2.31/2.33 * CEs [65] --> Loop 61 2.31/2.33 * CEs [66] --> Loop 62 2.31/2.33 * CEs [61] --> Loop 63 2.31/2.33 2.31/2.33 ### Ranking functions of CR eval_nestedLoop_3(V_10,V_14,V_3,V_6,V_9,V_N,V_i_0,V_i_1,V_j_0,V_k_0,V_m,V_n,B) 2.31/2.33 2.31/2.33 #### Partial ranking functions of CR eval_nestedLoop_3(V_10,V_14,V_3,V_6,V_9,V_N,V_i_0,V_i_1,V_j_0,V_k_0,V_m,V_n,B) 2.31/2.33 2.31/2.33 2.31/2.33 ### Specialization of cost equations eval_nestedLoop_start/13 2.31/2.33 * CE 1 is refined into CE [67,68,69,70,71,72,73,74,75,76,77,78,79,80,81] 2.31/2.33 2.31/2.33 2.31/2.33 ### Cost equations --> "Loop" of eval_nestedLoop_start/13 2.31/2.33 * CEs [81] --> Loop 64 2.31/2.33 * CEs [80] --> Loop 65 2.31/2.33 * CEs [79] --> Loop 66 2.31/2.33 * CEs [78] --> Loop 67 2.31/2.33 * CEs [77] --> Loop 68 2.31/2.33 * CEs [76] --> Loop 69 2.31/2.33 * CEs [75] --> Loop 70 2.31/2.33 * CEs [74] --> Loop 71 2.31/2.33 * CEs [73] --> Loop 72 2.31/2.33 * CEs [72] --> Loop 73 2.31/2.33 * CEs [71] --> Loop 74 2.31/2.33 * CEs [70] --> Loop 75 2.31/2.33 * CEs [69] --> Loop 76 2.31/2.33 * CEs [68] --> Loop 77 2.31/2.33 * CEs [67] --> Loop 78 2.31/2.33 2.31/2.33 ### Ranking functions of CR eval_nestedLoop_start(V_10,V_14,V_3,V_6,V_9,V_N,V_i_0,V_i_1,V_j_0,V_k_0,V_m,V_n,B) 2.31/2.33 2.31/2.33 #### Partial ranking functions of CR eval_nestedLoop_start(V_10,V_14,V_3,V_6,V_9,V_N,V_i_0,V_i_1,V_j_0,V_k_0,V_m,V_n,B) 2.31/2.33 2.31/2.33 2.31/2.33 Computing Bounds 2.31/2.33 ===================================== 2.31/2.33 2.31/2.33 #### Cost of chains of eval_nestedLoop_bb4_in(V_10,V_N,V_i_1,V_j_0,V_k_0,B,C,D,E): 2.31/2.33 * Chain [[22],25]: 1*it(22)+0 2.31/2.33 Such that:it(22) =< -V_k_0+D 2.31/2.33 2.31/2.33 with precondition: [B=2,D=E,0>=C,V_N>=0,V_j_0>=0,V_k_0>=V_i_1,D>=V_k_0+1,V_N>=D] 2.31/2.33 2.31/2.33 * Chain [[22],24]: 1*it(22)+0 2.31/2.33 Such that:it(22) =< -V_k_0+E 2.31/2.33 2.31/2.33 with precondition: [B=2,V_N=D,V_N=E,V_N>=0,V_j_0>=0,V_k_0>=V_i_1,V_N>=V_k_0+1] 2.31/2.33 2.31/2.33 * Chain [[22],23]: 1*it(22)+0 2.31/2.33 Such that:it(22) =< V_N-V_k_0 2.31/2.33 2.31/2.33 with precondition: [B=3,V_N>=0,V_j_0>=0,V_k_0>=V_i_1,V_N>=V_k_0+1] 2.31/2.33 2.31/2.33 * Chain [25]: 0 2.31/2.33 with precondition: [B=2,V_k_0=D,V_k_0=E,0>=C,V_N>=0,V_j_0>=0,V_k_0>=V_i_1] 2.31/2.33 2.31/2.33 * Chain [24]: 0 2.31/2.33 with precondition: [B=2,V_k_0=D,V_k_0=E,V_N>=0,V_j_0>=0,V_k_0>=V_N,V_k_0>=V_i_1] 2.31/2.33 2.31/2.33 * Chain [23]: 0 2.31/2.33 with precondition: [B=3,V_N>=0,V_j_0>=0,V_k_0>=V_i_1] 2.31/2.33 2.31/2.33 2.31/2.33 #### Cost of chains of eval_nestedLoop_bb2_in(V_10,V_6,V_9,V_N,V_i_1,V_j_0,V_k_0,V_m,B,C,D,E,F,G,H): 2.31/2.33 * Chain [[26,27,28,29],34]: 2*it(26)+2*it(27)+3*s(1)+0 2.31/2.33 Such that:aux(5) =< V_N-V_i_1 2.31/2.33 aux(6) =< -V_j_0+V_m 2.31/2.33 s(1) =< aux(5) 2.31/2.33 it(26) =< aux(5) 2.31/2.33 it(26) =< aux(6) 2.31/2.33 it(27) =< aux(6) 2.31/2.33 2.31/2.33 with precondition: [B=3,V_N>=0,V_j_0>=0,V_N>=V_i_1+1,V_m>=V_j_0+2] 2.31/2.33 2.31/2.33 * Chain [[26,27,28,29],33]: 2*it(26)+2*it(27)+2*s(6)+0 2.31/2.33 Such that:aux(1) =< V_N-V_i_1 2.31/2.33 aux(7) =< -V_j_0+V_m 2.31/2.33 it(26) =< aux(1) 2.31/2.33 s(6) =< aux(1) 2.31/2.33 it(26) =< aux(7) 2.31/2.33 it(27) =< aux(7) 2.31/2.33 2.31/2.33 with precondition: [B=3,V_N>=0,V_j_0>=0,V_m>=V_j_0+1] 2.31/2.33 2.31/2.33 * Chain [[26,27,28,29],32]: 2*it(26)+2*it(27)+2*s(6)+0 2.31/2.33 Such that:aux(1) =< V_N-V_i_1 2.31/2.33 aux(8) =< -V_j_0+V_m 2.31/2.33 it(26) =< aux(1) 2.31/2.33 s(6) =< aux(1) 2.31/2.33 it(26) =< aux(8) 2.31/2.33 it(27) =< aux(8) 2.31/2.33 2.31/2.33 with precondition: [B=3,V_N>=0,V_j_0>=0,V_m>=V_j_0+2] 2.31/2.33 2.31/2.33 * Chain [[26,27,28,29],31]: 2*it(26)+2*it(27)+2*s(6)+0 2.31/2.33 Such that:aux(1) =< V_N-V_i_1 2.31/2.33 aux(2) =< -V_i_1+H 2.31/2.33 aux(9) =< -V_j_0+V_m 2.31/2.33 it(26) =< aux(1) 2.31/2.33 s(6) =< aux(1) 2.31/2.33 it(26) =< aux(2) 2.31/2.33 s(6) =< aux(2) 2.31/2.33 it(26) =< aux(9) 2.31/2.33 it(27) =< aux(9) 2.31/2.33 2.31/2.33 with precondition: [B=4,V_m=E,V_m=G,F=H,V_N>=0,V_j_0>=0,F>=V_i_1,V_m>=V_j_0+1] 2.31/2.33 2.31/2.33 * Chain [[26,27,28,29],30]: 2*it(26)+2*it(27)+2*s(6)+0 2.31/2.33 Such that:aux(1) =< V_N-V_i_1 2.31/2.33 aux(2) =< -V_i_1+H 2.31/2.33 aux(3) =< -V_j_0+V_m 2.31/2.33 aux(4) =< -V_j_0+E 2.31/2.33 it(26) =< aux(1) 2.31/2.33 s(6) =< aux(1) 2.31/2.33 it(26) =< aux(2) 2.31/2.33 s(6) =< aux(2) 2.31/2.33 it(26) =< aux(3) 2.31/2.33 it(27) =< aux(3) 2.31/2.33 it(26) =< aux(4) 2.31/2.33 it(27) =< aux(4) 2.31/2.33 2.31/2.33 with precondition: [B=4,E=G,F=H,0>=D,V_N>=0,V_j_0>=0,F>=V_i_1,E>=V_j_0+1,V_m>=E] 2.31/2.33 2.31/2.33 * Chain [34]: 1*s(1)+0 2.31/2.33 Such that:s(1) =< V_N-V_i_1 2.31/2.33 2.31/2.33 with precondition: [B=3,V_N>=0,V_j_0>=0,V_N>=V_i_1+1,V_m>=V_j_0+1] 2.31/2.33 2.31/2.33 * Chain [33]: 0 2.31/2.33 with precondition: [B=3,V_N>=0,V_j_0>=0,V_m>=V_j_0] 2.31/2.33 2.31/2.33 * Chain [32]: 0 2.31/2.33 with precondition: [B=3,V_N>=0,V_j_0>=0,V_m>=V_j_0+1] 2.31/2.33 2.31/2.33 * Chain [31]: 0 2.31/2.33 with precondition: [B=4,C=V_10,E=V_9,F=V_i_1,V_m=V_j_0,H=V_k_0,V_m=G,V_N>=0,V_m>=0] 2.31/2.33 2.31/2.33 * Chain [30]: 0 2.31/2.33 with precondition: [B=4,C=V_10,E=V_9,F=V_i_1,H=V_k_0,V_j_0=G,0>=D,V_N>=0,V_j_0>=0,V_m>=V_j_0] 2.31/2.33 2.31/2.33 2.31/2.33 #### Cost of chains of eval_nestedLoop_bb1_in(V_10,V_14,V_3,V_6,V_9,V_N,V_i_0,V_i_1,V_j_0,V_k_0,V_m,V_n,B,C,D,E,F,G,H,I,J,K): 2.31/2.33 * Chain [[35,36,37,38],46]: 4*it(35)+2*s(39)+2*s(40)+2*s(41)+2*s(46)+2*s(47)+2*s(48)+0 2.31/2.33 Such that:aux(10) =< V_N 2.31/2.33 aux(12) =< V_N-V_i_0 2.31/2.33 aux(19) =< -V_i_0+V_n 2.31/2.33 aux(13) =< V_m 2.31/2.33 it(35) =< aux(19) 2.31/2.33 aux(14) =< aux(13) 2.31/2.33 aux(15) =< aux(12) 2.31/2.33 s(42) =< it(35)*aux(13) 2.31/2.33 s(45) =< it(35)*aux(12) 2.31/2.33 s(45) =< it(35)*aux(10) 2.31/2.33 s(43) =< it(35)*aux(14) 2.31/2.33 s(51) =< it(35)*aux(15) 2.31/2.33 s(46) =< s(51) 2.31/2.33 s(47) =< s(51) 2.31/2.33 s(46) =< s(43) 2.31/2.33 s(48) =< s(43) 2.31/2.33 s(39) =< s(45) 2.31/2.33 s(40) =< s(45) 2.31/2.33 s(39) =< s(43) 2.31/2.33 s(41) =< s(43) 2.31/2.33 s(39) =< s(42) 2.31/2.33 s(41) =< s(42) 2.31/2.33 2.31/2.33 with precondition: [B=3,V_N>=0,V_i_0>=0,V_m>=0,V_n>=V_i_0+1] 2.31/2.33 2.31/2.33 * Chain [[35,36,37,38],45]: 4*it(35)+2*s(39)+2*s(40)+2*s(41)+2*s(46)+2*s(47)+2*s(48)+0 2.31/2.33 Such that:aux(10) =< V_N 2.31/2.33 aux(12) =< V_N-V_i_0 2.31/2.33 aux(13) =< V_m 2.31/2.33 aux(21) =< -V_i_0+V_n 2.31/2.33 it(35) =< aux(21) 2.31/2.33 aux(14) =< aux(13) 2.31/2.33 aux(15) =< aux(12) 2.31/2.33 s(42) =< it(35)*aux(13) 2.31/2.33 s(45) =< it(35)*aux(12) 2.31/2.33 s(45) =< it(35)*aux(10) 2.31/2.33 s(43) =< it(35)*aux(14) 2.31/2.33 s(51) =< it(35)*aux(15) 2.31/2.33 s(46) =< s(51) 2.31/2.33 s(47) =< s(51) 2.31/2.33 s(46) =< s(43) 2.31/2.33 s(48) =< s(43) 2.31/2.33 s(39) =< s(45) 2.31/2.33 s(40) =< s(45) 2.31/2.33 s(39) =< s(43) 2.31/2.33 s(41) =< s(43) 2.31/2.33 s(39) =< s(42) 2.31/2.33 s(41) =< s(42) 2.31/2.33 2.31/2.33 with precondition: [B=3,V_N>=0,V_i_0>=0,V_m>=0,V_n>=V_i_0+2] 2.31/2.33 2.31/2.33 * Chain [[35,36,37,38],44]: 4*it(35)+2*s(39)+2*s(40)+2*s(41)+2*s(46)+2*s(47)+2*s(48)+1*s(52)+0 2.31/2.33 Such that:aux(10) =< V_N 2.31/2.33 aux(19) =< -V_i_0+V_n 2.31/2.33 aux(13) =< V_m 2.31/2.33 aux(22) =< V_N-V_i_0 2.31/2.33 s(52) =< aux(22) 2.31/2.33 it(35) =< aux(19) 2.31/2.33 it(35) =< aux(22) 2.31/2.33 aux(14) =< aux(13) 2.31/2.33 aux(15) =< aux(22) 2.31/2.33 s(42) =< it(35)*aux(13) 2.31/2.33 s(45) =< it(35)*aux(22) 2.31/2.33 s(45) =< it(35)*aux(10) 2.31/2.33 s(43) =< it(35)*aux(14) 2.31/2.33 s(51) =< it(35)*aux(15) 2.31/2.33 s(46) =< s(51) 2.31/2.33 s(47) =< s(51) 2.31/2.33 s(46) =< s(43) 2.31/2.33 s(48) =< s(43) 2.31/2.33 s(39) =< s(45) 2.31/2.33 s(40) =< s(45) 2.31/2.33 s(39) =< s(43) 2.31/2.33 s(41) =< s(43) 2.31/2.33 s(39) =< s(42) 2.31/2.33 s(41) =< s(42) 2.31/2.33 2.31/2.33 with precondition: [B=3,V_i_0>=0,V_m>=1,V_N>=V_i_0+2,V_n>=V_i_0+2] 2.31/2.33 2.31/2.33 * Chain [[35,36,37,38],43]: 4*it(35)+2*s(39)+2*s(40)+2*s(41)+2*s(46)+2*s(47)+2*s(48)+2*s(55)+2*s(56)+2*s(57)+0 2.31/2.33 Such that:aux(10) =< V_N 2.31/2.33 aux(23) =< V_N-V_i_0 2.31/2.33 aux(24) =< -V_i_0+V_n 2.31/2.33 aux(25) =< V_m 2.31/2.33 s(55) =< aux(23) 2.31/2.33 s(56) =< aux(23) 2.31/2.33 s(55) =< aux(25) 2.31/2.33 s(57) =< aux(25) 2.31/2.33 it(35) =< aux(24) 2.31/2.33 aux(14) =< aux(25) 2.31/2.33 aux(15) =< aux(23) 2.31/2.33 s(42) =< it(35)*aux(25) 2.31/2.33 s(45) =< it(35)*aux(23) 2.31/2.33 s(45) =< it(35)*aux(10) 2.31/2.33 s(43) =< it(35)*aux(14) 2.31/2.33 s(51) =< it(35)*aux(15) 2.31/2.33 s(46) =< s(51) 2.31/2.33 s(47) =< s(51) 2.31/2.33 s(46) =< s(43) 2.31/2.33 s(48) =< s(43) 2.31/2.33 s(39) =< s(45) 2.31/2.33 s(40) =< s(45) 2.31/2.33 s(39) =< s(43) 2.31/2.33 s(41) =< s(43) 2.31/2.33 s(39) =< s(42) 2.31/2.33 s(41) =< s(42) 2.31/2.33 2.31/2.33 with precondition: [B=3,V_N>=0,V_i_0>=0,V_m>=1,V_n>=V_i_0+2] 2.31/2.33 2.31/2.33 * Chain [[35,36,37,38],42]: 4*it(35)+2*s(39)+2*s(40)+2*s(41)+2*s(46)+2*s(47)+2*s(48)+3*s(60)+2*s(61)+2*s(62)+0 2.31/2.33 Such that:aux(10) =< V_N 2.31/2.33 aux(26) =< V_N-V_i_0 2.31/2.33 aux(27) =< -V_i_0+V_n 2.31/2.33 aux(28) =< V_m 2.31/2.33 aux(20) =< aux(26) 2.31/2.33 aux(20) =< aux(27) 2.31/2.33 s(60) =< aux(26) 2.31/2.33 s(61) =< aux(26) 2.31/2.33 s(61) =< aux(28) 2.31/2.33 s(62) =< aux(28) 2.31/2.33 it(35) =< aux(27) 2.31/2.33 it(35) =< aux(20) 2.31/2.33 aux(14) =< aux(28) 2.31/2.33 aux(15) =< aux(26) 2.31/2.33 s(42) =< it(35)*aux(28) 2.31/2.33 s(45) =< it(35)*aux(26) 2.31/2.33 s(45) =< it(35)*aux(10) 2.31/2.33 s(43) =< it(35)*aux(14) 2.31/2.33 s(51) =< it(35)*aux(15) 2.31/2.33 s(46) =< s(51) 2.31/2.33 s(47) =< s(51) 2.31/2.33 s(46) =< s(43) 2.31/2.33 s(48) =< s(43) 2.31/2.33 s(39) =< s(45) 2.31/2.33 s(40) =< s(45) 2.31/2.33 s(39) =< s(43) 2.31/2.33 s(41) =< s(43) 2.31/2.33 s(39) =< s(42) 2.31/2.33 s(41) =< s(42) 2.31/2.33 2.31/2.33 with precondition: [B=3,V_i_0>=0,V_m>=2,V_N>=V_i_0+2,V_n>=V_i_0+2] 2.31/2.33 2.31/2.33 * Chain [[35,36,37,38],41]: 4*it(35)+2*s(39)+2*s(40)+2*s(41)+2*s(46)+2*s(47)+2*s(48)+2*s(65)+2*s(66)+2*s(67)+0 2.31/2.33 Such that:aux(10) =< V_N 2.31/2.33 aux(29) =< V_N-V_i_0 2.31/2.33 aux(30) =< -V_i_0+V_n 2.31/2.33 aux(31) =< V_m 2.31/2.33 s(65) =< aux(29) 2.31/2.33 s(66) =< aux(29) 2.31/2.33 s(65) =< aux(31) 2.31/2.33 s(67) =< aux(31) 2.31/2.33 it(35) =< aux(30) 2.31/2.33 aux(14) =< aux(31) 2.31/2.33 aux(15) =< aux(29) 2.31/2.33 s(42) =< it(35)*aux(31) 2.31/2.33 s(45) =< it(35)*aux(29) 2.31/2.33 s(45) =< it(35)*aux(10) 2.31/2.33 s(43) =< it(35)*aux(14) 2.31/2.33 s(51) =< it(35)*aux(15) 2.31/2.33 s(46) =< s(51) 2.31/2.33 s(47) =< s(51) 2.31/2.33 s(46) =< s(43) 2.31/2.33 s(48) =< s(43) 2.31/2.33 s(39) =< s(45) 2.31/2.33 s(40) =< s(45) 2.31/2.33 s(39) =< s(43) 2.31/2.33 s(41) =< s(43) 2.31/2.33 s(39) =< s(42) 2.31/2.33 s(41) =< s(42) 2.31/2.33 2.31/2.33 with precondition: [B=3,V_N>=0,V_i_0>=0,V_m>=2,V_n>=V_i_0+2] 2.31/2.33 2.31/2.33 * Chain [[35,36,37,38],40]: 4*it(35)+2*s(39)+2*s(40)+2*s(41)+2*s(46)+2*s(47)+2*s(48)+0 2.31/2.33 Such that:aux(10) =< V_N 2.31/2.33 aux(12) =< V_N-V_i_0 2.31/2.33 aux(19) =< -V_i_0+V_n 2.31/2.33 aux(20) =< -V_i_0+I+1 2.31/2.33 aux(13) =< V_m 2.31/2.33 it(35) =< aux(19) 2.31/2.33 it(35) =< aux(20) 2.31/2.33 aux(14) =< aux(13) 2.31/2.33 aux(15) =< aux(12) 2.31/2.33 s(42) =< it(35)*aux(13) 2.31/2.33 s(45) =< it(35)*aux(12) 2.31/2.33 s(45) =< it(35)*aux(10) 2.31/2.33 s(43) =< it(35)*aux(14) 2.31/2.33 s(51) =< it(35)*aux(15) 2.31/2.33 s(46) =< s(51) 2.31/2.33 s(47) =< s(51) 2.31/2.33 s(46) =< s(43) 2.31/2.33 s(48) =< s(43) 2.31/2.33 s(39) =< s(45) 2.31/2.33 s(40) =< s(45) 2.31/2.33 s(39) =< s(43) 2.31/2.33 s(41) =< s(43) 2.31/2.33 s(39) =< s(42) 2.31/2.33 s(41) =< s(42) 2.31/2.33 2.31/2.33 with precondition: [B=5,I+1=D,I+1=H,0>=E,V_N>=0,V_i_0>=0,J>=0,V_n>=V_i_0+1,I>=V_i_0,V_m>=J] 2.31/2.33 2.31/2.33 * Chain [[35,36,37,38],39]: 4*it(35)+2*s(39)+2*s(40)+2*s(41)+2*s(46)+2*s(47)+2*s(48)+0 2.31/2.33 Such that:aux(10) =< V_N 2.31/2.33 aux(12) =< V_N-V_i_0 2.31/2.33 aux(19) =< -V_i_0+V_n 2.31/2.33 aux(20) =< -V_i_0+D 2.31/2.33 aux(13) =< V_m 2.31/2.33 it(35) =< aux(19) 2.31/2.33 it(35) =< aux(20) 2.31/2.33 aux(14) =< aux(13) 2.31/2.33 aux(15) =< aux(12) 2.31/2.33 s(42) =< it(35)*aux(13) 2.31/2.33 s(45) =< it(35)*aux(12) 2.31/2.33 s(45) =< it(35)*aux(10) 2.31/2.33 s(43) =< it(35)*aux(14) 2.31/2.33 s(51) =< it(35)*aux(15) 2.31/2.33 s(46) =< s(51) 2.31/2.33 s(47) =< s(51) 2.31/2.33 s(46) =< s(43) 2.31/2.33 s(48) =< s(43) 2.31/2.33 s(39) =< s(45) 2.31/2.33 s(40) =< s(45) 2.31/2.33 s(39) =< s(43) 2.31/2.33 s(41) =< s(43) 2.31/2.33 s(39) =< s(42) 2.31/2.33 s(41) =< s(42) 2.31/2.33 2.31/2.33 with precondition: [B=5,H=D,H=I+1,V_N>=0,V_i_0>=0,J>=0,V_n>=V_i_0+1,H>=V_n,V_m>=J] 2.31/2.33 2.31/2.33 * Chain [46]: 0 2.31/2.33 with precondition: [B=3,V_N>=0,V_i_0>=0,V_m>=0,V_n>=0] 2.31/2.33 2.31/2.33 * Chain [45]: 0 2.31/2.33 with precondition: [B=3,V_N>=0,V_i_0>=0,V_m>=0,V_n>=V_i_0+1] 2.31/2.33 2.31/2.33 * Chain [44]: 1*s(52)+0 2.31/2.33 Such that:s(52) =< V_N-V_i_0 2.31/2.33 2.31/2.33 with precondition: [B=3,V_i_0>=0,V_m>=1,V_N>=V_i_0+1,V_n>=V_i_0+1] 2.31/2.33 2.31/2.33 * Chain [43]: 2*s(55)+2*s(56)+2*s(57)+0 2.31/2.33 Such that:s(53) =< V_N-V_i_0 2.31/2.33 s(54) =< V_m 2.31/2.33 s(55) =< s(53) 2.31/2.33 s(56) =< s(53) 2.31/2.33 s(55) =< s(54) 2.31/2.33 s(57) =< s(54) 2.31/2.33 2.31/2.33 with precondition: [B=3,V_N>=0,V_i_0>=0,V_m>=1,V_n>=V_i_0+1] 2.31/2.33 2.31/2.33 * Chain [42]: 3*s(60)+2*s(61)+2*s(62)+0 2.31/2.33 Such that:s(58) =< V_N-V_i_0 2.31/2.33 s(59) =< V_m 2.31/2.33 s(60) =< s(58) 2.31/2.33 s(61) =< s(58) 2.31/2.33 s(61) =< s(59) 2.31/2.33 s(62) =< s(59) 2.31/2.33 2.31/2.33 with precondition: [B=3,V_i_0>=0,V_m>=2,V_N>=V_i_0+1,V_n>=V_i_0+1] 2.31/2.33 2.31/2.33 * Chain [41]: 2*s(65)+2*s(66)+2*s(67)+0 2.31/2.33 Such that:s(63) =< V_N-V_i_0 2.31/2.33 s(64) =< V_m 2.31/2.33 s(65) =< s(63) 2.31/2.33 s(66) =< s(63) 2.31/2.33 s(65) =< s(64) 2.31/2.33 s(67) =< s(64) 2.31/2.33 2.31/2.33 with precondition: [B=3,V_N>=0,V_i_0>=0,V_m>=2,V_n>=V_i_0+1] 2.31/2.33 2.31/2.33 * Chain [40]: 0 2.31/2.33 with precondition: [B=5,C=V_10,D=V_14,F=V_6,G=V_9,I=V_i_1,J=V_j_0,K=V_k_0,V_i_0=H,0>=E,V_N>=0,V_i_0>=0,V_m>=0,V_n>=0] 2.31/2.33 2.31/2.33 * Chain [39]: 0 2.31/2.33 with precondition: [B=5,C=V_10,D=V_14,F=V_6,G=V_9,I=V_i_1,J=V_j_0,K=V_k_0,V_i_0=H,V_N>=0,V_m>=0,V_n>=0,V_i_0>=V_n] 2.31/2.33 2.31/2.33 2.31/2.33 #### Cost of chains of eval_nestedLoop_bb1_in_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N): 2.31/2.33 * Chain [48]: 0 2.31/2.33 with precondition: [A=3,G>=0,L>=0,M>=0] 2.31/2.33 2.31/2.33 * Chain [47]: 0 2.31/2.33 with precondition: [A=5,G>=0,L>=0,M>=0] 2.31/2.33 2.31/2.33 2.31/2.33 #### Cost of chains of eval_nestedLoop_3(V_10,V_14,V_3,V_6,V_9,V_N,V_i_0,V_i_1,V_j_0,V_k_0,V_m,V_n,B): 2.31/2.33 * Chain [63]: 0 2.31/2.33 with precondition: [V_n=0,V_N>=0,V_m>=0] 2.31/2.33 2.31/2.33 * Chain [62]: 0 2.31/2.33 with precondition: [0>=V_N+1] 2.31/2.33 2.31/2.33 * Chain [61]: 0 2.31/2.33 with precondition: [0>=V_m+1] 2.31/2.33 2.31/2.33 * Chain [60]: 0 2.31/2.33 with precondition: [0>=V_n+1] 2.31/2.33 2.31/2.33 * Chain [59]: 0 2.31/2.33 with precondition: [V_N>=0,V_m>=0,V_n>=0] 2.31/2.33 2.31/2.33 * Chain [58]: 12*s(89)+6*s(96)+6*s(97)+6*s(98)+6*s(99)+6*s(100)+6*s(101)+0 2.31/2.33 Such that:aux(35) =< V_N 2.31/2.33 aux(36) =< V_m 2.31/2.33 aux(37) =< V_n 2.31/2.33 s(89) =< aux(37) 2.31/2.33 s(90) =< aux(36) 2.31/2.33 s(91) =< aux(35) 2.31/2.33 s(92) =< s(89)*aux(36) 2.31/2.33 s(93) =< s(89)*aux(35) 2.31/2.33 s(94) =< s(89)*s(90) 2.31/2.33 s(95) =< s(89)*s(91) 2.31/2.33 s(96) =< s(95) 2.31/2.33 s(97) =< s(95) 2.31/2.33 s(96) =< s(94) 2.31/2.33 s(98) =< s(94) 2.31/2.33 s(99) =< s(93) 2.31/2.33 s(100) =< s(93) 2.31/2.33 s(99) =< s(94) 2.31/2.33 s(101) =< s(94) 2.31/2.33 s(99) =< s(92) 2.31/2.33 s(101) =< s(92) 2.31/2.33 2.31/2.33 with precondition: [V_N>=0,V_m>=0,V_n>=1] 2.31/2.33 2.31/2.33 * Chain [57]: 4*s(142)+2*s(149)+2*s(150)+2*s(151)+2*s(152)+2*s(153)+2*s(154)+0 2.31/2.33 Such that:s(140) =< V_m 2.31/2.33 s(141) =< V_n 2.31/2.33 aux(38) =< V_N 2.31/2.33 s(142) =< s(141) 2.31/2.33 s(143) =< s(140) 2.31/2.33 s(144) =< aux(38) 2.31/2.33 s(145) =< s(142)*s(140) 2.31/2.33 s(146) =< s(142)*aux(38) 2.31/2.33 s(147) =< s(142)*s(143) 2.31/2.33 s(148) =< s(142)*s(144) 2.31/2.33 s(149) =< s(148) 2.31/2.33 s(150) =< s(148) 2.31/2.33 s(149) =< s(147) 2.31/2.33 s(151) =< s(147) 2.31/2.33 s(152) =< s(146) 2.31/2.33 s(153) =< s(146) 2.31/2.33 s(152) =< s(147) 2.31/2.33 s(154) =< s(147) 2.31/2.33 s(152) =< s(145) 2.31/2.33 s(154) =< s(145) 2.31/2.33 2.31/2.33 with precondition: [V_N>=0,V_m>=0,V_n>=2] 2.31/2.33 2.31/2.33 * Chain [56]: 2*s(157)+2*s(158)+2*s(159)+0 2.31/2.33 Such that:s(155) =< V_N 2.31/2.33 s(156) =< V_m 2.31/2.33 s(157) =< s(155) 2.31/2.33 s(158) =< s(155) 2.31/2.33 s(157) =< s(156) 2.31/2.33 s(159) =< s(156) 2.31/2.33 2.31/2.33 with precondition: [V_N>=0,V_m>=1,V_n>=1] 2.31/2.33 2.31/2.33 * Chain [55]: 2*s(164)+2*s(165)+2*s(166)+4*s(167)+2*s(174)+2*s(175)+2*s(176)+2*s(177)+2*s(178)+2*s(179)+0 2.31/2.33 Such that:s(163) =< V_m 2.31/2.33 s(162) =< V_n 2.31/2.33 aux(39) =< V_N 2.31/2.33 s(164) =< aux(39) 2.31/2.33 s(165) =< aux(39) 2.31/2.33 s(164) =< s(163) 2.31/2.33 s(166) =< s(163) 2.31/2.33 s(167) =< s(162) 2.31/2.33 s(168) =< s(163) 2.31/2.33 s(169) =< aux(39) 2.31/2.33 s(170) =< s(167)*s(163) 2.31/2.33 s(171) =< s(167)*aux(39) 2.31/2.33 s(172) =< s(167)*s(168) 2.31/2.33 s(173) =< s(167)*s(169) 2.31/2.33 s(174) =< s(173) 2.31/2.33 s(175) =< s(173) 2.31/2.33 s(174) =< s(172) 2.31/2.33 s(176) =< s(172) 2.31/2.33 s(177) =< s(171) 2.31/2.33 s(178) =< s(171) 2.31/2.33 s(177) =< s(172) 2.31/2.33 s(179) =< s(172) 2.31/2.33 s(177) =< s(170) 2.31/2.33 s(179) =< s(170) 2.31/2.33 2.31/2.33 with precondition: [V_N>=0,V_m>=1,V_n>=2] 2.31/2.33 2.31/2.33 * Chain [54]: 2*s(182)+2*s(183)+2*s(184)+0 2.31/2.33 Such that:s(180) =< V_N 2.31/2.33 s(181) =< V_m 2.31/2.33 s(182) =< s(180) 2.31/2.33 s(183) =< s(180) 2.31/2.33 s(182) =< s(181) 2.31/2.33 s(184) =< s(181) 2.31/2.33 2.31/2.33 with precondition: [V_N>=0,V_m>=2,V_n>=1] 2.31/2.33 2.31/2.33 * Chain [53]: 2*s(189)+2*s(190)+2*s(191)+4*s(192)+2*s(199)+2*s(200)+2*s(201)+2*s(202)+2*s(203)+2*s(204)+0 2.31/2.33 Such that:s(188) =< V_m 2.31/2.33 s(187) =< V_n 2.31/2.33 aux(40) =< V_N 2.31/2.33 s(189) =< aux(40) 2.31/2.33 s(190) =< aux(40) 2.31/2.33 s(189) =< s(188) 2.31/2.33 s(191) =< s(188) 2.31/2.33 s(192) =< s(187) 2.31/2.33 s(193) =< s(188) 2.31/2.33 s(194) =< aux(40) 2.31/2.33 s(195) =< s(192)*s(188) 2.31/2.33 s(196) =< s(192)*aux(40) 2.31/2.33 s(197) =< s(192)*s(193) 2.31/2.33 s(198) =< s(192)*s(194) 2.31/2.33 s(199) =< s(198) 2.31/2.33 s(200) =< s(198) 2.31/2.33 s(199) =< s(197) 2.31/2.33 s(201) =< s(197) 2.31/2.33 s(202) =< s(196) 2.31/2.33 s(203) =< s(196) 2.31/2.33 s(202) =< s(197) 2.31/2.33 s(204) =< s(197) 2.31/2.33 s(202) =< s(195) 2.31/2.33 s(204) =< s(195) 2.31/2.33 2.31/2.33 with precondition: [V_N>=0,V_m>=2,V_n>=2] 2.31/2.33 2.31/2.33 * Chain [52]: 1*s(205)+0 2.31/2.33 Such that:s(205) =< V_N 2.31/2.33 2.31/2.33 with precondition: [V_N>=1,V_m>=1,V_n>=1] 2.31/2.33 2.31/2.33 * Chain [51]: 3*s(208)+2*s(209)+2*s(210)+0 2.31/2.33 Such that:s(206) =< V_N 2.31/2.33 s(207) =< V_m 2.31/2.33 s(208) =< s(206) 2.31/2.33 s(209) =< s(206) 2.31/2.33 s(209) =< s(207) 2.31/2.33 s(210) =< s(207) 2.31/2.33 2.31/2.33 with precondition: [V_N>=1,V_m>=2,V_n>=1] 2.31/2.33 2.31/2.33 * Chain [50]: 1*s(215)+4*s(216)+2*s(223)+2*s(224)+2*s(225)+2*s(226)+2*s(227)+2*s(228)+0 2.31/2.33 Such that:s(213) =< V_m 2.31/2.33 s(212) =< V_n 2.31/2.33 aux(41) =< V_N 2.31/2.33 s(215) =< aux(41) 2.31/2.33 s(216) =< s(212) 2.31/2.33 s(216) =< aux(41) 2.31/2.33 s(217) =< s(213) 2.31/2.33 s(218) =< aux(41) 2.31/2.33 s(219) =< s(216)*s(213) 2.31/2.33 s(220) =< s(216)*aux(41) 2.31/2.33 s(221) =< s(216)*s(217) 2.31/2.33 s(222) =< s(216)*s(218) 2.31/2.33 s(223) =< s(222) 2.31/2.33 s(224) =< s(222) 2.31/2.33 s(223) =< s(221) 2.31/2.33 s(225) =< s(221) 2.31/2.33 s(226) =< s(220) 2.31/2.33 s(227) =< s(220) 2.31/2.33 s(226) =< s(221) 2.31/2.33 s(228) =< s(221) 2.31/2.33 s(226) =< s(219) 2.31/2.33 s(228) =< s(219) 2.31/2.33 2.31/2.33 with precondition: [V_N>=2,V_m>=1,V_n>=2] 2.31/2.33 2.31/2.33 * Chain [49]: 3*s(234)+2*s(235)+2*s(236)+4*s(237)+2*s(244)+2*s(245)+2*s(246)+2*s(247)+2*s(248)+2*s(249)+0 2.31/2.33 Such that:s(232) =< V_m 2.31/2.33 s(231) =< V_n 2.31/2.33 aux(42) =< V_N 2.31/2.33 s(233) =< aux(42) 2.31/2.33 s(233) =< s(231) 2.31/2.33 s(234) =< aux(42) 2.31/2.33 s(235) =< aux(42) 2.31/2.33 s(235) =< s(232) 2.31/2.33 s(236) =< s(232) 2.31/2.33 s(237) =< s(231) 2.31/2.33 s(237) =< s(233) 2.31/2.33 s(238) =< s(232) 2.31/2.33 s(239) =< aux(42) 2.31/2.33 s(240) =< s(237)*s(232) 2.31/2.33 s(241) =< s(237)*aux(42) 2.31/2.33 s(242) =< s(237)*s(238) 2.31/2.33 s(243) =< s(237)*s(239) 2.31/2.33 s(244) =< s(243) 2.31/2.33 s(245) =< s(243) 2.31/2.33 s(244) =< s(242) 2.31/2.33 s(246) =< s(242) 2.31/2.33 s(247) =< s(241) 2.31/2.33 s(248) =< s(241) 2.31/2.33 s(247) =< s(242) 2.31/2.33 s(249) =< s(242) 2.31/2.33 s(247) =< s(240) 2.31/2.33 s(249) =< s(240) 2.31/2.33 2.31/2.33 with precondition: [V_N>=2,V_m>=2,V_n>=2] 2.31/2.33 2.31/2.33 2.31/2.33 #### Cost of chains of eval_nestedLoop_start(V_10,V_14,V_3,V_6,V_9,V_N,V_i_0,V_i_1,V_j_0,V_k_0,V_m,V_n,B): 2.31/2.33 * Chain [78]: 0 2.31/2.33 with precondition: [V_n=0,V_N>=0,V_m>=0] 2.31/2.33 2.31/2.33 * Chain [77]: 0 2.31/2.33 with precondition: [0>=V_N+1] 2.31/2.33 2.31/2.33 * Chain [76]: 0 2.31/2.33 with precondition: [0>=V_m+1] 2.31/2.33 2.31/2.33 * Chain [75]: 0 2.31/2.33 with precondition: [0>=V_n+1] 2.31/2.33 2.31/2.33 * Chain [74]: 0 2.31/2.33 with precondition: [V_N>=0,V_m>=0,V_n>=0] 2.31/2.33 2.31/2.34 * Chain [73]: 12*s(253)+6*s(260)+6*s(261)+6*s(262)+6*s(263)+6*s(264)+6*s(265)+0 2.31/2.34 Such that:s(250) =< V_N 2.31/2.34 s(251) =< V_m 2.31/2.34 s(252) =< V_n 2.31/2.34 s(253) =< s(252) 2.31/2.34 s(254) =< s(251) 2.31/2.34 s(255) =< s(250) 2.31/2.34 s(256) =< s(253)*s(251) 2.31/2.34 s(257) =< s(253)*s(250) 2.31/2.34 s(258) =< s(253)*s(254) 2.31/2.34 s(259) =< s(253)*s(255) 2.31/2.34 s(260) =< s(259) 2.31/2.34 s(261) =< s(259) 2.31/2.34 s(260) =< s(258) 2.31/2.34 s(262) =< s(258) 2.31/2.34 s(263) =< s(257) 2.31/2.34 s(264) =< s(257) 2.31/2.34 s(263) =< s(258) 2.31/2.34 s(265) =< s(258) 2.31/2.34 s(263) =< s(256) 2.31/2.34 s(265) =< s(256) 2.31/2.34 2.31/2.34 with precondition: [V_N>=0,V_m>=0,V_n>=1] 2.31/2.34 2.31/2.34 * Chain [72]: 4*s(269)+2*s(276)+2*s(277)+2*s(278)+2*s(279)+2*s(280)+2*s(281)+0 2.31/2.34 Such that:s(268) =< V_N 2.31/2.34 s(266) =< V_m 2.31/2.34 s(267) =< V_n 2.31/2.34 s(269) =< s(267) 2.31/2.34 s(270) =< s(266) 2.31/2.34 s(271) =< s(268) 2.31/2.34 s(272) =< s(269)*s(266) 2.31/2.34 s(273) =< s(269)*s(268) 2.31/2.34 s(274) =< s(269)*s(270) 2.31/2.34 s(275) =< s(269)*s(271) 2.31/2.34 s(276) =< s(275) 2.31/2.34 s(277) =< s(275) 2.31/2.34 s(276) =< s(274) 2.31/2.34 s(278) =< s(274) 2.31/2.34 s(279) =< s(273) 2.31/2.34 s(280) =< s(273) 2.31/2.34 s(279) =< s(274) 2.31/2.34 s(281) =< s(274) 2.31/2.34 s(279) =< s(272) 2.31/2.34 s(281) =< s(272) 2.31/2.34 2.31/2.34 with precondition: [V_N>=0,V_m>=0,V_n>=2] 2.31/2.34 2.31/2.34 * Chain [71]: 2*s(284)+2*s(285)+2*s(286)+0 2.31/2.34 Such that:s(282) =< V_N 2.31/2.34 s(283) =< V_m 2.31/2.34 s(284) =< s(282) 2.31/2.34 s(285) =< s(282) 2.31/2.34 s(284) =< s(283) 2.31/2.34 s(286) =< s(283) 2.31/2.34 2.31/2.34 with precondition: [V_N>=0,V_m>=1,V_n>=1] 2.31/2.34 2.31/2.34 * Chain [70]: 2*s(290)+2*s(291)+2*s(292)+4*s(293)+2*s(300)+2*s(301)+2*s(302)+2*s(303)+2*s(304)+2*s(305)+0 2.31/2.34 Such that:s(289) =< V_N 2.31/2.34 s(287) =< V_m 2.31/2.34 s(288) =< V_n 2.31/2.34 s(290) =< s(289) 2.31/2.34 s(291) =< s(289) 2.31/2.34 s(290) =< s(287) 2.31/2.34 s(292) =< s(287) 2.31/2.34 s(293) =< s(288) 2.31/2.34 s(294) =< s(287) 2.31/2.34 s(295) =< s(289) 2.31/2.34 s(296) =< s(293)*s(287) 2.31/2.34 s(297) =< s(293)*s(289) 2.31/2.34 s(298) =< s(293)*s(294) 2.31/2.34 s(299) =< s(293)*s(295) 2.31/2.34 s(300) =< s(299) 2.31/2.34 s(301) =< s(299) 2.31/2.34 s(300) =< s(298) 2.31/2.34 s(302) =< s(298) 2.31/2.34 s(303) =< s(297) 2.31/2.34 s(304) =< s(297) 2.31/2.34 s(303) =< s(298) 2.31/2.34 s(305) =< s(298) 2.31/2.34 s(303) =< s(296) 2.31/2.34 s(305) =< s(296) 2.31/2.34 2.31/2.34 with precondition: [V_N>=0,V_m>=1,V_n>=2] 2.31/2.34 2.31/2.34 * Chain [69]: 2*s(308)+2*s(309)+2*s(310)+0 2.31/2.34 Such that:s(306) =< V_N 2.31/2.34 s(307) =< V_m 2.31/2.34 s(308) =< s(306) 2.31/2.34 s(309) =< s(306) 2.31/2.34 s(308) =< s(307) 2.31/2.34 s(310) =< s(307) 2.31/2.34 2.31/2.34 with precondition: [V_N>=0,V_m>=2,V_n>=1] 2.31/2.34 2.31/2.34 * Chain [68]: 2*s(314)+2*s(315)+2*s(316)+4*s(317)+2*s(324)+2*s(325)+2*s(326)+2*s(327)+2*s(328)+2*s(329)+0 2.31/2.34 Such that:s(313) =< V_N 2.31/2.34 s(311) =< V_m 2.31/2.34 s(312) =< V_n 2.31/2.34 s(314) =< s(313) 2.31/2.34 s(315) =< s(313) 2.31/2.34 s(314) =< s(311) 2.31/2.34 s(316) =< s(311) 2.31/2.34 s(317) =< s(312) 2.31/2.34 s(318) =< s(311) 2.31/2.34 s(319) =< s(313) 2.31/2.34 s(320) =< s(317)*s(311) 2.31/2.34 s(321) =< s(317)*s(313) 2.31/2.34 s(322) =< s(317)*s(318) 2.31/2.34 s(323) =< s(317)*s(319) 2.31/2.34 s(324) =< s(323) 2.31/2.34 s(325) =< s(323) 2.31/2.34 s(324) =< s(322) 2.31/2.34 s(326) =< s(322) 2.31/2.34 s(327) =< s(321) 2.31/2.34 s(328) =< s(321) 2.31/2.34 s(327) =< s(322) 2.31/2.34 s(329) =< s(322) 2.31/2.34 s(327) =< s(320) 2.31/2.34 s(329) =< s(320) 2.31/2.34 2.31/2.34 with precondition: [V_N>=0,V_m>=2,V_n>=2] 2.31/2.34 2.31/2.34 * Chain [67]: 1*s(330)+0 2.31/2.34 Such that:s(330) =< V_N 2.31/2.34 2.31/2.34 with precondition: [V_N>=1,V_m>=1,V_n>=1] 2.31/2.34 2.31/2.34 * Chain [66]: 3*s(333)+2*s(334)+2*s(335)+0 2.31/2.34 Such that:s(331) =< V_N 2.31/2.34 s(332) =< V_m 2.31/2.34 s(333) =< s(331) 2.31/2.34 s(334) =< s(331) 2.31/2.34 s(334) =< s(332) 2.31/2.34 s(335) =< s(332) 2.31/2.34 2.31/2.34 with precondition: [V_N>=1,V_m>=2,V_n>=1] 2.31/2.34 2.31/2.34 * Chain [65]: 1*s(339)+4*s(340)+2*s(347)+2*s(348)+2*s(349)+2*s(350)+2*s(351)+2*s(352)+0 2.31/2.34 Such that:s(338) =< V_N 2.31/2.34 s(336) =< V_m 2.31/2.34 s(337) =< V_n 2.31/2.34 s(339) =< s(338) 2.31/2.34 s(340) =< s(337) 2.31/2.34 s(340) =< s(338) 2.31/2.34 s(341) =< s(336) 2.31/2.34 s(342) =< s(338) 2.31/2.34 s(343) =< s(340)*s(336) 2.31/2.34 s(344) =< s(340)*s(338) 2.31/2.34 s(345) =< s(340)*s(341) 2.31/2.34 s(346) =< s(340)*s(342) 2.31/2.34 s(347) =< s(346) 2.31/2.34 s(348) =< s(346) 2.31/2.34 s(347) =< s(345) 2.31/2.34 s(349) =< s(345) 2.31/2.34 s(350) =< s(344) 2.31/2.34 s(351) =< s(344) 2.31/2.34 s(350) =< s(345) 2.31/2.34 s(352) =< s(345) 2.31/2.34 s(350) =< s(343) 2.31/2.34 s(352) =< s(343) 2.31/2.34 2.31/2.34 with precondition: [V_N>=2,V_m>=1,V_n>=2] 2.31/2.34 2.31/2.34 * Chain [64]: 3*s(357)+2*s(358)+2*s(359)+4*s(360)+2*s(367)+2*s(368)+2*s(369)+2*s(370)+2*s(371)+2*s(372)+0 2.31/2.34 Such that:s(355) =< V_N 2.31/2.34 s(353) =< V_m 2.31/2.34 s(354) =< V_n 2.31/2.34 s(356) =< s(355) 2.31/2.34 s(356) =< s(354) 2.31/2.34 s(357) =< s(355) 2.31/2.34 s(358) =< s(355) 2.31/2.34 s(358) =< s(353) 2.31/2.34 s(359) =< s(353) 2.31/2.34 s(360) =< s(354) 2.31/2.34 s(360) =< s(356) 2.31/2.34 s(361) =< s(353) 2.31/2.34 s(362) =< s(355) 2.31/2.34 s(363) =< s(360)*s(353) 2.31/2.34 s(364) =< s(360)*s(355) 2.31/2.34 s(365) =< s(360)*s(361) 2.31/2.34 s(366) =< s(360)*s(362) 2.31/2.34 s(367) =< s(366) 2.31/2.34 s(368) =< s(366) 2.31/2.34 s(367) =< s(365) 2.31/2.34 s(369) =< s(365) 2.31/2.34 s(370) =< s(364) 2.31/2.34 s(371) =< s(364) 2.31/2.34 s(370) =< s(365) 2.31/2.34 s(372) =< s(365) 2.31/2.34 s(370) =< s(363) 2.31/2.34 s(372) =< s(363) 2.31/2.34 2.31/2.34 with precondition: [V_N>=2,V_m>=2,V_n>=2] 2.31/2.34 2.31/2.34 2.31/2.34 Closed-form bounds of eval_nestedLoop_start(V_10,V_14,V_3,V_6,V_9,V_N,V_i_0,V_i_1,V_j_0,V_k_0,V_m,V_n,B): 2.31/2.34 ------------------------------------- 2.31/2.34 * Chain [78] with precondition: [V_n=0,V_N>=0,V_m>=0] 2.31/2.34 - Upper bound: 0 2.31/2.34 - Complexity: constant 2.31/2.34 * Chain [77] with precondition: [0>=V_N+1] 2.31/2.34 - Upper bound: 0 2.31/2.34 - Complexity: constant 2.31/2.34 * Chain [76] with precondition: [0>=V_m+1] 2.31/2.34 - Upper bound: 0 2.31/2.34 - Complexity: constant 2.31/2.34 * Chain [75] with precondition: [0>=V_n+1] 2.31/2.34 - Upper bound: 0 2.31/2.34 - Complexity: constant 2.31/2.34 * Chain [74] with precondition: [V_N>=0,V_m>=0,V_n>=0] 2.31/2.34 - Upper bound: 0 2.31/2.34 - Complexity: constant 2.31/2.34 * Chain [73] with precondition: [V_N>=0,V_m>=0,V_n>=1] 2.31/2.34 - Upper bound: 24*V_N*V_n+12*V_m*V_n+12*V_n 2.31/2.34 - Complexity: n^2 2.31/2.34 * Chain [72] with precondition: [V_N>=0,V_m>=0,V_n>=2] 2.31/2.34 - Upper bound: 8*V_N*V_n+4*V_m*V_n+4*V_n 2.31/2.34 - Complexity: n^2 2.31/2.34 * Chain [71] with precondition: [V_N>=0,V_m>=1,V_n>=1] 2.31/2.34 - Upper bound: 4*V_N+2*V_m 2.31/2.34 - Complexity: n 2.31/2.34 * Chain [70] with precondition: [V_N>=0,V_m>=1,V_n>=2] 2.31/2.34 - Upper bound: 8*V_N*V_n+4*V_N+2*V_m+4*V_m*V_n+4*V_n 2.31/2.34 - Complexity: n^2 2.31/2.34 * Chain [69] with precondition: [V_N>=0,V_m>=2,V_n>=1] 2.31/2.34 - Upper bound: 4*V_N+2*V_m 2.31/2.34 - Complexity: n 2.31/2.34 * Chain [68] with precondition: [V_N>=0,V_m>=2,V_n>=2] 2.31/2.34 - Upper bound: 8*V_N*V_n+4*V_N+2*V_m+4*V_m*V_n+4*V_n 2.31/2.34 - Complexity: n^2 2.31/2.34 * Chain [67] with precondition: [V_N>=1,V_m>=1,V_n>=1] 2.31/2.34 - Upper bound: V_N 2.31/2.34 - Complexity: n 2.31/2.34 * Chain [66] with precondition: [V_N>=1,V_m>=2,V_n>=1] 2.31/2.34 - Upper bound: 5*V_N+2*V_m 2.31/2.34 - Complexity: n 2.31/2.34 * Chain [65] with precondition: [V_N>=2,V_m>=1,V_n>=2] 2.31/2.34 - Upper bound: 8*V_N*V_n+V_N+4*V_m*V_n+4*V_n 2.31/2.34 - Complexity: n^2 2.31/2.34 * Chain [64] with precondition: [V_N>=2,V_m>=2,V_n>=2] 2.31/2.34 - Upper bound: 8*V_N*V_n+5*V_N+2*V_m+4*V_m*V_n+4*V_n 2.31/2.34 - Complexity: n^2 2.31/2.34 2.31/2.34 ### Maximum cost of eval_nestedLoop_start(V_10,V_14,V_3,V_6,V_9,V_N,V_i_0,V_i_1,V_j_0,V_k_0,V_m,V_n,B): max([nat(V_m)*8*nat(V_n)+nat(V_N)*16*nat(V_n)+nat(V_n)*8+(nat(V_m)*4*nat(V_n)+nat(V_N)*8*nat(V_n)+nat(V_n)*4),nat(V_m)*4*nat(V_n)+nat(V_N)*8*nat(V_n)+nat(V_n)*4+nat(V_N)+(nat(V_m)*2+nat(V_N)*4)]) 2.31/2.34 Asymptotic class: n^2 2.31/2.34 * Total analysis performed in 2091 ms. 2.31/2.34 2.35/2.44 EOF