0.05/0.19 WORST_CASE(?,O(n^1)) 0.05/0.19 0.05/0.19 Preprocessing Cost Relations 0.05/0.19 ===================================== 0.05/0.19 0.05/0.19 #### Computed strongly connected components 0.05/0.19 0. recursive : [eval_speed_popl10_sequential_single_0/4,eval_speed_popl10_sequential_single_1/5,eval_speed_popl10_sequential_single_bb1_in/4,eval_speed_popl10_sequential_single_bb2_in/4,eval_speed_popl10_sequential_single_bb3_in/5] 0.05/0.19 1. recursive : [eval_speed_popl10_sequential_single_bb4_in/3,eval_speed_popl10_sequential_single_bb5_in/3] 0.05/0.19 2. non_recursive : [eval_speed_popl10_sequential_single_stop/1] 0.05/0.19 3. non_recursive : [eval_speed_popl10_sequential_single_bb6_in/1] 0.05/0.19 4. non_recursive : [eval_speed_popl10_sequential_single_bb4_in_loop_cont/2] 0.05/0.19 5. non_recursive : [eval_speed_popl10_sequential_single_bb1_in_loop_cont/4] 0.05/0.19 6. non_recursive : [eval_speed_popl10_sequential_single_bb0_in/2] 0.05/0.19 7. non_recursive : [eval_speed_popl10_sequential_single_start/2] 0.05/0.19 0.05/0.19 #### Obtained direct recursion through partial evaluation 0.05/0.19 0. SCC is partially evaluated into eval_speed_popl10_sequential_single_bb1_in/4 0.05/0.19 1. SCC is partially evaluated into eval_speed_popl10_sequential_single_bb4_in/3 0.05/0.19 2. SCC is completely evaluated into other SCCs 0.05/0.19 3. SCC is completely evaluated into other SCCs 0.05/0.19 4. SCC is completely evaluated into other SCCs 0.05/0.19 5. SCC is partially evaluated into eval_speed_popl10_sequential_single_bb1_in_loop_cont/4 0.05/0.19 6. SCC is partially evaluated into eval_speed_popl10_sequential_single_bb0_in/2 0.05/0.19 7. SCC is partially evaluated into eval_speed_popl10_sequential_single_start/2 0.05/0.19 0.05/0.19 Control-Flow Refinement of Cost Relations 0.05/0.19 ===================================== 0.05/0.19 0.05/0.19 ### Specialization of cost equations eval_speed_popl10_sequential_single_bb1_in/4 0.05/0.19 * CE 3 is refined into CE [9] 0.05/0.19 * CE 5 is refined into CE [10] 0.05/0.19 * CE 4 is refined into CE [11] 0.05/0.19 0.05/0.19 0.05/0.19 ### Cost equations --> "Loop" of eval_speed_popl10_sequential_single_bb1_in/4 0.05/0.19 * CEs [11] --> Loop 9 0.05/0.19 * CEs [9] --> Loop 10 0.05/0.19 * CEs [10] --> Loop 11 0.05/0.19 0.05/0.19 ### Ranking functions of CR eval_speed_popl10_sequential_single_bb1_in(V_n,V_x_0,B,C) 0.05/0.19 * RF of phase [9]: [V_n-V_x_0] 0.05/0.19 0.05/0.19 #### Partial ranking functions of CR eval_speed_popl10_sequential_single_bb1_in(V_n,V_x_0,B,C) 0.05/0.19 * Partial RF of phase [9]: 0.05/0.19 - RF of loop [9:1]: 0.05/0.19 V_n-V_x_0 0.05/0.19 0.05/0.19 0.05/0.19 ### Specialization of cost equations eval_speed_popl10_sequential_single_bb4_in/3 0.05/0.19 * CE 8 is refined into CE [12] 0.05/0.19 * CE 7 is refined into CE [13] 0.05/0.19 0.05/0.19 0.05/0.19 ### Cost equations --> "Loop" of eval_speed_popl10_sequential_single_bb4_in/3 0.05/0.19 * CEs [13] --> Loop 12 0.05/0.19 * CEs [12] --> Loop 13 0.05/0.19 0.05/0.19 ### Ranking functions of CR eval_speed_popl10_sequential_single_bb4_in(V_n,V_x_1,B) 0.05/0.19 * RF of phase [12]: [V_n-V_x_1] 0.05/0.19 0.05/0.19 #### Partial ranking functions of CR eval_speed_popl10_sequential_single_bb4_in(V_n,V_x_1,B) 0.05/0.19 * Partial RF of phase [12]: 0.05/0.19 - RF of loop [12:1]: 0.05/0.19 V_n-V_x_1 0.05/0.19 0.05/0.19 0.05/0.19 ### Specialization of cost equations eval_speed_popl10_sequential_single_bb1_in_loop_cont/4 0.05/0.19 * CE 6 is refined into CE [14,15] 0.05/0.19 0.05/0.19 0.05/0.19 ### Cost equations --> "Loop" of eval_speed_popl10_sequential_single_bb1_in_loop_cont/4 0.05/0.19 * CEs [15] --> Loop 14 0.05/0.19 * CEs [14] --> Loop 15 0.05/0.19 0.05/0.19 ### Ranking functions of CR eval_speed_popl10_sequential_single_bb1_in_loop_cont(A,B,C,D) 0.05/0.19 0.05/0.19 #### Partial ranking functions of CR eval_speed_popl10_sequential_single_bb1_in_loop_cont(A,B,C,D) 0.05/0.19 0.05/0.19 0.05/0.19 ### Specialization of cost equations eval_speed_popl10_sequential_single_bb0_in/2 0.05/0.19 * CE 2 is refined into CE [16,17,18,19] 0.05/0.19 0.05/0.19 0.05/0.19 ### Cost equations --> "Loop" of eval_speed_popl10_sequential_single_bb0_in/2 0.05/0.19 * CEs [19] --> Loop 16 0.05/0.19 * CEs [16,18] --> Loop 17 0.05/0.19 * CEs [17] --> Loop 18 0.05/0.19 0.05/0.19 ### Ranking functions of CR eval_speed_popl10_sequential_single_bb0_in(V_n,B) 0.05/0.19 0.05/0.19 #### Partial ranking functions of CR eval_speed_popl10_sequential_single_bb0_in(V_n,B) 0.05/0.19 0.05/0.19 0.05/0.19 ### Specialization of cost equations eval_speed_popl10_sequential_single_start/2 0.05/0.19 * CE 1 is refined into CE [20,21,22] 0.05/0.19 0.05/0.19 0.05/0.19 ### Cost equations --> "Loop" of eval_speed_popl10_sequential_single_start/2 0.05/0.19 * CEs [22] --> Loop 19 0.05/0.19 * CEs [21] --> Loop 20 0.05/0.19 * CEs [20] --> Loop 21 0.05/0.19 0.05/0.19 ### Ranking functions of CR eval_speed_popl10_sequential_single_start(V_n,B) 0.05/0.19 0.05/0.19 #### Partial ranking functions of CR eval_speed_popl10_sequential_single_start(V_n,B) 0.05/0.19 0.05/0.19 0.05/0.19 Computing Bounds 0.05/0.19 ===================================== 0.05/0.19 0.05/0.19 #### Cost of chains of eval_speed_popl10_sequential_single_bb1_in(V_n,V_x_0,B,C): 0.05/0.19 * Chain [[9],11]: 1*it(9)+0 0.05/0.19 Such that:it(9) =< -V_x_0+C 0.05/0.19 0.05/0.19 with precondition: [B=3,V_n=C,V_x_0>=0,V_n>=V_x_0+1] 0.05/0.19 0.05/0.19 * Chain [[9],10]: 1*it(9)+0 0.05/0.19 Such that:it(9) =< -V_x_0+C 0.05/0.19 0.05/0.19 with precondition: [B=3,V_x_0>=0,C>=V_x_0+1,V_n>=C+1] 0.05/0.19 0.05/0.19 * Chain [11]: 0 0.05/0.19 with precondition: [B=3,V_x_0=C,V_x_0>=0,V_x_0>=V_n] 0.05/0.19 0.05/0.19 * Chain [10]: 0 0.05/0.19 with precondition: [B=3,V_x_0=C,V_x_0>=0,V_n>=V_x_0+1] 0.05/0.19 0.05/0.19 0.05/0.19 #### Cost of chains of eval_speed_popl10_sequential_single_bb4_in(V_n,V_x_1,B): 0.05/0.19 * Chain [[12],13]: 1*it(12)+0 0.05/0.19 Such that:it(12) =< V_n-V_x_1 0.05/0.19 0.05/0.19 with precondition: [B=2,V_n>=V_x_1+1] 0.05/0.19 0.05/0.19 * Chain [13]: 0 0.05/0.19 with precondition: [B=2,V_x_1>=V_n] 0.05/0.19 0.05/0.19 0.05/0.19 #### Cost of chains of eval_speed_popl10_sequential_single_bb1_in_loop_cont(A,B,C,D): 0.05/0.19 * Chain [15]: 0 0.05/0.19 with precondition: [A=3,C>=B] 0.05/0.19 0.05/0.19 * Chain [14]: 1*s(1)+0 0.05/0.19 Such that:s(1) =< B-C 0.05/0.19 0.05/0.19 with precondition: [A=3,B>=C+1] 0.05/0.19 0.05/0.19 0.05/0.19 #### Cost of chains of eval_speed_popl10_sequential_single_bb0_in(V_n,B): 0.05/0.19 * Chain [18]: 0 0.05/0.19 with precondition: [0>=V_n] 0.05/0.19 0.05/0.19 * Chain [17]: 2*s(2)+0 0.05/0.19 Such that:aux(1) =< V_n 0.05/0.19 s(2) =< aux(1) 0.05/0.19 0.05/0.19 with precondition: [V_n>=1] 0.05/0.19 0.05/0.19 * Chain [16]: 2*s(4)+0 0.05/0.19 Such that:aux(2) =< V_n 0.05/0.19 s(4) =< aux(2) 0.05/0.19 0.05/0.19 with precondition: [V_n>=2] 0.05/0.19 0.05/0.19 0.05/0.19 #### Cost of chains of eval_speed_popl10_sequential_single_start(V_n,B): 0.05/0.19 * Chain [21]: 0 0.05/0.19 with precondition: [0>=V_n] 0.05/0.19 0.05/0.19 * Chain [20]: 2*s(7)+0 0.05/0.19 Such that:s(6) =< V_n 0.05/0.19 s(7) =< s(6) 0.05/0.19 0.05/0.19 with precondition: [V_n>=1] 0.05/0.19 0.05/0.19 * Chain [19]: 2*s(9)+0 0.05/0.19 Such that:s(8) =< V_n 0.05/0.19 s(9) =< s(8) 0.05/0.19 0.05/0.19 with precondition: [V_n>=2] 0.05/0.19 0.05/0.19 0.05/0.19 Closed-form bounds of eval_speed_popl10_sequential_single_start(V_n,B): 0.05/0.19 ------------------------------------- 0.05/0.19 * Chain [21] with precondition: [0>=V_n] 0.05/0.19 - Upper bound: 0 0.05/0.19 - Complexity: constant 0.05/0.19 * Chain [20] with precondition: [V_n>=1] 0.05/0.19 - Upper bound: 2*V_n 0.05/0.19 - Complexity: n 0.05/0.19 * Chain [19] with precondition: [V_n>=2] 0.05/0.19 - Upper bound: 2*V_n 0.05/0.19 - Complexity: n 0.05/0.19 0.05/0.19 ### Maximum cost of eval_speed_popl10_sequential_single_start(V_n,B): nat(V_n)*2 0.05/0.19 Asymptotic class: n 0.05/0.19 * Total analysis performed in 113 ms. 0.05/0.19 0.05/0.29 EOF