0.73/0.77 WORST_CASE(?,O(n^1)) 0.73/0.77 0.73/0.77 Preprocessing Cost Relations 0.73/0.77 ===================================== 0.73/0.77 0.73/0.77 #### Computed strongly connected components 0.73/0.77 0. recursive : [eval_ex1_10/8,eval_ex1_9/8,eval_ex1_bb3_in/8,eval_ex1_bb4_in/8,eval_ex1_bb5_in/8] 0.73/0.77 1. recursive : [eval_ex1_15/12,eval_ex1_16/12,eval_ex1__critedge_in/12,eval_ex1_bb1_in/12,eval_ex1_bb2_in/12,eval_ex1_bb3_in_loop_cont/13] 0.73/0.77 2. non_recursive : [eval_ex1_stop/7] 0.73/0.77 3. non_recursive : [eval_ex1_bb6_in/7] 0.73/0.77 4. non_recursive : [exit_location/1] 0.73/0.77 5. non_recursive : [eval_ex1_bb1_in_loop_cont/8] 0.73/0.77 6. non_recursive : [eval_ex1_6/7] 0.73/0.77 7. non_recursive : [eval_ex1_5/7] 0.73/0.77 8. non_recursive : [eval_ex1_4/7] 0.73/0.77 9. non_recursive : [eval_ex1_3/7] 0.73/0.77 10. non_recursive : [eval_ex1_2/7] 0.73/0.77 11. non_recursive : [eval_ex1_1/7] 0.73/0.77 12. non_recursive : [eval_ex1_0/7] 0.73/0.77 13. non_recursive : [eval_ex1_bb0_in/7] 0.73/0.77 14. non_recursive : [eval_ex1_start/7] 0.73/0.77 0.73/0.77 #### Obtained direct recursion through partial evaluation 0.73/0.77 0. SCC is partially evaluated into eval_ex1_bb3_in/8 0.73/0.77 1. SCC is partially evaluated into eval_ex1_bb1_in/12 0.73/0.77 2. SCC is completely evaluated into other SCCs 0.73/0.77 3. SCC is completely evaluated into other SCCs 0.73/0.77 4. SCC is completely evaluated into other SCCs 0.73/0.77 5. SCC is partially evaluated into eval_ex1_bb1_in_loop_cont/8 0.73/0.77 6. SCC is partially evaluated into eval_ex1_6/7 0.73/0.77 7. SCC is completely evaluated into other SCCs 0.73/0.77 8. SCC is completely evaluated into other SCCs 0.73/0.77 9. SCC is completely evaluated into other SCCs 0.73/0.77 10. SCC is completely evaluated into other SCCs 0.73/0.77 11. SCC is completely evaluated into other SCCs 0.73/0.77 12. SCC is completely evaluated into other SCCs 0.73/0.77 13. SCC is completely evaluated into other SCCs 0.73/0.77 14. SCC is partially evaluated into eval_ex1_start/7 0.73/0.77 0.73/0.77 Control-Flow Refinement of Cost Relations 0.73/0.77 ===================================== 0.73/0.77 0.73/0.77 ### Specialization of cost equations eval_ex1_bb3_in/8 0.73/0.77 * CE 13 is refined into CE [14] 0.73/0.77 * CE 10 is refined into CE [15] 0.73/0.77 * CE 12 is refined into CE [16] 0.73/0.77 * CE 11 is refined into CE [17] 0.73/0.77 0.73/0.77 0.73/0.77 ### Cost equations --> "Loop" of eval_ex1_bb3_in/8 0.73/0.77 * CEs [17] --> Loop 14 0.73/0.77 * CEs [14] --> Loop 15 0.73/0.77 * CEs [15] --> Loop 16 0.73/0.77 * CEs [16] --> Loop 17 0.73/0.77 0.73/0.77 ### Ranking functions of CR eval_ex1_bb3_in(V_3,V_i_1,V_j_0,V_n,B,C,D,E) 0.73/0.77 * RF of phase [14]: [-V_i_1+V_n] 0.73/0.77 0.73/0.77 #### Partial ranking functions of CR eval_ex1_bb3_in(V_3,V_i_1,V_j_0,V_n,B,C,D,E) 0.73/0.77 * Partial RF of phase [14]: 0.73/0.77 - RF of loop [14:1]: 0.73/0.77 -V_i_1+V_n 0.73/0.77 0.73/0.77 0.73/0.77 ### Specialization of cost equations eval_ex1_bb1_in/12 0.73/0.77 * CE 6 is refined into CE [18] 0.73/0.77 * CE 5 is refined into CE [19,20] 0.73/0.77 * CE 7 is refined into CE [21] 0.73/0.77 * CE 3 is refined into CE [22,23] 0.73/0.77 * CE 4 is refined into CE [24,25] 0.73/0.77 0.73/0.77 0.73/0.77 ### Cost equations --> "Loop" of eval_ex1_bb1_in/12 0.73/0.77 * CEs [25] --> Loop 18 0.73/0.77 * CEs [24] --> Loop 19 0.73/0.77 * CEs [23] --> Loop 20 0.73/0.77 * CEs [22] --> Loop 21 0.73/0.77 * CEs [18] --> Loop 22 0.73/0.77 * CEs [20] --> Loop 23 0.73/0.77 * CEs [19] --> Loop 24 0.73/0.77 * CEs [21] --> Loop 25 0.73/0.77 0.73/0.77 ### Ranking functions of CR eval_ex1_bb1_in(V_3,V_8,V_i_0,V_i_1,V_j_0,V_n,B,C,D,E,F,G) 0.73/0.77 * RF of phase [18,20]: [-V_i_0+V_n-1] 0.73/0.77 0.73/0.77 #### Partial ranking functions of CR eval_ex1_bb1_in(V_3,V_8,V_i_0,V_i_1,V_j_0,V_n,B,C,D,E,F,G) 0.73/0.77 * Partial RF of phase [18,20]: 0.73/0.77 - RF of loop [18:1]: 0.73/0.77 -V_i_0+V_n-2 0.73/0.77 - RF of loop [20:1]: 0.73/0.77 -V_i_0+V_n-1 0.73/0.77 0.73/0.77 0.73/0.77 ### Specialization of cost equations eval_ex1_bb1_in_loop_cont/8 0.73/0.77 * CE 8 is refined into CE [26] 0.73/0.77 * CE 9 is refined into CE [27] 0.73/0.77 0.73/0.77 0.73/0.77 ### Cost equations --> "Loop" of eval_ex1_bb1_in_loop_cont/8 0.73/0.77 * CEs [26] --> Loop 26 0.73/0.77 * CEs [27] --> Loop 27 0.73/0.77 0.73/0.77 ### Ranking functions of CR eval_ex1_bb1_in_loop_cont(A,B,C,D,E,F,G,H) 0.73/0.77 0.73/0.77 #### Partial ranking functions of CR eval_ex1_bb1_in_loop_cont(A,B,C,D,E,F,G,H) 0.73/0.77 0.73/0.77 0.73/0.77 ### Specialization of cost equations eval_ex1_6/7 0.73/0.77 * CE 2 is refined into CE [28,29,30,31,32,33,34,35,36,37] 0.73/0.77 0.73/0.77 0.73/0.77 ### Cost equations --> "Loop" of eval_ex1_6/7 0.73/0.77 * CEs [32,36] --> Loop 28 0.73/0.77 * CEs [31,34,35] --> Loop 29 0.73/0.77 * CEs [30] --> Loop 30 0.73/0.77 * CEs [37] --> Loop 31 0.73/0.77 * CEs [28,33] --> Loop 32 0.73/0.77 * CEs [29] --> Loop 33 0.73/0.77 0.73/0.77 ### Ranking functions of CR eval_ex1_6(V_3,V_8,V_i_0,V_i_1,V_j_0,V_n,B) 0.73/0.77 0.73/0.77 #### Partial ranking functions of CR eval_ex1_6(V_3,V_8,V_i_0,V_i_1,V_j_0,V_n,B) 0.73/0.77 0.73/0.77 0.73/0.77 ### Specialization of cost equations eval_ex1_start/7 0.73/0.77 * CE 1 is refined into CE [38,39,40,41,42,43] 0.73/0.77 0.73/0.77 0.73/0.77 ### Cost equations --> "Loop" of eval_ex1_start/7 0.73/0.77 * CEs [43] --> Loop 34 0.73/0.77 * CEs [42] --> Loop 35 0.73/0.77 * CEs [41] --> Loop 36 0.73/0.77 * CEs [40] --> Loop 37 0.73/0.77 * CEs [39] --> Loop 38 0.73/0.77 * CEs [38] --> Loop 39 0.73/0.77 0.73/0.77 ### Ranking functions of CR eval_ex1_start(V_3,V_8,V_i_0,V_i_1,V_j_0,V_n,B) 0.73/0.77 0.73/0.77 #### Partial ranking functions of CR eval_ex1_start(V_3,V_8,V_i_0,V_i_1,V_j_0,V_n,B) 0.73/0.77 0.73/0.77 0.73/0.77 Computing Bounds 0.73/0.77 ===================================== 0.73/0.77 0.73/0.77 #### Cost of chains of eval_ex1_bb3_in(V_3,V_i_1,V_j_0,V_n,B,C,D,E): 0.73/0.77 * Chain [[14],17]: 1*it(14)+0 0.73/0.77 Such that:it(14) =< -V_j_0+E 0.73/0.77 0.73/0.77 with precondition: [B=2,V_n=D,V_i_1+E=V_j_0+V_n,V_j_0>=0,C>=1,V_n>=V_i_1+1] 0.73/0.77 0.73/0.77 * Chain [[14],16]: 1*it(14)+0 0.73/0.77 Such that:it(14) =< -V_i_1+D 0.73/0.77 0.73/0.77 with precondition: [B=2,V_i_1+E=V_j_0+D,0>=C,V_j_0>=0,D>=V_i_1+1,V_n>=D+1] 0.73/0.77 0.73/0.77 * Chain [[14],15]: 1*it(14)+0 0.73/0.77 Such that:it(14) =< -V_i_1+V_n 0.73/0.77 0.73/0.77 with precondition: [B=3,V_j_0>=0,V_n>=V_i_1+1] 0.73/0.77 0.73/0.77 * Chain [17]: 0 0.73/0.77 with precondition: [B=2,C=V_3,V_n=V_i_1,V_n=D,V_j_0=E,V_j_0>=0] 0.73/0.77 0.73/0.77 * Chain [16]: 0 0.73/0.77 with precondition: [B=2,V_i_1=D,V_j_0=E,0>=C,V_j_0>=0,V_n>=V_i_1+1] 0.73/0.77 0.73/0.77 * Chain [15]: 0 0.73/0.77 with precondition: [B=3,V_j_0>=0,V_n>=V_i_1] 0.73/0.77 0.73/0.77 0.73/0.77 #### Cost of chains of eval_ex1_bb1_in(V_3,V_8,V_i_0,V_i_1,V_j_0,V_n,B,C,D,E,F,G): 0.73/0.77 * Chain [[18,20],25]: 3*it(18)+0 0.73/0.77 Such that:aux(3) =< -V_i_0+V_n 0.73/0.77 it(18) =< aux(3) 0.73/0.77 0.73/0.77 with precondition: [B=3,V_i_0>=0,V_n>=V_i_0+2] 0.73/0.77 0.73/0.77 * Chain [[18,20],24]: 3*it(18)+0 0.73/0.77 Such that:aux(4) =< -V_i_0+V_n 0.73/0.77 it(18) =< aux(4) 0.73/0.77 0.73/0.77 with precondition: [B=3,V_i_0>=0,V_n>=V_i_0+2] 0.73/0.77 0.73/0.77 * Chain [[18,20],23]: 4*it(18)+0 0.73/0.77 Such that:aux(5) =< -V_i_0+V_n 0.73/0.77 it(18) =< aux(5) 0.73/0.77 0.73/0.77 with precondition: [B=3,V_i_0>=0,V_n>=V_i_0+3] 0.73/0.77 0.73/0.77 * Chain [[18,20],21,25]: 3*it(18)+1 0.73/0.77 Such that:aux(6) =< -V_i_0+V_n 0.73/0.77 it(18) =< aux(6) 0.73/0.77 0.73/0.77 with precondition: [B=3,V_i_0>=0,V_n>=V_i_0+2] 0.73/0.77 0.73/0.77 * Chain [[18,20],21,22]: 3*it(18)+1 0.73/0.77 Such that:aux(7) =< -V_i_0+V_n 0.73/0.77 it(18) =< aux(7) 0.73/0.77 0.73/0.77 with precondition: [B=4,G=0,V_n=D+1,V_n=E,V_n=F,0>=C,V_i_0>=0,V_n>=V_i_0+2] 0.73/0.77 0.73/0.77 * Chain [[18,20],19,25]: 4*it(18)+1 0.73/0.77 Such that:aux(8) =< -V_i_0+V_n 0.73/0.77 it(18) =< aux(8) 0.73/0.77 0.73/0.77 with precondition: [B=3,V_i_0>=0,V_n>=V_i_0+3] 0.73/0.77 0.73/0.77 * Chain [[18,20],19,24]: 4*it(18)+1 0.73/0.77 Such that:aux(9) =< -V_i_0+V_n 0.73/0.77 it(18) =< aux(9) 0.73/0.77 0.73/0.77 with precondition: [B=3,V_i_0>=0,V_n>=V_i_0+3] 0.73/0.77 0.73/0.77 * Chain [[18,20],19,21,25]: 4*it(18)+2 0.73/0.77 Such that:aux(10) =< -V_i_0+V_n 0.73/0.77 it(18) =< aux(10) 0.73/0.77 0.73/0.77 with precondition: [B=3,V_i_0>=0,V_n>=V_i_0+3] 0.73/0.77 0.73/0.77 * Chain [[18,20],19,21,22]: 4*it(18)+2 0.73/0.77 Such that:aux(11) =< -V_i_0+V_n 0.73/0.77 it(18) =< aux(11) 0.73/0.77 0.73/0.77 with precondition: [B=4,G=0,V_n=D+1,V_n=E,V_n=F,V_i_0>=0,C>=1,V_n>=V_i_0+3] 0.73/0.77 0.73/0.77 * Chain [25]: 0 0.73/0.77 with precondition: [B=3,V_i_0>=0] 0.73/0.77 0.73/0.77 * Chain [24]: 0 0.73/0.77 with precondition: [B=3,V_i_0>=0,V_n>=V_i_0+1] 0.73/0.77 0.73/0.77 * Chain [23]: 1*s(4)+0 0.73/0.77 Such that:s(4) =< -V_i_0+V_n 0.73/0.77 0.73/0.77 with precondition: [B=3,V_i_0>=0,V_n>=V_i_0+2] 0.73/0.77 0.73/0.77 * Chain [22]: 0 0.73/0.77 with precondition: [B=4,C=V_3,D=V_8,F=V_i_1,G=V_j_0,V_i_0=E,V_i_0>=0,V_i_0>=V_n] 0.73/0.77 0.73/0.77 * Chain [21,25]: 1 0.73/0.77 with precondition: [B=3,V_n=V_i_0+1,V_n>=1] 0.73/0.77 0.73/0.77 * Chain [21,22]: 1 0.73/0.77 with precondition: [B=4,G=0,V_n=V_i_0+1,V_3=C,V_n=D+1,V_n=E,V_n=F,V_n>=1] 0.73/0.77 0.73/0.77 * Chain [19,25]: 1*s(5)+1 0.73/0.77 Such that:s(5) =< -V_i_0+V_n 0.73/0.77 0.73/0.77 with precondition: [B=3,V_i_0>=0,V_n>=V_i_0+2] 0.73/0.77 0.73/0.77 * Chain [19,24]: 1*s(5)+1 0.73/0.77 Such that:s(5) =< -V_i_0+V_n 0.73/0.77 0.73/0.77 with precondition: [B=3,V_i_0>=0,V_n>=V_i_0+2] 0.73/0.77 0.73/0.77 * Chain [19,21,25]: 1*s(5)+2 0.73/0.77 Such that:s(5) =< -V_i_0+V_n 0.73/0.77 0.73/0.77 with precondition: [B=3,V_i_0>=0,V_n>=V_i_0+2] 0.73/0.77 0.73/0.77 * Chain [19,21,22]: 1*s(5)+2 0.73/0.77 Such that:s(5) =< -V_i_0+D 0.73/0.77 0.73/0.77 with precondition: [B=4,G=0,V_n=D+1,V_n=E,V_n=F,V_i_0>=0,C>=1,V_n>=V_i_0+2] 0.73/0.77 0.73/0.77 0.73/0.77 #### Cost of chains of eval_ex1_bb1_in_loop_cont(A,B,C,D,E,F,G,H): 0.73/0.77 * Chain [27]: 0 0.73/0.77 with precondition: [A=3] 0.73/0.77 0.73/0.77 * Chain [26]: 0 0.73/0.77 with precondition: [A=4] 0.73/0.77 0.73/0.77 0.73/0.77 #### Cost of chains of eval_ex1_6(V_3,V_8,V_i_0,V_i_1,V_j_0,V_n,B): 0.73/0.77 * Chain [33]: 0 0.73/0.77 with precondition: [] 0.73/0.77 0.73/0.77 * Chain [32]: 1 0.73/0.77 with precondition: [V_n=1] 0.73/0.77 0.73/0.77 * Chain [31]: 0 0.73/0.77 with precondition: [0>=V_n] 0.73/0.77 0.73/0.77 * Chain [30]: 0 0.73/0.77 with precondition: [V_n>=1] 0.73/0.77 0.73/0.77 * Chain [29]: 17*s(25)+2 0.73/0.77 Such that:aux(14) =< V_n 0.73/0.77 s(25) =< aux(14) 0.73/0.77 0.73/0.77 with precondition: [V_n>=2] 0.73/0.77 0.73/0.77 * Chain [28]: 20*s(30)+2 0.73/0.77 Such that:aux(15) =< V_n 0.73/0.77 s(30) =< aux(15) 0.73/0.77 0.73/0.77 with precondition: [V_n>=3] 0.73/0.77 0.73/0.77 0.73/0.77 #### Cost of chains of eval_ex1_start(V_3,V_8,V_i_0,V_i_1,V_j_0,V_n,B): 0.73/0.77 * Chain [39]: 0 0.73/0.77 with precondition: [] 0.73/0.77 0.73/0.77 * Chain [38]: 1 0.73/0.77 with precondition: [V_n=1] 0.73/0.77 0.73/0.77 * Chain [37]: 0 0.73/0.77 with precondition: [0>=V_n] 0.73/0.77 0.73/0.77 * Chain [36]: 0 0.73/0.77 with precondition: [V_n>=1] 0.73/0.77 0.73/0.77 * Chain [35]: 17*s(34)+2 0.73/0.77 Such that:s(33) =< V_n 0.73/0.77 s(34) =< s(33) 0.73/0.77 0.73/0.77 with precondition: [V_n>=2] 0.73/0.77 0.73/0.77 * Chain [34]: 20*s(36)+2 0.73/0.77 Such that:s(35) =< V_n 0.73/0.77 s(36) =< s(35) 0.73/0.77 0.73/0.77 with precondition: [V_n>=3] 0.73/0.77 0.73/0.77 0.73/0.77 Closed-form bounds of eval_ex1_start(V_3,V_8,V_i_0,V_i_1,V_j_0,V_n,B): 0.73/0.77 ------------------------------------- 0.73/0.77 * Chain [39] with precondition: [] 0.73/0.77 - Upper bound: 0 0.73/0.77 - Complexity: constant 0.73/0.77 * Chain [38] with precondition: [V_n=1] 0.73/0.77 - Upper bound: 1 0.73/0.77 - Complexity: constant 0.73/0.77 * Chain [37] with precondition: [0>=V_n] 0.73/0.77 - Upper bound: 0 0.73/0.77 - Complexity: constant 0.73/0.77 * Chain [36] with precondition: [V_n>=1] 0.73/0.77 - Upper bound: 0 0.73/0.77 - Complexity: constant 0.73/0.77 * Chain [35] with precondition: [V_n>=2] 0.73/0.77 - Upper bound: 17*V_n+2 0.73/0.77 - Complexity: n 0.73/0.77 * Chain [34] with precondition: [V_n>=3] 0.73/0.77 - Upper bound: 20*V_n+2 0.73/0.77 - Complexity: n 0.73/0.77 0.73/0.77 ### Maximum cost of eval_ex1_start(V_3,V_8,V_i_0,V_i_1,V_j_0,V_n,B): nat(V_n)*20+1+1 0.73/0.77 Asymptotic class: n 0.73/0.77 * Total analysis performed in 660 ms. 0.73/0.77 0.77/0.87 EOF