0.04/0.17 WORST_CASE(?,O(n^1)) 0.04/0.17 0.04/0.17 Preprocessing Cost Relations 0.04/0.17 ===================================== 0.04/0.17 0.04/0.17 #### Computed strongly connected components 0.04/0.17 0. recursive : [eval_peed_pldi09_fig4_4_bb1_in/3,eval_peed_pldi09_fig4_4_bb2_in/3] 0.04/0.17 1. non_recursive : [eval_peed_pldi09_fig4_4_stop/1] 0.04/0.17 2. non_recursive : [eval_peed_pldi09_fig4_4_bb3_in/1] 0.04/0.17 3. non_recursive : [eval_peed_pldi09_fig4_4_bb1_in_loop_cont/2] 0.04/0.17 4. non_recursive : [eval_peed_pldi09_fig4_4_bb0_in/3] 0.04/0.17 5. non_recursive : [eval_peed_pldi09_fig4_4_start/3] 0.04/0.17 0.04/0.17 #### Obtained direct recursion through partial evaluation 0.04/0.17 0. SCC is partially evaluated into eval_peed_pldi09_fig4_4_bb1_in/3 0.04/0.17 1. SCC is completely evaluated into other SCCs 0.04/0.17 2. SCC is completely evaluated into other SCCs 0.04/0.17 3. SCC is completely evaluated into other SCCs 0.04/0.17 4. SCC is partially evaluated into eval_peed_pldi09_fig4_4_bb0_in/3 0.04/0.17 5. SCC is partially evaluated into eval_peed_pldi09_fig4_4_start/3 0.04/0.17 0.04/0.17 Control-Flow Refinement of Cost Relations 0.04/0.17 ===================================== 0.04/0.17 0.04/0.17 ### Specialization of cost equations eval_peed_pldi09_fig4_4_bb1_in/3 0.04/0.17 * CE 6 is refined into CE [7] 0.04/0.17 * CE 4 is refined into CE [8] 0.04/0.17 * CE 5 is refined into CE [9] 0.04/0.17 0.04/0.17 0.04/0.17 ### Cost equations --> "Loop" of eval_peed_pldi09_fig4_4_bb1_in/3 0.04/0.17 * CEs [8] --> Loop 7 0.04/0.17 * CEs [9] --> Loop 8 0.04/0.17 * CEs [7] --> Loop 9 0.04/0.17 0.04/0.17 ### Ranking functions of CR eval_peed_pldi09_fig4_4_bb1_in(V_m,V_i_0,B) 0.04/0.17 * RF of phase [7]: [V_i_0,-V_m+V_i_0+1] 0.04/0.17 * RF of phase [8]: [V_i_0] 0.04/0.17 0.04/0.17 #### Partial ranking functions of CR eval_peed_pldi09_fig4_4_bb1_in(V_m,V_i_0,B) 0.04/0.17 * Partial RF of phase [7]: 0.04/0.17 - RF of loop [7:1]: 0.04/0.17 V_i_0 0.04/0.17 -V_m+V_i_0+1 0.04/0.17 * Partial RF of phase [8]: 0.04/0.17 - RF of loop [8:1]: 0.04/0.17 V_i_0 0.04/0.17 0.04/0.17 0.04/0.17 ### Specialization of cost equations eval_peed_pldi09_fig4_4_bb0_in/3 0.04/0.17 * CE 3 is refined into CE [10,11,12,13] 0.04/0.17 * CE 2 is refined into CE [14] 0.04/0.17 0.04/0.17 0.04/0.17 ### Cost equations --> "Loop" of eval_peed_pldi09_fig4_4_bb0_in/3 0.04/0.17 * CEs [12] --> Loop 10 0.04/0.17 * CEs [11] --> Loop 11 0.04/0.17 * CEs [13] --> Loop 12 0.04/0.17 * CEs [14] --> Loop 13 0.04/0.17 * CEs [10] --> Loop 14 0.04/0.17 0.04/0.17 ### Ranking functions of CR eval_peed_pldi09_fig4_4_bb0_in(V_n,V_m,B) 0.04/0.17 0.04/0.17 #### Partial ranking functions of CR eval_peed_pldi09_fig4_4_bb0_in(V_n,V_m,B) 0.04/0.17 0.04/0.17 0.04/0.17 ### Specialization of cost equations eval_peed_pldi09_fig4_4_start/3 0.04/0.17 * CE 1 is refined into CE [15,16,17,18,19] 0.04/0.17 0.04/0.17 0.04/0.17 ### Cost equations --> "Loop" of eval_peed_pldi09_fig4_4_start/3 0.04/0.17 * CEs [19] --> Loop 15 0.04/0.17 * CEs [18] --> Loop 16 0.04/0.17 * CEs [17] --> Loop 17 0.04/0.17 * CEs [16] --> Loop 18 0.04/0.17 * CEs [15] --> Loop 19 0.04/0.17 0.04/0.17 ### Ranking functions of CR eval_peed_pldi09_fig4_4_start(V_n,V_m,B) 0.04/0.17 0.04/0.17 #### Partial ranking functions of CR eval_peed_pldi09_fig4_4_start(V_n,V_m,B) 0.04/0.17 0.04/0.17 0.04/0.17 Computing Bounds 0.04/0.17 ===================================== 0.04/0.17 0.04/0.17 #### Cost of chains of eval_peed_pldi09_fig4_4_bb1_in(V_m,V_i_0,B): 0.04/0.17 * Chain [[8],9]: 1*it(8)+0 0.04/0.17 Such that:it(8) =< V_i_0 0.04/0.17 0.04/0.17 with precondition: [B=2,V_i_0>=1,V_m>=V_i_0+1] 0.04/0.17 0.04/0.17 * Chain [[7],[8],9]: 1*it(7)+1*it(8)+0 0.04/0.17 Such that:it(8) =< -V_m+V_i_0 0.04/0.17 it(7) =< -V_m+V_i_0+1 0.04/0.17 it(8) =< V_m 0.04/0.17 0.04/0.17 with precondition: [B=2,V_m>=2,V_i_0>=V_m+1] 0.04/0.17 0.04/0.17 * Chain [[7],9]: 1*it(7)+0 0.04/0.17 Such that:it(7) =< -V_m+V_i_0+1 0.04/0.17 0.04/0.17 with precondition: [B=2,V_m>=1,V_i_0>=V_m] 0.04/0.17 0.04/0.17 * Chain [9]: 0 0.04/0.17 with precondition: [B=2,0>=V_i_0,V_m>=1] 0.04/0.17 0.04/0.17 0.04/0.17 #### Cost of chains of eval_peed_pldi09_fig4_4_bb0_in(V_n,V_m,B): 0.04/0.17 * Chain [14]: 0 0.04/0.17 with precondition: [0>=V_n,V_m>=1] 0.04/0.17 0.04/0.17 * Chain [13]: 0 0.04/0.17 with precondition: [0>=V_m] 0.04/0.17 0.04/0.17 * Chain [12]: 1*s(1)+0 0.04/0.17 Such that:s(1) =< V_n 0.04/0.17 0.04/0.17 with precondition: [V_n>=1,V_m>=V_n+1] 0.04/0.17 0.04/0.17 * Chain [11]: 1*s(2)+0 0.04/0.17 Such that:s(2) =< V_n-V_m+1 0.04/0.17 0.04/0.17 with precondition: [V_m>=1,V_n>=V_m] 0.04/0.17 0.04/0.17 * Chain [10]: 1*s(3)+1*s(4)+0 0.04/0.17 Such that:s(3) =< V_n-V_m 0.04/0.17 s(4) =< V_n-V_m+1 0.04/0.17 s(3) =< V_m 0.04/0.17 0.04/0.17 with precondition: [V_m>=2,V_n>=V_m+1] 0.04/0.17 0.04/0.17 0.04/0.17 #### Cost of chains of eval_peed_pldi09_fig4_4_start(V_n,V_m,B): 0.04/0.17 * Chain [19]: 0 0.04/0.17 with precondition: [0>=V_n,V_m>=1] 0.04/0.17 0.04/0.17 * Chain [18]: 0 0.04/0.17 with precondition: [0>=V_m] 0.04/0.17 0.04/0.17 * Chain [17]: 1*s(5)+0 0.04/0.17 Such that:s(5) =< V_n 0.04/0.17 0.04/0.17 with precondition: [V_n>=1,V_m>=V_n+1] 0.04/0.17 0.04/0.17 * Chain [16]: 1*s(6)+0 0.04/0.17 Such that:s(6) =< V_n-V_m+1 0.04/0.17 0.04/0.17 with precondition: [V_m>=1,V_n>=V_m] 0.04/0.17 0.04/0.17 * Chain [15]: 1*s(7)+1*s(8)+0 0.04/0.17 Such that:s(7) =< V_n-V_m 0.04/0.17 s(8) =< V_n-V_m+1 0.04/0.17 s(7) =< V_m 0.04/0.17 0.04/0.17 with precondition: [V_m>=2,V_n>=V_m+1] 0.04/0.17 0.04/0.17 0.04/0.17 Closed-form bounds of eval_peed_pldi09_fig4_4_start(V_n,V_m,B): 0.04/0.17 ------------------------------------- 0.04/0.17 * Chain [19] with precondition: [0>=V_n,V_m>=1] 0.04/0.17 - Upper bound: 0 0.04/0.17 - Complexity: constant 0.04/0.17 * Chain [18] with precondition: [0>=V_m] 0.04/0.17 - Upper bound: 0 0.04/0.17 - Complexity: constant 0.04/0.17 * Chain [17] with precondition: [V_n>=1,V_m>=V_n+1] 0.04/0.17 - Upper bound: V_n 0.04/0.17 - Complexity: n 0.04/0.17 * Chain [16] with precondition: [V_m>=1,V_n>=V_m] 0.04/0.17 - Upper bound: V_n-V_m+1 0.04/0.17 - Complexity: n 0.04/0.17 * Chain [15] with precondition: [V_m>=2,V_n>=V_m+1] 0.04/0.17 - Upper bound: 2*V_n-2*V_m+1 0.04/0.17 - Complexity: n 0.04/0.17 0.04/0.17 ### Maximum cost of eval_peed_pldi09_fig4_4_start(V_n,V_m,B): max([nat(V_n),nat(V_n-V_m)+nat(V_n-V_m+1)]) 0.04/0.17 Asymptotic class: n 0.04/0.17 * Total analysis performed in 100 ms. 0.04/0.17 0.04/0.27 EOF