1.36/1.36 WORST_CASE(?,O(n^2)) 1.36/1.36 1.36/1.36 Preprocessing Cost Relations 1.36/1.36 ===================================== 1.36/1.36 1.36/1.36 #### Computed strongly connected components 1.36/1.36 0. non_recursive : [eval_nested_loop_stop/1] 1.36/1.36 1. non_recursive : [eval_nested_loop__critedge_in/1] 1.36/1.36 2. recursive : [eval_nested_loop_6/7,eval_nested_loop_7/8,eval_nested_loop_bb5_in/7,eval_nested_loop_bb6_in/7,eval_nested_loop_bb7_in/8] 1.36/1.36 3. recursive : [eval_nested_loop_2/7,eval_nested_loop_3/8,eval_nested_loop__critedge3_in/7,eval_nested_loop_bb3_in/7,eval_nested_loop_bb4_in/8,eval_nested_loop_bb5_in_loop_cont/8] 1.36/1.36 4. recursive : [eval_nested_loop_0/5,eval_nested_loop_1/6,eval_nested_loop__critedge2_in/8,eval_nested_loop__critedge3_in_loop_cont/9,eval_nested_loop_bb1_in/5,eval_nested_loop_bb2_in/5] 1.36/1.36 5. non_recursive : [eval_nested_loop_bb1_in_loop_cont/2] 1.36/1.36 6. non_recursive : [eval_nested_loop_bb0_in/4] 1.36/1.36 7. non_recursive : [eval_nested_loop_start/4] 1.36/1.36 1.36/1.36 #### Obtained direct recursion through partial evaluation 1.36/1.36 0. SCC is completely evaluated into other SCCs 1.36/1.36 1. SCC is completely evaluated into other SCCs 1.36/1.36 2. SCC is partially evaluated into eval_nested_loop_bb5_in/7 1.36/1.36 3. SCC is partially evaluated into eval_nested_loop__critedge3_in/7 1.36/1.36 4. SCC is partially evaluated into eval_nested_loop_bb1_in/5 1.36/1.36 5. SCC is completely evaluated into other SCCs 1.36/1.36 6. SCC is partially evaluated into eval_nested_loop_bb0_in/4 1.36/1.36 7. SCC is partially evaluated into eval_nested_loop_start/4 1.36/1.36 1.36/1.36 Control-Flow Refinement of Cost Relations 1.36/1.36 ===================================== 1.36/1.36 1.36/1.36 ### Specialization of cost equations eval_nested_loop_bb5_in/7 1.36/1.36 * CE 12 is refined into CE [15] 1.36/1.36 * CE 14 is refined into CE [16] 1.36/1.36 * CE 13 is refined into CE [17] 1.36/1.36 1.36/1.36 1.36/1.36 ### Cost equations --> "Loop" of eval_nested_loop_bb5_in/7 1.36/1.36 * CEs [17] --> Loop 15 1.36/1.36 * CEs [15] --> Loop 16 1.36/1.36 * CEs [16] --> Loop 17 1.36/1.36 1.36/1.36 ### Ranking functions of CR eval_nested_loop_bb5_in(V_N,V_j_0,V_i_1,V_7,V_k_0,B,C) 1.36/1.36 * RF of phase [15]: [V_N-V_k_0] 1.36/1.36 1.36/1.36 #### Partial ranking functions of CR eval_nested_loop_bb5_in(V_N,V_j_0,V_i_1,V_7,V_k_0,B,C) 1.36/1.36 * Partial RF of phase [15]: 1.36/1.36 - RF of loop [15:1]: 1.36/1.36 V_N-V_k_0 1.36/1.36 1.36/1.36 1.36/1.36 ### Specialization of cost equations eval_nested_loop__critedge3_in/7 1.36/1.36 * CE 9 is refined into CE [18] 1.36/1.36 * CE 11 is refined into CE [19] 1.36/1.36 * CE 10 is refined into CE [20,21,22,23] 1.36/1.36 1.36/1.36 1.36/1.36 ### Cost equations --> "Loop" of eval_nested_loop__critedge3_in/7 1.36/1.36 * CEs [23] --> Loop 18 1.36/1.36 * CEs [22] --> Loop 19 1.36/1.36 * CEs [21] --> Loop 20 1.36/1.36 * CEs [20] --> Loop 21 1.36/1.36 * CEs [18] --> Loop 22 1.36/1.36 * CEs [19] --> Loop 23 1.36/1.36 1.36/1.36 ### Ranking functions of CR eval_nested_loop__critedge3_in(V_m,V_N,V_j_0,V_i_1,B,C,D) 1.36/1.36 * RF of phase [18,19]: [V_m-V_j_0] 1.36/1.36 * RF of phase [20]: [V_m-V_j_0] 1.36/1.36 1.36/1.36 #### Partial ranking functions of CR eval_nested_loop__critedge3_in(V_m,V_N,V_j_0,V_i_1,B,C,D) 1.36/1.36 * Partial RF of phase [18,19]: 1.36/1.36 - RF of loop [18:1]: 1.36/1.36 V_N-V_i_1-1 1.36/1.36 - RF of loop [18:1,19:1]: 1.36/1.36 V_m-V_j_0 1.36/1.36 * Partial RF of phase [20]: 1.36/1.36 - RF of loop [20:1]: 1.36/1.36 V_m-V_j_0 1.36/1.36 1.36/1.36 1.36/1.36 ### Specialization of cost equations eval_nested_loop_bb1_in/5 1.36/1.36 * CE 6 is refined into CE [24] 1.36/1.36 * CE 8 is refined into CE [25] 1.36/1.36 * CE 7 is refined into CE [26,27,28,29,30,31,32,33,34,35,36,37] 1.36/1.36 1.36/1.36 1.36/1.36 ### Cost equations --> "Loop" of eval_nested_loop_bb1_in/5 1.36/1.36 * CEs [37] --> Loop 24 1.36/1.36 * CEs [33] --> Loop 25 1.36/1.36 * CEs [36] --> Loop 26 1.36/1.36 * CEs [32] --> Loop 27 1.36/1.36 * CEs [29] --> Loop 28 1.36/1.36 * CEs [35] --> Loop 29 1.36/1.36 * CEs [31,34] --> Loop 30 1.36/1.36 * CEs [28,30] --> Loop 31 1.36/1.36 * CEs [27] --> Loop 32 1.36/1.36 * CEs [26] --> Loop 33 1.36/1.36 * CEs [24] --> Loop 34 1.36/1.36 * CEs [25] --> Loop 35 1.36/1.36 1.36/1.36 ### Ranking functions of CR eval_nested_loop_bb1_in(V_n,V_m,V_N,V_i_0,B) 1.36/1.36 * RF of phase [24,25,26,27,28,29,30,31,32]: [V_n+V_N-V_i_0,V_n-V_i_0] 1.36/1.36 * RF of phase [33]: [V_n-V_i_0] 1.36/1.36 1.36/1.36 #### Partial ranking functions of CR eval_nested_loop_bb1_in(V_n,V_m,V_N,V_i_0,B) 1.36/1.36 * Partial RF of phase [24,25,26,27,28,29,30,31,32]: 1.36/1.36 - RF of loop [24:1,25:1]: 1.36/1.36 V_N-V_i_0 1.36/1.36 - RF of loop [24:1,25:1,26:1,27:1,28:1]: 1.36/1.36 V_n-V_i_0 1.36/1.36 - RF of loop [29:1,30:1,31:1,32:1]: 1.36/1.36 V_N/2-V_i_0/2 1.36/1.36 V_n/2-V_i_0/2 1.36/1.36 * Partial RF of phase [33]: 1.36/1.36 - RF of loop [33:1]: 1.36/1.36 V_n-V_i_0 1.36/1.36 1.36/1.36 1.36/1.36 ### Specialization of cost equations eval_nested_loop_bb0_in/4 1.36/1.36 * CE 5 is refined into CE [38,39,40,41,42,43] 1.36/1.36 * CE 4 is refined into CE [44] 1.36/1.36 * CE 3 is refined into CE [45] 1.36/1.36 * CE 2 is refined into CE [46] 1.36/1.36 1.36/1.36 1.36/1.36 ### Cost equations --> "Loop" of eval_nested_loop_bb0_in/4 1.36/1.36 * CEs [43] --> Loop 36 1.36/1.36 * CEs [42] --> Loop 37 1.36/1.36 * CEs [41] --> Loop 38 1.36/1.36 * CEs [44] --> Loop 39 1.36/1.36 * CEs [45] --> Loop 40 1.36/1.36 * CEs [46] --> Loop 41 1.36/1.36 * CEs [39] --> Loop 42 1.36/1.36 * CEs [38] --> Loop 43 1.36/1.36 * CEs [40] --> Loop 44 1.36/1.36 1.36/1.36 ### Ranking functions of CR eval_nested_loop_bb0_in(V_n,V_m,V_N,B) 1.36/1.36 1.36/1.36 #### Partial ranking functions of CR eval_nested_loop_bb0_in(V_n,V_m,V_N,B) 1.36/1.36 1.36/1.36 1.36/1.36 ### Specialization of cost equations eval_nested_loop_start/4 1.36/1.36 * CE 1 is refined into CE [47,48,49,50,51,52,53,54,55] 1.36/1.36 1.36/1.36 1.36/1.36 ### Cost equations --> "Loop" of eval_nested_loop_start/4 1.36/1.36 * CEs [55] --> Loop 45 1.36/1.36 * CEs [54] --> Loop 46 1.36/1.36 * CEs [53] --> Loop 47 1.36/1.36 * CEs [52] --> Loop 48 1.36/1.36 * CEs [51] --> Loop 49 1.36/1.36 * CEs [50] --> Loop 50 1.36/1.36 * CEs [49] --> Loop 51 1.36/1.36 * CEs [48] --> Loop 52 1.36/1.36 * CEs [47] --> Loop 53 1.36/1.36 1.36/1.36 ### Ranking functions of CR eval_nested_loop_start(V_n,V_m,V_N,B) 1.36/1.36 1.36/1.36 #### Partial ranking functions of CR eval_nested_loop_start(V_n,V_m,V_N,B) 1.36/1.36 1.36/1.36 1.36/1.36 Computing Bounds 1.36/1.36 ===================================== 1.36/1.36 1.36/1.36 #### Cost of chains of eval_nested_loop_bb5_in(V_N,V_j_0,V_i_1,V_7,V_k_0,B,C): 1.36/1.36 * Chain [[15],17]: 1*it(15)+0 1.36/1.36 Such that:it(15) =< -V_k_0+C 1.36/1.36 1.36/1.36 with precondition: [B=2,V_N=C,V_N>=0,V_j_0>=0,V_7>=1,V_k_0>=V_i_1,V_N>=V_k_0+1] 1.36/1.36 1.36/1.36 * Chain [[15],16]: 1*it(15)+0 1.36/1.36 Such that:it(15) =< -V_k_0+C 1.36/1.36 1.36/1.36 with precondition: [B=2,V_N>=0,V_j_0>=0,V_7>=1,V_k_0>=V_i_1,C>=V_k_0+1,V_N>=C+1] 1.36/1.36 1.36/1.36 * Chain [17]: 0 1.36/1.36 with precondition: [B=2,V_k_0=C,V_N>=0,V_j_0>=0,V_7>=1,V_k_0>=V_N,V_k_0>=V_i_1] 1.36/1.36 1.36/1.36 * Chain [16]: 0 1.36/1.36 with precondition: [B=2,V_k_0=C,V_N>=0,V_j_0>=0,V_7>=1,V_k_0>=V_i_1,V_N>=V_k_0+1] 1.36/1.36 1.36/1.36 1.36/1.36 #### Cost of chains of eval_nested_loop__critedge3_in(V_m,V_N,V_j_0,V_i_1,B,C,D): 1.36/1.36 * Chain [[20],23]: 1*it(20)+0 1.36/1.36 Such that:it(20) =< -V_j_0+C 1.36/1.36 1.36/1.36 with precondition: [B=3,V_m=C,V_i_1=D,V_N>=0,V_j_0>=0,V_i_1>=V_N,V_m>=V_j_0+1] 1.36/1.36 1.36/1.36 * Chain [[20],22]: 1*it(20)+0 1.36/1.36 Such that:it(20) =< -V_j_0+C 1.36/1.36 1.36/1.36 with precondition: [B=3,V_i_1=D,V_N>=0,V_j_0>=0,V_i_1>=V_N,C>=V_j_0+1,V_m>=C+1] 1.36/1.36 1.36/1.36 * Chain [[18,19],23]: 1*it(18)+1*it(19)+1*s(3)+0 1.36/1.36 Such that:aux(3) =< V_N-V_i_1 1.36/1.36 aux(4) =< -V_i_1+D 1.36/1.36 aux(5) =< V_m-V_j_0 1.36/1.36 it(18) =< aux(5) 1.36/1.36 it(19) =< aux(5) 1.36/1.36 it(18) =< aux(3) 1.36/1.36 s(3) =< aux(3) 1.36/1.36 it(18) =< aux(4) 1.36/1.36 s(3) =< aux(4) 1.36/1.36 1.36/1.36 with precondition: [B=3,V_m=C,V_N>=0,V_j_0>=0,V_m>=V_j_0+1,D>=V_i_1,V_N>=D+1] 1.36/1.36 1.36/1.36 * Chain [[18,19],22]: 1*it(18)+1*it(19)+1*s(3)+0 1.36/1.36 Such that:aux(1) =< V_m-V_j_0 1.36/1.36 aux(3) =< V_N-V_i_1 1.36/1.36 aux(2) =< -V_j_0+C 1.36/1.36 aux(4) =< -V_i_1+D 1.36/1.36 it(18) =< aux(1) 1.36/1.36 it(19) =< aux(1) 1.36/1.36 it(18) =< aux(2) 1.36/1.36 it(19) =< aux(2) 1.36/1.36 it(18) =< aux(3) 1.36/1.36 s(3) =< aux(3) 1.36/1.36 it(18) =< aux(4) 1.36/1.36 s(3) =< aux(4) 1.36/1.36 1.36/1.36 with precondition: [B=3,V_N>=0,V_j_0>=0,C>=V_j_0+1,D>=V_i_1,V_m>=C+1,V_N>=D+1] 1.36/1.36 1.36/1.36 * Chain [[18,19],21,[20],23]: 1*it(18)+2*it(19)+2*s(3)+1 1.36/1.36 Such that:aux(6) =< V_m-V_j_0 1.36/1.36 aux(7) =< -V_i_1+D 1.36/1.36 it(19) =< aux(6) 1.36/1.36 s(3) =< aux(7) 1.36/1.36 it(18) =< aux(6) 1.36/1.36 it(18) =< aux(7) 1.36/1.36 1.36/1.36 with precondition: [B=3,V_m=C,V_N=D,V_N>=0,V_j_0>=0,V_m>=V_j_0+3,V_N>=V_i_1+1] 1.36/1.36 1.36/1.36 * Chain [[18,19],21,[20],22]: 1*it(18)+1*it(19)+1*it(20)+2*s(3)+1 1.36/1.36 Such that:aux(1) =< V_m-V_j_0 1.36/1.36 aux(8) =< -V_j_0+C 1.36/1.36 aux(9) =< -V_i_1+D 1.36/1.36 it(20) =< aux(8) 1.36/1.36 s(3) =< aux(9) 1.36/1.36 it(18) =< aux(1) 1.36/1.36 it(19) =< aux(1) 1.36/1.36 it(18) =< aux(8) 1.36/1.36 it(19) =< aux(8) 1.36/1.36 it(18) =< aux(9) 1.36/1.36 1.36/1.36 with precondition: [B=3,V_N=D,V_N>=0,V_j_0>=0,C>=V_j_0+3,V_N>=V_i_1+1,V_m>=C+1] 1.36/1.36 1.36/1.36 * Chain [[18,19],21,23]: 1*it(18)+1*it(19)+2*s(3)+1 1.36/1.36 Such that:aux(10) =< -V_j_0+C 1.36/1.36 aux(11) =< -V_i_1+D 1.36/1.36 s(3) =< aux(11) 1.36/1.36 it(18) =< aux(10) 1.36/1.36 it(19) =< aux(10) 1.36/1.36 it(18) =< aux(11) 1.36/1.36 1.36/1.36 with precondition: [B=3,V_m=C,V_N=D,V_N>=0,V_j_0>=0,V_m>=V_j_0+2,V_N>=V_i_1+1] 1.36/1.36 1.36/1.36 * Chain [[18,19],21,22]: 1*it(18)+1*it(19)+2*s(3)+1 1.36/1.36 Such that:aux(1) =< V_m-V_j_0 1.36/1.36 aux(2) =< -V_j_0+C 1.36/1.36 aux(12) =< -V_i_1+D 1.36/1.36 s(3) =< aux(12) 1.36/1.36 it(18) =< aux(1) 1.36/1.36 it(19) =< aux(1) 1.36/1.36 it(18) =< aux(2) 1.36/1.36 it(19) =< aux(2) 1.36/1.36 it(18) =< aux(12) 1.36/1.36 1.36/1.36 with precondition: [B=3,V_N=D,V_N>=0,V_j_0>=0,C>=V_j_0+2,V_N>=V_i_1+1,V_m>=C+1] 1.36/1.36 1.36/1.36 * Chain [23]: 0 1.36/1.36 with precondition: [B=3,V_j_0=V_m,D=V_i_1,V_j_0=C,V_N>=0,V_j_0>=0] 1.36/1.36 1.36/1.36 * Chain [22]: 0 1.36/1.36 with precondition: [B=3,D=V_i_1,V_j_0=C,V_N>=0,V_j_0>=0,V_m>=V_j_0+1] 1.36/1.36 1.36/1.36 * Chain [21,[20],23]: 1*it(20)+1*s(4)+1 1.36/1.36 Such that:it(20) =< -V_j_0+C 1.36/1.36 s(4) =< -V_i_1+D 1.36/1.36 1.36/1.36 with precondition: [B=3,V_m=C,V_N=D,V_N>=0,V_j_0>=0,V_m>=V_j_0+2,V_N>=V_i_1+1] 1.36/1.36 1.36/1.36 * Chain [21,[20],22]: 1*it(20)+1*s(4)+1 1.36/1.36 Such that:it(20) =< -V_j_0+C 1.36/1.36 s(4) =< -V_i_1+D 1.36/1.36 1.36/1.36 with precondition: [B=3,V_N=D,V_N>=0,V_j_0>=0,C>=V_j_0+2,V_N>=V_i_1+1,V_m>=C+1] 1.36/1.36 1.36/1.36 * Chain [21,23]: 1*s(4)+1 1.36/1.36 Such that:s(4) =< -V_i_1+D 1.36/1.36 1.36/1.36 with precondition: [B=3,V_m=V_j_0+1,V_m=C,V_N=D,V_m>=1,V_N>=0,V_N>=V_i_1+1] 1.36/1.36 1.36/1.36 * Chain [21,22]: 1*s(4)+1 1.36/1.36 Such that:s(4) =< -V_i_1+D 1.36/1.36 1.36/1.36 with precondition: [B=3,C=V_j_0+1,V_N=D,V_N>=0,C>=1,V_N>=V_i_1+1,V_m>=C+1] 1.36/1.36 1.36/1.36 1.36/1.36 #### Cost of chains of eval_nested_loop_bb1_in(V_n,V_m,V_N,V_i_0,B): 1.36/1.36 * Chain [[33],35]: 1*it(33)+0 1.36/1.36 Such that:it(33) =< V_n-V_i_0 1.36/1.36 1.36/1.36 with precondition: [V_m=0,B=4,V_N>=0,V_i_0>=0,V_n>=V_i_0+1] 1.36/1.36 1.36/1.36 * Chain [[33],34]: 1*it(33)+0 1.36/1.36 Such that:it(33) =< V_n-V_i_0 1.36/1.36 1.36/1.36 with precondition: [V_m=0,B=4,V_N>=0,V_i_0>=0,V_n>=V_i_0+2] 1.36/1.36 1.36/1.36 * Chain [[24,25,26,27,28,29,30,31,32],35]: 2*it(24)+3*it(26)+2*it(29)+6*it(30)+1*s(91)+1*s(92)+1*s(93)+1*s(97)+1*s(98)+1*s(99)+2*s(103)+2*s(105)+11*s(106)+1*s(107)+6*s(110)+3*s(112)+1*s(120)+0 1.36/1.36 Such that:aux(34) =< V_n-V_i_0 1.36/1.36 aux(36) =< V_n/2-V_i_0/2 1.36/1.36 aux(23) =< V_m 1.36/1.36 aux(38) =< V_N-V_i_0 1.36/1.36 aux(39) =< V_N-V_i_0+1 1.36/1.36 aux(41) =< V_N/2-V_i_0/2 1.36/1.36 aux(43) =< V_n+V_N-V_i_0 1.36/1.36 aux(44) =< V_n/2+V_N/2-V_i_0/2 1.36/1.36 it(24) =< aux(43) 1.36/1.36 it(26) =< aux(43) 1.36/1.36 it(29) =< aux(43) 1.36/1.36 it(30) =< aux(43) 1.36/1.36 it(24) =< aux(34) 1.36/1.36 it(26) =< aux(34) 1.36/1.36 it(29) =< aux(34) 1.36/1.36 it(30) =< aux(34) 1.36/1.36 it(29) =< aux(36) 1.36/1.36 it(30) =< aux(36) 1.36/1.36 it(29) =< aux(44) 1.36/1.36 it(30) =< aux(44) 1.36/1.36 it(24) =< aux(38) 1.36/1.36 it(29) =< aux(38) 1.36/1.36 it(30) =< aux(38) 1.36/1.36 s(94) =< aux(38) 1.36/1.36 it(30) =< aux(39) 1.36/1.36 s(108) =< aux(39) 1.36/1.36 s(120) =< aux(39) 1.36/1.36 s(94) =< aux(43) 1.36/1.36 s(108) =< aux(43) 1.36/1.36 s(120) =< aux(43) 1.36/1.36 it(29) =< aux(41) 1.36/1.36 it(30) =< aux(41) 1.36/1.36 aux(26) =< aux(23) 1.36/1.36 aux(25) =< aux(38) 1.36/1.36 s(95) =< it(24)*aux(38) 1.36/1.36 s(96) =< it(24)*aux(23) 1.36/1.36 s(114) =< it(30)*aux(26) 1.36/1.36 s(109) =< it(29)*aux(26) 1.36/1.36 s(103) =< it(26)*aux(26) 1.36/1.36 s(102) =< it(24)*aux(26) 1.36/1.36 s(101) =< it(24)*aux(25) 1.36/1.36 s(106) =< s(108) 1.36/1.36 s(110) =< s(114) 1.36/1.36 s(112) =< s(114) 1.36/1.36 s(112) =< s(108) 1.36/1.36 s(105) =< s(109) 1.36/1.36 s(107) =< s(109) 1.36/1.36 s(107) =< s(108) 1.36/1.36 s(97) =< s(102) 1.36/1.36 s(98) =< s(102) 1.36/1.36 s(97) =< s(101) 1.36/1.36 s(99) =< s(101) 1.36/1.36 s(97) =< s(94) 1.36/1.36 s(99) =< s(94) 1.36/1.36 s(91) =< s(96) 1.36/1.37 s(92) =< s(96) 1.36/1.37 s(91) =< s(95) 1.36/1.37 s(93) =< s(95) 1.36/1.37 s(91) =< s(94) 1.36/1.37 s(93) =< s(94) 1.36/1.37 1.36/1.37 with precondition: [B=4,V_m>=1,V_N>=0,V_i_0>=0,V_n>=V_i_0+1] 1.36/1.37 1.36/1.37 * Chain [[24,25,26,27,28,29,30,31,32],34]: 2*it(24)+3*it(26)+2*it(29)+6*it(30)+1*s(91)+1*s(92)+1*s(93)+1*s(97)+1*s(98)+1*s(99)+2*s(103)+2*s(105)+11*s(106)+1*s(107)+6*s(110)+3*s(112)+1*s(120)+0 1.36/1.37 Such that:aux(32) =< V_n+V_N-V_i_0 1.36/1.37 aux(23) =< V_m 1.36/1.37 aux(38) =< V_N-V_i_0 1.36/1.37 aux(39) =< V_N-V_i_0+1 1.36/1.37 aux(41) =< V_N/2-V_i_0/2 1.36/1.37 aux(45) =< V_n-V_i_0 1.36/1.37 aux(46) =< V_n/2-V_i_0/2 1.36/1.37 it(24) =< aux(32) 1.36/1.37 it(26) =< aux(32) 1.36/1.37 it(29) =< aux(32) 1.36/1.37 it(30) =< aux(32) 1.36/1.37 it(24) =< aux(45) 1.36/1.37 it(26) =< aux(45) 1.36/1.37 it(29) =< aux(45) 1.36/1.37 it(30) =< aux(45) 1.36/1.37 it(29) =< aux(46) 1.36/1.37 it(30) =< aux(46) 1.36/1.37 it(24) =< aux(38) 1.36/1.37 it(29) =< aux(38) 1.36/1.37 it(30) =< aux(38) 1.36/1.37 s(94) =< aux(38) 1.36/1.37 it(30) =< aux(39) 1.36/1.37 s(108) =< aux(39) 1.36/1.37 s(120) =< aux(39) 1.36/1.37 s(94) =< aux(45) 1.36/1.37 s(108) =< aux(45) 1.36/1.37 s(120) =< aux(45) 1.36/1.37 it(29) =< aux(41) 1.36/1.37 it(30) =< aux(41) 1.36/1.37 aux(26) =< aux(23) 1.36/1.37 aux(25) =< aux(38) 1.36/1.37 s(95) =< it(24)*aux(38) 1.36/1.37 s(96) =< it(24)*aux(23) 1.36/1.37 s(114) =< it(30)*aux(26) 1.36/1.37 s(109) =< it(29)*aux(26) 1.36/1.37 s(103) =< it(26)*aux(26) 1.36/1.37 s(102) =< it(24)*aux(26) 1.36/1.37 s(101) =< it(24)*aux(25) 1.36/1.37 s(106) =< s(108) 1.36/1.37 s(110) =< s(114) 1.36/1.37 s(112) =< s(114) 1.36/1.37 s(112) =< s(108) 1.36/1.37 s(105) =< s(109) 1.36/1.37 s(107) =< s(109) 1.36/1.37 s(107) =< s(108) 1.36/1.37 s(97) =< s(102) 1.36/1.37 s(98) =< s(102) 1.36/1.37 s(97) =< s(101) 1.36/1.37 s(99) =< s(101) 1.36/1.37 s(97) =< s(94) 1.36/1.37 s(99) =< s(94) 1.36/1.37 s(91) =< s(96) 1.36/1.37 s(92) =< s(96) 1.36/1.37 s(91) =< s(95) 1.36/1.37 s(93) =< s(95) 1.36/1.37 s(91) =< s(94) 1.36/1.37 s(93) =< s(94) 1.36/1.37 1.36/1.37 with precondition: [B=4,V_m>=1,V_N>=0,V_i_0>=0,V_n>=V_i_0+2] 1.36/1.37 1.36/1.37 * Chain [35]: 0 1.36/1.37 with precondition: [B=4,V_n>=0,V_m>=0,V_i_0>=V_n,V_N+V_n>=V_i_0] 1.36/1.37 1.36/1.37 * Chain [34]: 0 1.36/1.37 with precondition: [B=4,V_m>=0,V_N>=0,V_i_0>=0,V_n>=V_i_0+1] 1.36/1.37 1.36/1.37 1.36/1.37 #### Cost of chains of eval_nested_loop_bb0_in(V_n,V_m,V_N,B): 1.36/1.37 * Chain [44]: 0 1.36/1.37 with precondition: [V_n=0,V_m>=0,V_N>=0] 1.36/1.37 1.36/1.37 * Chain [43]: 1*s(121)+0 1.36/1.37 Such that:s(121) =< V_n 1.36/1.37 1.36/1.37 with precondition: [V_m=0,V_n>=1,V_N>=0] 1.36/1.37 1.36/1.37 * Chain [42]: 1*s(122)+0 1.36/1.37 Such that:s(122) =< V_n 1.36/1.37 1.36/1.37 with precondition: [V_m=0,V_n>=2,V_N>=0] 1.36/1.37 1.36/1.37 * Chain [41]: 0 1.36/1.37 with precondition: [0>=V_n+1] 1.36/1.37 1.36/1.37 * Chain [40]: 0 1.36/1.37 with precondition: [0>=V_m+1] 1.36/1.37 1.36/1.37 * Chain [39]: 0 1.36/1.37 with precondition: [0>=V_N+1] 1.36/1.37 1.36/1.37 * Chain [38]: 0 1.36/1.37 with precondition: [V_n>=1,V_m>=0,V_N>=0] 1.36/1.37 1.36/1.37 * Chain [37]: 2*s(131)+3*s(132)+2*s(133)+6*s(134)+1*s(137)+2*s(144)+11*s(147)+6*s(148)+3*s(149)+2*s(150)+1*s(151)+1*s(152)+1*s(153)+1*s(154)+1*s(155)+1*s(156)+1*s(157)+0 1.36/1.37 Such that:s(123) =< V_n 1.36/1.37 s(129) =< V_n+V_N 1.36/1.37 s(124) =< V_n/2 1.36/1.37 s(130) =< V_n/2+V_N/2 1.36/1.37 s(125) =< V_m 1.36/1.37 s(126) =< V_N 1.36/1.37 s(127) =< V_N+1 1.36/1.37 s(128) =< V_N/2 1.36/1.37 s(131) =< s(129) 1.36/1.37 s(132) =< s(129) 1.36/1.37 s(133) =< s(129) 1.36/1.37 s(134) =< s(129) 1.36/1.37 s(131) =< s(123) 1.36/1.37 s(132) =< s(123) 1.36/1.37 s(133) =< s(123) 1.36/1.37 s(134) =< s(123) 1.36/1.37 s(133) =< s(124) 1.36/1.37 s(134) =< s(124) 1.36/1.37 s(133) =< s(130) 1.36/1.37 s(134) =< s(130) 1.36/1.37 s(131) =< s(126) 1.36/1.37 s(133) =< s(126) 1.36/1.37 s(134) =< s(126) 1.36/1.37 s(135) =< s(126) 1.36/1.37 s(134) =< s(127) 1.36/1.37 s(136) =< s(127) 1.36/1.37 s(137) =< s(127) 1.36/1.37 s(135) =< s(129) 1.36/1.37 s(136) =< s(129) 1.36/1.37 s(137) =< s(129) 1.36/1.37 s(133) =< s(128) 1.36/1.37 s(134) =< s(128) 1.36/1.37 s(138) =< s(125) 1.36/1.37 s(139) =< s(126) 1.36/1.37 s(140) =< s(131)*s(126) 1.36/1.37 s(141) =< s(131)*s(125) 1.36/1.37 s(142) =< s(134)*s(138) 1.36/1.37 s(143) =< s(133)*s(138) 1.36/1.37 s(144) =< s(132)*s(138) 1.36/1.37 s(145) =< s(131)*s(138) 1.36/1.37 s(146) =< s(131)*s(139) 1.36/1.37 s(147) =< s(136) 1.36/1.37 s(148) =< s(142) 1.36/1.37 s(149) =< s(142) 1.36/1.37 s(149) =< s(136) 1.36/1.37 s(150) =< s(143) 1.36/1.37 s(151) =< s(143) 1.36/1.37 s(151) =< s(136) 1.36/1.37 s(152) =< s(145) 1.36/1.37 s(153) =< s(145) 1.36/1.37 s(152) =< s(146) 1.36/1.37 s(154) =< s(146) 1.36/1.37 s(152) =< s(135) 1.36/1.37 s(154) =< s(135) 1.36/1.37 s(155) =< s(141) 1.36/1.37 s(156) =< s(141) 1.36/1.37 s(155) =< s(140) 1.36/1.37 s(157) =< s(140) 1.36/1.37 s(155) =< s(135) 1.36/1.37 s(157) =< s(135) 1.36/1.37 1.36/1.37 with precondition: [V_n>=1,V_m>=1,V_N>=0] 1.36/1.37 1.36/1.37 * Chain [36]: 2*s(165)+3*s(166)+2*s(167)+6*s(168)+1*s(171)+2*s(178)+11*s(181)+6*s(182)+3*s(183)+2*s(184)+1*s(185)+1*s(186)+1*s(187)+1*s(188)+1*s(189)+1*s(190)+1*s(191)+0 1.36/1.37 Such that:s(163) =< V_n 1.36/1.37 s(158) =< V_n+V_N 1.36/1.37 s(164) =< V_n/2 1.36/1.37 s(159) =< V_m 1.36/1.37 s(160) =< V_N 1.36/1.37 s(161) =< V_N+1 1.36/1.37 s(162) =< V_N/2 1.36/1.37 s(165) =< s(158) 1.36/1.37 s(166) =< s(158) 1.36/1.37 s(167) =< s(158) 1.36/1.37 s(168) =< s(158) 1.36/1.37 s(165) =< s(163) 1.36/1.37 s(166) =< s(163) 1.36/1.37 s(167) =< s(163) 1.36/1.37 s(168) =< s(163) 1.36/1.37 s(167) =< s(164) 1.36/1.37 s(168) =< s(164) 1.36/1.37 s(165) =< s(160) 1.36/1.37 s(167) =< s(160) 1.36/1.37 s(168) =< s(160) 1.36/1.37 s(169) =< s(160) 1.36/1.37 s(168) =< s(161) 1.36/1.37 s(170) =< s(161) 1.36/1.37 s(171) =< s(161) 1.36/1.37 s(169) =< s(163) 1.36/1.37 s(170) =< s(163) 1.36/1.37 s(171) =< s(163) 1.36/1.37 s(167) =< s(162) 1.36/1.37 s(168) =< s(162) 1.36/1.37 s(172) =< s(159) 1.36/1.37 s(173) =< s(160) 1.36/1.37 s(174) =< s(165)*s(160) 1.36/1.37 s(175) =< s(165)*s(159) 1.36/1.37 s(176) =< s(168)*s(172) 1.36/1.37 s(177) =< s(167)*s(172) 1.36/1.37 s(178) =< s(166)*s(172) 1.36/1.37 s(179) =< s(165)*s(172) 1.36/1.37 s(180) =< s(165)*s(173) 1.36/1.37 s(181) =< s(170) 1.36/1.37 s(182) =< s(176) 1.36/1.37 s(183) =< s(176) 1.36/1.37 s(183) =< s(170) 1.36/1.37 s(184) =< s(177) 1.36/1.37 s(185) =< s(177) 1.36/1.37 s(185) =< s(170) 1.36/1.37 s(186) =< s(179) 1.36/1.37 s(187) =< s(179) 1.36/1.37 s(186) =< s(180) 1.36/1.37 s(188) =< s(180) 1.36/1.37 s(186) =< s(169) 1.36/1.37 s(188) =< s(169) 1.36/1.37 s(189) =< s(175) 1.36/1.37 s(190) =< s(175) 1.36/1.37 s(189) =< s(174) 1.36/1.37 s(191) =< s(174) 1.36/1.37 s(189) =< s(169) 1.36/1.37 s(191) =< s(169) 1.36/1.37 1.36/1.37 with precondition: [V_n>=2,V_m>=1,V_N>=0] 1.36/1.37 1.36/1.37 1.36/1.37 #### Cost of chains of eval_nested_loop_start(V_n,V_m,V_N,B): 1.36/1.37 * Chain [53]: 0 1.36/1.37 with precondition: [V_n=0,V_m>=0,V_N>=0] 1.36/1.37 1.36/1.37 * Chain [52]: 1*s(192)+0 1.36/1.37 Such that:s(192) =< V_n 1.36/1.37 1.36/1.37 with precondition: [V_m=0,V_n>=1,V_N>=0] 1.36/1.37 1.36/1.37 * Chain [51]: 1*s(193)+0 1.36/1.37 Such that:s(193) =< V_n 1.36/1.37 1.36/1.37 with precondition: [V_m=0,V_n>=2,V_N>=0] 1.36/1.37 1.36/1.37 * Chain [50]: 0 1.36/1.37 with precondition: [0>=V_n+1] 1.36/1.37 1.36/1.37 * Chain [49]: 0 1.36/1.37 with precondition: [0>=V_m+1] 1.36/1.37 1.36/1.37 * Chain [48]: 0 1.36/1.37 with precondition: [0>=V_N+1] 1.36/1.37 1.36/1.37 * Chain [47]: 0 1.36/1.37 with precondition: [V_n>=1,V_m>=0,V_N>=0] 1.36/1.37 1.36/1.37 * Chain [46]: 2*s(202)+3*s(203)+2*s(204)+6*s(205)+1*s(208)+2*s(215)+11*s(218)+6*s(219)+3*s(220)+2*s(221)+1*s(222)+1*s(223)+1*s(224)+1*s(225)+1*s(226)+1*s(227)+1*s(228)+0 1.36/1.37 Such that:s(194) =< V_n 1.36/1.37 s(195) =< V_n+V_N 1.36/1.37 s(196) =< V_n/2 1.36/1.37 s(197) =< V_n/2+V_N/2 1.36/1.37 s(198) =< V_m 1.36/1.37 s(199) =< V_N 1.36/1.37 s(200) =< V_N+1 1.36/1.37 s(201) =< V_N/2 1.36/1.37 s(202) =< s(195) 1.36/1.37 s(203) =< s(195) 1.36/1.37 s(204) =< s(195) 1.36/1.37 s(205) =< s(195) 1.36/1.37 s(202) =< s(194) 1.36/1.37 s(203) =< s(194) 1.36/1.37 s(204) =< s(194) 1.36/1.37 s(205) =< s(194) 1.36/1.37 s(204) =< s(196) 1.36/1.37 s(205) =< s(196) 1.36/1.37 s(204) =< s(197) 1.36/1.37 s(205) =< s(197) 1.36/1.37 s(202) =< s(199) 1.36/1.37 s(204) =< s(199) 1.36/1.37 s(205) =< s(199) 1.36/1.37 s(206) =< s(199) 1.36/1.37 s(205) =< s(200) 1.36/1.37 s(207) =< s(200) 1.36/1.37 s(208) =< s(200) 1.36/1.37 s(206) =< s(195) 1.36/1.37 s(207) =< s(195) 1.36/1.37 s(208) =< s(195) 1.36/1.37 s(204) =< s(201) 1.36/1.37 s(205) =< s(201) 1.36/1.37 s(209) =< s(198) 1.36/1.37 s(210) =< s(199) 1.36/1.37 s(211) =< s(202)*s(199) 1.36/1.37 s(212) =< s(202)*s(198) 1.36/1.37 s(213) =< s(205)*s(209) 1.36/1.37 s(214) =< s(204)*s(209) 1.36/1.37 s(215) =< s(203)*s(209) 1.36/1.37 s(216) =< s(202)*s(209) 1.36/1.37 s(217) =< s(202)*s(210) 1.36/1.37 s(218) =< s(207) 1.36/1.37 s(219) =< s(213) 1.36/1.37 s(220) =< s(213) 1.36/1.37 s(220) =< s(207) 1.36/1.37 s(221) =< s(214) 1.36/1.37 s(222) =< s(214) 1.36/1.37 s(222) =< s(207) 1.36/1.37 s(223) =< s(216) 1.36/1.37 s(224) =< s(216) 1.36/1.37 s(223) =< s(217) 1.36/1.37 s(225) =< s(217) 1.36/1.37 s(223) =< s(206) 1.36/1.37 s(225) =< s(206) 1.36/1.37 s(226) =< s(212) 1.36/1.37 s(227) =< s(212) 1.36/1.37 s(226) =< s(211) 1.36/1.37 s(228) =< s(211) 1.36/1.37 s(226) =< s(206) 1.36/1.37 s(228) =< s(206) 1.36/1.37 1.36/1.37 with precondition: [V_n>=1,V_m>=1,V_N>=0] 1.36/1.37 1.36/1.37 * Chain [45]: 2*s(236)+3*s(237)+2*s(238)+6*s(239)+1*s(242)+2*s(249)+11*s(252)+6*s(253)+3*s(254)+2*s(255)+1*s(256)+1*s(257)+1*s(258)+1*s(259)+1*s(260)+1*s(261)+1*s(262)+0 1.36/1.37 Such that:s(229) =< V_n 1.36/1.37 s(230) =< V_n+V_N 1.36/1.37 s(231) =< V_n/2 1.36/1.37 s(232) =< V_m 1.36/1.37 s(233) =< V_N 1.36/1.37 s(234) =< V_N+1 1.36/1.37 s(235) =< V_N/2 1.36/1.37 s(236) =< s(230) 1.36/1.37 s(237) =< s(230) 1.36/1.37 s(238) =< s(230) 1.36/1.37 s(239) =< s(230) 1.36/1.37 s(236) =< s(229) 1.36/1.37 s(237) =< s(229) 1.36/1.37 s(238) =< s(229) 1.36/1.37 s(239) =< s(229) 1.36/1.37 s(238) =< s(231) 1.36/1.37 s(239) =< s(231) 1.36/1.37 s(236) =< s(233) 1.36/1.37 s(238) =< s(233) 1.36/1.37 s(239) =< s(233) 1.36/1.37 s(240) =< s(233) 1.36/1.37 s(239) =< s(234) 1.36/1.37 s(241) =< s(234) 1.36/1.37 s(242) =< s(234) 1.36/1.37 s(240) =< s(229) 1.36/1.37 s(241) =< s(229) 1.36/1.37 s(242) =< s(229) 1.36/1.37 s(238) =< s(235) 1.36/1.37 s(239) =< s(235) 1.36/1.37 s(243) =< s(232) 1.36/1.37 s(244) =< s(233) 1.36/1.37 s(245) =< s(236)*s(233) 1.36/1.37 s(246) =< s(236)*s(232) 1.36/1.37 s(247) =< s(239)*s(243) 1.36/1.37 s(248) =< s(238)*s(243) 1.36/1.37 s(249) =< s(237)*s(243) 1.36/1.37 s(250) =< s(236)*s(243) 1.36/1.37 s(251) =< s(236)*s(244) 1.36/1.37 s(252) =< s(241) 1.36/1.37 s(253) =< s(247) 1.36/1.37 s(254) =< s(247) 1.36/1.37 s(254) =< s(241) 1.36/1.37 s(255) =< s(248) 1.36/1.37 s(256) =< s(248) 1.36/1.37 s(256) =< s(241) 1.36/1.37 s(257) =< s(250) 1.36/1.37 s(258) =< s(250) 1.36/1.37 s(257) =< s(251) 1.36/1.37 s(259) =< s(251) 1.36/1.37 s(257) =< s(240) 1.36/1.37 s(259) =< s(240) 1.36/1.37 s(260) =< s(246) 1.36/1.37 s(261) =< s(246) 1.36/1.37 s(260) =< s(245) 1.36/1.37 s(262) =< s(245) 1.36/1.37 s(260) =< s(240) 1.36/1.37 s(262) =< s(240) 1.36/1.37 1.36/1.37 with precondition: [V_n>=2,V_m>=1,V_N>=0] 1.36/1.37 1.36/1.37 1.36/1.37 Closed-form bounds of eval_nested_loop_start(V_n,V_m,V_N,B): 1.36/1.37 ------------------------------------- 1.36/1.37 * Chain [53] with precondition: [V_n=0,V_m>=0,V_N>=0] 1.36/1.37 - Upper bound: 0 1.36/1.37 - Complexity: constant 1.36/1.37 * Chain [52] with precondition: [V_m=0,V_n>=1,V_N>=0] 1.36/1.37 - Upper bound: V_n 1.36/1.37 - Complexity: n 1.36/1.37 * Chain [51] with precondition: [V_m=0,V_n>=2,V_N>=0] 1.36/1.37 - Upper bound: V_n 1.36/1.37 - Complexity: n 1.36/1.37 * Chain [50] with precondition: [0>=V_n+1] 1.36/1.37 - Upper bound: 0 1.36/1.37 - Complexity: constant 1.36/1.37 * Chain [49] with precondition: [0>=V_m+1] 1.36/1.37 - Upper bound: 0 1.36/1.37 - Complexity: constant 1.36/1.37 * Chain [48] with precondition: [0>=V_N+1] 1.36/1.37 - Upper bound: 0 1.36/1.37 - Complexity: constant 1.36/1.37 * Chain [47] with precondition: [V_n>=1,V_m>=0,V_N>=0] 1.36/1.37 - Upper bound: 0 1.36/1.37 - Complexity: constant 1.36/1.37 * Chain [46] with precondition: [V_n>=1,V_m>=1,V_N>=0] 1.36/1.37 - Upper bound: (V_n+V_N)*(12*V_m)+4*V_N+(13*V_n+13*V_N)+(16*V_N+16) 1.36/1.37 - Complexity: n^2 1.36/1.37 * Chain [45] with precondition: [V_n>=2,V_m>=1,V_N>=0] 1.36/1.37 - Upper bound: (V_n+V_N)*(12*V_m)+4*V_N+(13*V_n+13*V_N)+(16*V_N+16) 1.36/1.37 - Complexity: n^2 1.36/1.37 1.36/1.37 ### Maximum cost of eval_nested_loop_start(V_n,V_m,V_N,B): max([nat(V_n),nat(V_m)*12*nat(V_n+V_N)+nat(V_N)*4+nat(V_n+V_N)*13+nat(V_N+1)*16]) 1.36/1.37 Asymptotic class: n^2 1.36/1.37 * Total analysis performed in 1162 ms. 1.36/1.37 1.38/1.47 EOF