0.34/0.35 WORST_CASE(?,O(n^1)) 0.34/0.35 0.34/0.35 Preprocessing Cost Relations 0.34/0.35 ===================================== 0.34/0.35 0.34/0.35 #### Computed strongly connected components 0.34/0.35 0. recursive : [eval_start_bb2_in/5,eval_start_bb3_in/5] 0.34/0.35 1. non_recursive : [eval_start_stop/5] 0.34/0.35 2. non_recursive : [eval_start_bb4_in/5] 0.34/0.35 3. non_recursive : [exit_location/1] 0.34/0.35 4. non_recursive : [eval_start_bb2_in_loop_cont/6] 0.34/0.35 5. non_recursive : [eval_start_9/5] 0.34/0.35 6. non_recursive : [eval_start_8/5] 0.34/0.35 7. non_recursive : [eval_start_bb5_in/5] 0.34/0.35 8. non_recursive : [eval_start_bb1_in/5] 0.34/0.35 9. non_recursive : [eval_start_11/5] 0.34/0.35 10. non_recursive : [eval_start_10/5] 0.34/0.35 11. non_recursive : [eval_start_bb6_in/5] 0.34/0.35 12. non_recursive : [eval_start_3/5] 0.34/0.35 13. non_recursive : [eval_start_2/5] 0.34/0.35 14. non_recursive : [eval_start_1/5] 0.34/0.35 15. non_recursive : [eval_start_0/5] 0.34/0.35 16. non_recursive : [eval_start_bb0_in/5] 0.34/0.35 17. non_recursive : [eval_start_start/5] 0.34/0.35 0.34/0.35 #### Obtained direct recursion through partial evaluation 0.34/0.35 0. SCC is partially evaluated into eval_start_bb2_in/5 0.34/0.35 1. SCC is completely evaluated into other SCCs 0.34/0.35 2. SCC is completely evaluated into other SCCs 0.34/0.35 3. SCC is completely evaluated into other SCCs 0.34/0.35 4. SCC is partially evaluated into eval_start_bb2_in_loop_cont/6 0.34/0.35 5. SCC is completely evaluated into other SCCs 0.34/0.35 6. SCC is completely evaluated into other SCCs 0.34/0.35 7. SCC is completely evaluated into other SCCs 0.34/0.35 8. SCC is partially evaluated into eval_start_bb1_in/5 0.34/0.35 9. SCC is completely evaluated into other SCCs 0.34/0.35 10. SCC is completely evaluated into other SCCs 0.34/0.35 11. SCC is completely evaluated into other SCCs 0.34/0.35 12. SCC is partially evaluated into eval_start_3/5 0.34/0.35 13. SCC is completely evaluated into other SCCs 0.34/0.35 14. SCC is completely evaluated into other SCCs 0.34/0.35 15. SCC is completely evaluated into other SCCs 0.34/0.35 16. SCC is completely evaluated into other SCCs 0.34/0.35 17. SCC is partially evaluated into eval_start_start/5 0.34/0.35 0.34/0.35 Control-Flow Refinement of Cost Relations 0.34/0.35 ===================================== 0.34/0.35 0.34/0.35 ### Specialization of cost equations eval_start_bb2_in/5 0.34/0.35 * CE 11 is refined into CE [14] 0.34/0.35 * CE 10 is refined into CE [15] 0.34/0.35 * CE 9 is refined into CE [16] 0.34/0.35 * CE 6 is refined into CE [17] 0.34/0.35 * CE 7 is refined into CE [18] 0.34/0.35 * CE 8 is refined into CE [19] 0.34/0.35 0.34/0.35 0.34/0.35 ### Cost equations --> "Loop" of eval_start_bb2_in/5 0.34/0.35 * CEs [17] --> Loop 14 0.34/0.35 * CEs [18] --> Loop 15 0.34/0.35 * CEs [19] --> Loop 16 0.34/0.35 * CEs [14] --> Loop 17 0.34/0.35 * CEs [15] --> Loop 18 0.34/0.35 * CEs [16] --> Loop 19 0.34/0.35 0.34/0.35 ### Ranking functions of CR eval_start_bb2_in(V_dir,V_i_0,V_n,B,C) 0.34/0.35 * RF of phase [14]: [V_i_0] 0.34/0.35 * RF of phase [15]: [V_i_0] 0.34/0.35 * RF of phase [16]: [-V_i_0+V_n] 0.34/0.35 0.34/0.35 #### Partial ranking functions of CR eval_start_bb2_in(V_dir,V_i_0,V_n,B,C) 0.34/0.35 * Partial RF of phase [14]: 0.34/0.35 - RF of loop [14:1]: 0.34/0.35 V_i_0 0.34/0.35 * Partial RF of phase [15]: 0.34/0.35 - RF of loop [15:1]: 0.34/0.35 V_i_0 0.34/0.35 * Partial RF of phase [16]: 0.34/0.35 - RF of loop [16:1]: 0.34/0.35 -V_i_0+V_n 0.34/0.35 0.34/0.35 0.34/0.35 ### Specialization of cost equations eval_start_bb2_in_loop_cont/6 0.34/0.35 * CE 13 is refined into CE [20] 0.34/0.35 * CE 12 is refined into CE [21] 0.34/0.35 0.34/0.35 0.34/0.35 ### Cost equations --> "Loop" of eval_start_bb2_in_loop_cont/6 0.34/0.35 * CEs [20] --> Loop 20 0.34/0.35 * CEs [21] --> Loop 21 0.34/0.35 0.34/0.35 ### Ranking functions of CR eval_start_bb2_in_loop_cont(A,B,C,D,E,F) 0.34/0.35 0.34/0.35 #### Partial ranking functions of CR eval_start_bb2_in_loop_cont(A,B,C,D,E,F) 0.34/0.35 0.34/0.35 0.34/0.35 ### Specialization of cost equations eval_start_bb1_in/5 0.34/0.35 * CE 4 is refined into CE [22] 0.34/0.35 * CE 5 is refined into CE [23,24,25,26,27,28,29] 0.34/0.35 0.34/0.35 0.34/0.35 ### Cost equations --> "Loop" of eval_start_bb1_in/5 0.34/0.35 * CEs [22] --> Loop 22 0.34/0.35 * CEs [29] --> Loop 23 0.34/0.35 * CEs [26,28] --> Loop 24 0.34/0.35 * CEs [25,27] --> Loop 25 0.34/0.35 * CEs [23,24] --> Loop 26 0.34/0.35 0.34/0.35 ### Ranking functions of CR eval_start_bb1_in(V_dir,V_i_0,V_m,V_n,B) 0.34/0.35 0.34/0.35 #### Partial ranking functions of CR eval_start_bb1_in(V_dir,V_i_0,V_m,V_n,B) 0.34/0.35 0.34/0.35 0.34/0.35 ### Specialization of cost equations eval_start_3/5 0.34/0.35 * CE 2 is refined into CE [30,31,32,33,34] 0.34/0.35 * CE 3 is refined into CE [35] 0.34/0.35 0.34/0.35 0.34/0.35 ### Cost equations --> "Loop" of eval_start_3/5 0.34/0.35 * CEs [34] --> Loop 27 0.34/0.35 * CEs [33] --> Loop 28 0.34/0.35 * CEs [32] --> Loop 29 0.34/0.35 * CEs [35] --> Loop 30 0.34/0.35 * CEs [31] --> Loop 31 0.34/0.35 * CEs [30] --> Loop 32 0.34/0.35 0.34/0.35 ### Ranking functions of CR eval_start_3(V_dir,V_i_0,V_m,V_n,B) 0.34/0.35 0.34/0.35 #### Partial ranking functions of CR eval_start_3(V_dir,V_i_0,V_m,V_n,B) 0.34/0.35 0.34/0.35 0.34/0.35 ### Specialization of cost equations eval_start_start/5 0.34/0.35 * CE 1 is refined into CE [36,37,38,39,40,41] 0.34/0.35 0.34/0.35 0.34/0.35 ### Cost equations --> "Loop" of eval_start_start/5 0.34/0.35 * CEs [41] --> Loop 33 0.34/0.35 * CEs [40] --> Loop 34 0.34/0.35 * CEs [39] --> Loop 35 0.34/0.35 * CEs [38] --> Loop 36 0.34/0.35 * CEs [37] --> Loop 37 0.34/0.35 * CEs [36] --> Loop 38 0.34/0.35 0.34/0.35 ### Ranking functions of CR eval_start_start(V_dir,V_i_0,V_m,V_n,B) 0.34/0.35 0.34/0.35 #### Partial ranking functions of CR eval_start_start(V_dir,V_i_0,V_m,V_n,B) 0.34/0.35 0.34/0.35 0.34/0.35 Computing Bounds 0.34/0.35 ===================================== 0.34/0.35 0.34/0.35 #### Cost of chains of eval_start_bb2_in(V_dir,V_i_0,V_n,B,C): 0.34/0.35 * Chain [[16],18]: 1*it(16)+0 0.34/0.35 Such that:it(16) =< -V_i_0+C 0.34/0.35 0.34/0.35 with precondition: [V_dir=1,B=2,V_n=C,V_i_0>=1,V_n>=V_i_0+1] 0.34/0.35 0.34/0.35 * Chain [[16],17]: 1*it(16)+0 0.34/0.35 Such that:it(16) =< -V_i_0+V_n 0.34/0.35 0.34/0.35 with precondition: [V_dir=1,B=3,V_i_0>=1,V_n>=V_i_0+1] 0.34/0.35 0.34/0.35 * Chain [[15],19]: 1*it(15)+0 0.34/0.35 Such that:it(15) =< V_i_0 0.34/0.35 0.34/0.35 with precondition: [B=2,C=0,0>=V_dir,V_i_0>=1,V_n>=V_i_0+1] 0.34/0.35 0.34/0.35 * Chain [[15],17]: 1*it(15)+0 0.34/0.35 Such that:it(15) =< V_i_0 0.34/0.35 0.34/0.35 with precondition: [B=3,0>=V_dir,V_i_0>=1,V_n>=V_i_0+1] 0.34/0.35 0.34/0.35 * Chain [[14],19]: 1*it(14)+0 0.34/0.35 Such that:it(14) =< V_i_0 0.34/0.35 0.34/0.35 with precondition: [B=2,C=0,V_dir>=2,V_i_0>=1,V_n>=V_i_0+1] 0.34/0.35 0.34/0.35 * Chain [[14],17]: 1*it(14)+0 0.34/0.35 Such that:it(14) =< V_i_0 0.34/0.35 0.34/0.35 with precondition: [B=3,V_dir>=2,V_i_0>=1,V_n>=V_i_0+1] 0.34/0.35 0.34/0.35 * Chain [17]: 0 0.34/0.35 with precondition: [B=3,V_i_0>=0,V_n>=2,V_n>=V_i_0] 0.34/0.35 0.34/0.35 0.34/0.35 #### Cost of chains of eval_start_bb2_in_loop_cont(A,B,C,D,E,F): 0.34/0.35 * Chain [21]: 0 0.34/0.35 with precondition: [A=2,D>=1,E>=D+1] 0.34/0.35 0.34/0.35 * Chain [20]: 0 0.34/0.35 with precondition: [A=3,D>=1,E>=D+1] 0.34/0.35 0.34/0.35 0.34/0.35 #### Cost of chains of eval_start_bb1_in(V_dir,V_i_0,V_m,V_n,B): 0.34/0.35 * Chain [26]: 2*s(1)+0 0.34/0.35 Such that:aux(1) =< -V_m+V_n 0.34/0.35 s(1) =< aux(1) 0.34/0.35 0.34/0.35 with precondition: [V_dir=1,V_m>=1,V_n>=V_m+1] 0.34/0.35 0.34/0.35 * Chain [25]: 2*s(3)+0 0.34/0.35 Such that:aux(2) =< V_m 0.34/0.35 s(3) =< aux(2) 0.34/0.35 0.34/0.35 with precondition: [0>=V_dir,V_m>=1,V_n>=V_m+1] 0.34/0.35 0.34/0.35 * Chain [24]: 2*s(5)+0 0.34/0.35 Such that:aux(3) =< V_m 0.34/0.35 s(5) =< aux(3) 0.34/0.35 0.34/0.35 with precondition: [V_dir>=2,V_m>=1,V_n>=V_m+1] 0.34/0.35 0.34/0.35 * Chain [23]: 0 0.34/0.35 with precondition: [V_m>=1,V_n>=V_m+1] 0.34/0.35 0.34/0.35 * Chain [22]: 0 0.34/0.35 with precondition: [V_m>=1,V_m>=V_n] 0.34/0.35 0.34/0.35 0.34/0.35 #### Cost of chains of eval_start_3(V_dir,V_i_0,V_m,V_n,B): 0.34/0.35 * Chain [32]: 2*s(8)+0 0.34/0.35 Such that:s(7) =< -V_m+V_n 0.34/0.35 s(8) =< s(7) 0.34/0.35 0.34/0.35 with precondition: [V_dir=1,V_m>=1,V_n>=V_m+1] 0.34/0.35 0.34/0.35 * Chain [31]: 2*s(10)+0 0.34/0.35 Such that:s(9) =< V_m 0.34/0.35 s(10) =< s(9) 0.34/0.35 0.34/0.35 with precondition: [0>=V_dir,V_m>=1,V_n>=V_m+1] 0.34/0.35 0.34/0.35 * Chain [30]: 0 0.34/0.35 with precondition: [0>=V_m] 0.34/0.35 0.34/0.35 * Chain [29]: 2*s(12)+0 0.34/0.35 Such that:s(11) =< V_m 0.34/0.35 s(12) =< s(11) 0.34/0.35 0.34/0.35 with precondition: [V_dir>=2,V_m>=1,V_n>=V_m+1] 0.34/0.35 0.34/0.35 * Chain [28]: 0 0.34/0.35 with precondition: [V_m>=1,V_n>=V_m+1] 0.34/0.35 0.34/0.35 * Chain [27]: 0 0.34/0.35 with precondition: [V_m>=1,V_m>=V_n] 0.34/0.35 0.34/0.35 0.34/0.35 #### Cost of chains of eval_start_start(V_dir,V_i_0,V_m,V_n,B): 0.34/0.35 * Chain [38]: 2*s(14)+0 0.34/0.35 Such that:s(13) =< -V_m+V_n 0.34/0.35 s(14) =< s(13) 0.34/0.35 0.34/0.35 with precondition: [V_dir=1,V_m>=1,V_n>=V_m+1] 0.34/0.35 0.34/0.35 * Chain [37]: 2*s(16)+0 0.34/0.35 Such that:s(15) =< V_m 0.34/0.35 s(16) =< s(15) 0.34/0.35 0.34/0.35 with precondition: [0>=V_dir,V_m>=1,V_n>=V_m+1] 0.34/0.35 0.34/0.35 * Chain [36]: 0 0.34/0.35 with precondition: [0>=V_m] 0.34/0.35 0.34/0.35 * Chain [35]: 2*s(18)+0 0.34/0.35 Such that:s(17) =< V_m 0.34/0.35 s(18) =< s(17) 0.34/0.35 0.34/0.35 with precondition: [V_dir>=2,V_m>=1,V_n>=V_m+1] 0.34/0.35 0.34/0.35 * Chain [34]: 0 0.34/0.35 with precondition: [V_m>=1,V_n>=V_m+1] 0.34/0.35 0.34/0.35 * Chain [33]: 0 0.34/0.35 with precondition: [V_m>=1,V_m>=V_n] 0.34/0.35 0.34/0.35 0.34/0.35 Closed-form bounds of eval_start_start(V_dir,V_i_0,V_m,V_n,B): 0.34/0.35 ------------------------------------- 0.34/0.35 * Chain [38] with precondition: [V_dir=1,V_m>=1,V_n>=V_m+1] 0.34/0.35 - Upper bound: -2*V_m+2*V_n 0.34/0.35 - Complexity: n 0.34/0.35 * Chain [37] with precondition: [0>=V_dir,V_m>=1,V_n>=V_m+1] 0.34/0.35 - Upper bound: 2*V_m 0.34/0.35 - Complexity: n 0.34/0.35 * Chain [36] with precondition: [0>=V_m] 0.34/0.35 - Upper bound: 0 0.34/0.35 - Complexity: constant 0.34/0.35 * Chain [35] with precondition: [V_dir>=2,V_m>=1,V_n>=V_m+1] 0.34/0.35 - Upper bound: 2*V_m 0.34/0.35 - Complexity: n 0.34/0.35 * Chain [34] with precondition: [V_m>=1,V_n>=V_m+1] 0.34/0.35 - Upper bound: 0 0.34/0.35 - Complexity: constant 0.34/0.35 * Chain [33] with precondition: [V_m>=1,V_m>=V_n] 0.34/0.35 - Upper bound: 0 0.34/0.35 - Complexity: constant 0.34/0.35 0.34/0.35 ### Maximum cost of eval_start_start(V_dir,V_i_0,V_m,V_n,B): max([nat(V_m)*2,nat(-V_m+V_n)*2]) 0.34/0.35 Asymptotic class: n 0.34/0.35 * Total analysis performed in 274 ms. 0.34/0.35 0.36/0.45 EOF