0.05/0.22 WORST_CASE(?,O(n^1)) 0.05/0.22 0.05/0.22 Preprocessing Cost Relations 0.05/0.22 ===================================== 0.05/0.22 0.05/0.22 #### Computed strongly connected components 0.05/0.22 0. recursive : [eval_peed_pldi09_fig4_5_bb1_in/4,eval_peed_pldi09_fig4_5_bb2_in/4] 0.05/0.22 1. non_recursive : [eval_peed_pldi09_fig4_5_stop/1] 0.05/0.22 2. non_recursive : [eval_peed_pldi09_fig4_5_bb3_in/1] 0.05/0.22 3. non_recursive : [eval_peed_pldi09_fig4_5_bb1_in_loop_cont/2] 0.05/0.22 4. non_recursive : [eval_peed_pldi09_fig4_5_bb0_in/4] 0.05/0.22 5. non_recursive : [eval_peed_pldi09_fig4_5_start/4] 0.05/0.22 0.05/0.22 #### Obtained direct recursion through partial evaluation 0.05/0.22 0. SCC is partially evaluated into eval_peed_pldi09_fig4_5_bb1_in/4 0.05/0.22 1. SCC is completely evaluated into other SCCs 0.05/0.22 2. SCC is completely evaluated into other SCCs 0.05/0.22 3. SCC is completely evaluated into other SCCs 0.05/0.22 4. SCC is partially evaluated into eval_peed_pldi09_fig4_5_bb0_in/4 0.05/0.22 5. SCC is partially evaluated into eval_peed_pldi09_fig4_5_start/4 0.05/0.22 0.05/0.22 Control-Flow Refinement of Cost Relations 0.05/0.22 ===================================== 0.05/0.22 0.05/0.22 ### Specialization of cost equations eval_peed_pldi09_fig4_5_bb1_in/4 0.05/0.22 * CE 9 is refined into CE [10] 0.05/0.22 * CE 8 is refined into CE [11] 0.05/0.22 * CE 5 is refined into CE [12] 0.05/0.22 * CE 6 is refined into CE [13] 0.05/0.22 * CE 7 is refined into CE [14] 0.05/0.22 0.05/0.22 0.05/0.22 ### Cost equations --> "Loop" of eval_peed_pldi09_fig4_5_bb1_in/4 0.05/0.22 * CEs [12] --> Loop 10 0.05/0.22 * CEs [13] --> Loop 11 0.05/0.22 * CEs [14] --> Loop 12 0.05/0.22 * CEs [10] --> Loop 13 0.05/0.22 * CEs [11] --> Loop 14 0.05/0.22 0.05/0.22 ### Ranking functions of CR eval_peed_pldi09_fig4_5_bb1_in(V_n,V_dir,V_i_0,B) 0.05/0.22 * RF of phase [10]: [V_i_0] 0.05/0.22 * RF of phase [11]: [V_i_0] 0.05/0.22 * RF of phase [12]: [V_n-V_i_0] 0.05/0.22 0.05/0.22 #### Partial ranking functions of CR eval_peed_pldi09_fig4_5_bb1_in(V_n,V_dir,V_i_0,B) 0.05/0.22 * Partial RF of phase [10]: 0.05/0.22 - RF of loop [10:1]: 0.05/0.22 V_i_0 0.05/0.22 * Partial RF of phase [11]: 0.05/0.22 - RF of loop [11:1]: 0.05/0.22 V_i_0 0.05/0.22 * Partial RF of phase [12]: 0.05/0.22 - RF of loop [12:1]: 0.05/0.22 V_n-V_i_0 0.05/0.22 0.05/0.22 0.05/0.22 ### Specialization of cost equations eval_peed_pldi09_fig4_5_bb0_in/4 0.05/0.22 * CE 3 is refined into CE [15] 0.05/0.22 * CE 4 is refined into CE [16,17,18] 0.05/0.22 * CE 2 is refined into CE [19] 0.05/0.22 0.05/0.22 0.05/0.22 ### Cost equations --> "Loop" of eval_peed_pldi09_fig4_5_bb0_in/4 0.05/0.22 * CEs [15] --> Loop 15 0.05/0.22 * CEs [18] --> Loop 16 0.05/0.22 * CEs [17] --> Loop 17 0.05/0.22 * CEs [19] --> Loop 18 0.05/0.22 * CEs [16] --> Loop 19 0.05/0.22 0.05/0.22 ### Ranking functions of CR eval_peed_pldi09_fig4_5_bb0_in(V_n,V_m,V_dir,B) 0.05/0.22 0.05/0.22 #### Partial ranking functions of CR eval_peed_pldi09_fig4_5_bb0_in(V_n,V_m,V_dir,B) 0.05/0.22 0.05/0.22 0.05/0.22 ### Specialization of cost equations eval_peed_pldi09_fig4_5_start/4 0.05/0.22 * CE 1 is refined into CE [20,21,22,23,24] 0.05/0.22 0.05/0.22 0.05/0.22 ### Cost equations --> "Loop" of eval_peed_pldi09_fig4_5_start/4 0.05/0.22 * CEs [24] --> Loop 20 0.05/0.22 * CEs [23] --> Loop 21 0.05/0.22 * CEs [22] --> Loop 22 0.05/0.22 * CEs [21] --> Loop 23 0.05/0.22 * CEs [20] --> Loop 24 0.05/0.22 0.05/0.22 ### Ranking functions of CR eval_peed_pldi09_fig4_5_start(V_n,V_m,V_dir,B) 0.05/0.22 0.05/0.22 #### Partial ranking functions of CR eval_peed_pldi09_fig4_5_start(V_n,V_m,V_dir,B) 0.05/0.22 0.05/0.22 0.05/0.22 Computing Bounds 0.05/0.22 ===================================== 0.05/0.22 0.05/0.22 #### Cost of chains of eval_peed_pldi09_fig4_5_bb1_in(V_n,V_dir,V_i_0,B): 0.05/0.22 * Chain [[12],13]: 1*it(12)+0 0.05/0.22 Such that:it(12) =< V_n-V_i_0 0.05/0.22 0.05/0.22 with precondition: [V_dir=1,B=2,V_i_0>=1,V_n>=V_i_0+1] 0.05/0.22 0.05/0.22 * Chain [[11],14]: 1*it(11)+0 0.05/0.22 Such that:it(11) =< V_i_0 0.05/0.22 0.05/0.22 with precondition: [B=2,0>=V_dir,V_i_0>=1,V_n>=V_i_0+1] 0.05/0.22 0.05/0.22 * Chain [[10],14]: 1*it(10)+0 0.05/0.22 Such that:it(10) =< V_i_0 0.05/0.22 0.05/0.22 with precondition: [B=2,V_dir>=2,V_i_0>=1,V_n>=V_i_0+1] 0.05/0.22 0.05/0.22 0.05/0.22 #### Cost of chains of eval_peed_pldi09_fig4_5_bb0_in(V_n,V_m,V_dir,B): 0.05/0.22 * Chain [19]: 1*s(1)+0 0.05/0.22 Such that:s(1) =< V_n-V_m 0.05/0.22 0.05/0.22 with precondition: [V_dir=1,V_m>=1,V_n>=V_m+1] 0.05/0.22 0.05/0.22 * Chain [18]: 0 0.05/0.22 with precondition: [0>=V_m] 0.05/0.22 0.05/0.22 * Chain [17]: 1*s(2)+0 0.05/0.22 Such that:s(2) =< V_m 0.05/0.22 0.05/0.22 with precondition: [0>=V_dir,V_m>=1,V_n>=V_m+1] 0.05/0.22 0.05/0.22 * Chain [16]: 1*s(3)+0 0.05/0.22 Such that:s(3) =< V_m 0.05/0.22 0.05/0.22 with precondition: [V_m>=1,V_dir>=2,V_n>=V_m+1] 0.05/0.22 0.05/0.22 * Chain [15]: 0 0.05/0.22 with precondition: [V_m>=V_n] 0.05/0.22 0.05/0.22 0.05/0.22 #### Cost of chains of eval_peed_pldi09_fig4_5_start(V_n,V_m,V_dir,B): 0.05/0.22 * Chain [24]: 1*s(4)+0 0.05/0.22 Such that:s(4) =< V_n-V_m 0.05/0.22 0.05/0.22 with precondition: [V_dir=1,V_m>=1,V_n>=V_m+1] 0.05/0.22 0.05/0.22 * Chain [23]: 0 0.05/0.22 with precondition: [0>=V_m] 0.05/0.22 0.05/0.22 * Chain [22]: 1*s(5)+0 0.05/0.22 Such that:s(5) =< V_m 0.05/0.22 0.05/0.22 with precondition: [0>=V_dir,V_m>=1,V_n>=V_m+1] 0.05/0.22 0.05/0.22 * Chain [21]: 1*s(6)+0 0.05/0.22 Such that:s(6) =< V_m 0.05/0.22 0.05/0.22 with precondition: [V_m>=1,V_dir>=2,V_n>=V_m+1] 0.05/0.22 0.05/0.22 * Chain [20]: 0 0.05/0.22 with precondition: [V_m>=V_n] 0.05/0.22 0.05/0.22 0.05/0.22 Closed-form bounds of eval_peed_pldi09_fig4_5_start(V_n,V_m,V_dir,B): 0.05/0.22 ------------------------------------- 0.05/0.22 * Chain [24] with precondition: [V_dir=1,V_m>=1,V_n>=V_m+1] 0.05/0.22 - Upper bound: V_n-V_m 0.05/0.22 - Complexity: n 0.05/0.22 * Chain [23] with precondition: [0>=V_m] 0.05/0.22 - Upper bound: 0 0.05/0.22 - Complexity: constant 0.05/0.22 * Chain [22] with precondition: [0>=V_dir,V_m>=1,V_n>=V_m+1] 0.05/0.22 - Upper bound: V_m 0.05/0.22 - Complexity: n 0.05/0.22 * Chain [21] with precondition: [V_m>=1,V_dir>=2,V_n>=V_m+1] 0.05/0.22 - Upper bound: V_m 0.05/0.22 - Complexity: n 0.05/0.22 * Chain [20] with precondition: [V_m>=V_n] 0.05/0.22 - Upper bound: 0 0.05/0.22 - Complexity: constant 0.05/0.22 0.05/0.22 ### Maximum cost of eval_peed_pldi09_fig4_5_start(V_n,V_m,V_dir,B): max([nat(V_m),nat(V_n-V_m)]) 0.05/0.22 Asymptotic class: n 0.05/0.22 * Total analysis performed in 147 ms. 0.05/0.22 0.05/0.32 EOF