0.03/0.27 WORST_CASE(?,O(n^2)) 0.03/0.27 0.03/0.27 Preprocessing Cost Relations 0.03/0.27 ===================================== 0.03/0.27 0.03/0.27 #### Computed strongly connected components 0.03/0.27 0. recursive : [eval_speedSimpleMultipleDep_bb1_in/7,eval_speedSimpleMultipleDep_bb2_in/7] 0.03/0.27 1. non_recursive : [eval_speedSimpleMultipleDep_stop/5] 0.03/0.27 2. non_recursive : [eval_speedSimpleMultipleDep_bb3_in/5] 0.03/0.27 3. non_recursive : [exit_location/1] 0.03/0.27 4. non_recursive : [eval_speedSimpleMultipleDep_bb1_in_loop_cont/6] 0.03/0.27 5. non_recursive : [eval_speedSimpleMultipleDep_7/5] 0.03/0.27 6. non_recursive : [eval_speedSimpleMultipleDep_6/5] 0.03/0.27 7. non_recursive : [eval_speedSimpleMultipleDep_5/5] 0.03/0.27 8. non_recursive : [eval_speedSimpleMultipleDep_4/5] 0.03/0.27 9. non_recursive : [eval_speedSimpleMultipleDep_3/5] 0.03/0.27 10. non_recursive : [eval_speedSimpleMultipleDep_2/5] 0.03/0.27 11. non_recursive : [eval_speedSimpleMultipleDep_1/5] 0.03/0.27 12. non_recursive : [eval_speedSimpleMultipleDep_0/5] 0.03/0.27 13. non_recursive : [eval_speedSimpleMultipleDep_bb0_in/5] 0.03/0.27 14. non_recursive : [eval_speedSimpleMultipleDep_start/5] 0.03/0.27 0.03/0.27 #### Obtained direct recursion through partial evaluation 0.03/0.27 0. SCC is partially evaluated into eval_speedSimpleMultipleDep_bb1_in/7 0.03/0.27 1. SCC is completely evaluated into other SCCs 0.03/0.27 2. SCC is completely evaluated into other SCCs 0.03/0.27 3. SCC is completely evaluated into other SCCs 0.03/0.27 4. SCC is partially evaluated into eval_speedSimpleMultipleDep_bb1_in_loop_cont/6 0.03/0.27 5. SCC is partially evaluated into eval_speedSimpleMultipleDep_7/5 0.03/0.27 6. SCC is completely evaluated into other SCCs 0.03/0.27 7. SCC is completely evaluated into other SCCs 0.03/0.27 8. SCC is completely evaluated into other SCCs 0.03/0.27 9. SCC is completely evaluated into other SCCs 0.03/0.27 10. SCC is completely evaluated into other SCCs 0.03/0.27 11. SCC is completely evaluated into other SCCs 0.03/0.27 12. SCC is completely evaluated into other SCCs 0.03/0.27 13. SCC is completely evaluated into other SCCs 0.03/0.27 14. SCC is partially evaluated into eval_speedSimpleMultipleDep_start/5 0.03/0.27 0.03/0.27 Control-Flow Refinement of Cost Relations 0.03/0.27 ===================================== 0.03/0.27 0.03/0.27 ### Specialization of cost equations eval_speedSimpleMultipleDep_bb1_in/7 0.03/0.27 * CE 6 is refined into CE [9] 0.03/0.27 * CE 5 is refined into CE [10] 0.03/0.27 * CE 4 is refined into CE [11] 0.03/0.27 * CE 3 is refined into CE [12] 0.03/0.27 0.03/0.27 0.03/0.27 ### Cost equations --> "Loop" of eval_speedSimpleMultipleDep_bb1_in/7 0.03/0.27 * CEs [11] --> Loop 9 0.03/0.27 * CEs [12] --> Loop 10 0.03/0.27 * CEs [9] --> Loop 11 0.03/0.27 * CEs [10] --> Loop 12 0.03/0.27 0.03/0.27 ### Ranking functions of CR eval_speedSimpleMultipleDep_bb1_in(V_m,V_n,V_x_0,V_y_0,B,C,D) 0.03/0.27 0.03/0.27 #### Partial ranking functions of CR eval_speedSimpleMultipleDep_bb1_in(V_m,V_n,V_x_0,V_y_0,B,C,D) 0.03/0.27 * Partial RF of phase [9,10]: 0.03/0.27 - RF of loop [9:1]: 0.03/0.27 V_m-V_y_0 depends on loops [10:1] 0.03/0.27 - RF of loop [10:1]: 0.03/0.27 V_n-V_x_0 0.03/0.27 0.03/0.27 0.03/0.27 ### Specialization of cost equations eval_speedSimpleMultipleDep_bb1_in_loop_cont/6 0.03/0.27 * CE 8 is refined into CE [13] 0.03/0.27 * CE 7 is refined into CE [14] 0.03/0.27 0.03/0.27 0.03/0.27 ### Cost equations --> "Loop" of eval_speedSimpleMultipleDep_bb1_in_loop_cont/6 0.03/0.27 * CEs [13] --> Loop 13 0.03/0.27 * CEs [14] --> Loop 14 0.03/0.27 0.03/0.27 ### Ranking functions of CR eval_speedSimpleMultipleDep_bb1_in_loop_cont(A,B,C,D,E,F) 0.03/0.27 0.03/0.27 #### Partial ranking functions of CR eval_speedSimpleMultipleDep_bb1_in_loop_cont(A,B,C,D,E,F) 0.03/0.27 0.03/0.27 0.03/0.27 ### Specialization of cost equations eval_speedSimpleMultipleDep_7/5 0.03/0.27 * CE 2 is refined into CE [15,16,17,18] 0.03/0.27 0.03/0.27 0.03/0.27 ### Cost equations --> "Loop" of eval_speedSimpleMultipleDep_7/5 0.03/0.27 * CEs [15,18] --> Loop 15 0.03/0.27 * CEs [16] --> Loop 16 0.03/0.27 * CEs [17] --> Loop 17 0.03/0.27 0.03/0.27 ### Ranking functions of CR eval_speedSimpleMultipleDep_7(V_m,V_n,V_x_0,V_y_0,B) 0.03/0.27 0.03/0.27 #### Partial ranking functions of CR eval_speedSimpleMultipleDep_7(V_m,V_n,V_x_0,V_y_0,B) 0.03/0.27 0.03/0.27 0.03/0.27 ### Specialization of cost equations eval_speedSimpleMultipleDep_start/5 0.03/0.27 * CE 1 is refined into CE [19,20,21] 0.03/0.27 0.03/0.27 0.03/0.27 ### Cost equations --> "Loop" of eval_speedSimpleMultipleDep_start/5 0.03/0.27 * CEs [21] --> Loop 18 0.03/0.27 * CEs [20] --> Loop 19 0.03/0.27 * CEs [19] --> Loop 20 0.03/0.27 0.03/0.27 ### Ranking functions of CR eval_speedSimpleMultipleDep_start(V_m,V_n,V_x_0,V_y_0,B) 0.03/0.27 0.03/0.27 #### Partial ranking functions of CR eval_speedSimpleMultipleDep_start(V_m,V_n,V_x_0,V_y_0,B) 0.03/0.27 0.03/0.27 0.03/0.27 Computing Bounds 0.03/0.27 ===================================== 0.03/0.27 0.03/0.27 #### Cost of chains of eval_speedSimpleMultipleDep_bb1_in(V_m,V_n,V_x_0,V_y_0,B,C,D): 0.03/0.27 * Chain [[9,10],12]: 1*it(9)+1*it(10)+0 0.03/0.27 Such that:aux(7) =< V_m 0.03/0.27 aux(2) =< V_m-V_y_0 0.03/0.27 it(10) =< -V_x_0+C 0.03/0.27 aux(1) =< it(10)*aux(7) 0.03/0.27 it(9) =< aux(1)+aux(2) 0.03/0.27 0.03/0.27 with precondition: [B=2,D=0,V_n=C,V_x_0>=0,V_y_0>=0,V_n>=V_x_0+1] 0.03/0.27 0.03/0.27 * Chain [[9,10],11]: 1*it(9)+1*it(10)+0 0.03/0.27 Such that:aux(7) =< V_m 0.03/0.27 aux(2) =< V_m-V_y_0 0.03/0.27 it(10) =< V_n-V_x_0 0.03/0.27 aux(1) =< it(10)*aux(7) 0.03/0.27 it(9) =< aux(1)+aux(2) 0.03/0.27 0.03/0.27 with precondition: [B=3,V_x_0>=0,V_y_0>=0,V_n>=V_x_0+1] 0.03/0.27 0.03/0.27 * Chain [12]: 0 0.03/0.27 with precondition: [B=2,V_x_0=C,V_y_0=D,V_x_0>=0,V_y_0>=0,V_x_0>=V_n] 0.03/0.27 0.03/0.27 * Chain [11]: 0 0.03/0.27 with precondition: [B=3,V_x_0>=0,V_y_0>=0] 0.03/0.27 0.03/0.27 0.03/0.27 #### Cost of chains of eval_speedSimpleMultipleDep_bb1_in_loop_cont(A,B,C,D,E,F): 0.03/0.27 * Chain [14]: 0 0.03/0.27 with precondition: [A=2] 0.03/0.27 0.03/0.27 * Chain [13]: 0 0.03/0.27 with precondition: [A=3] 0.03/0.27 0.03/0.27 0.03/0.27 #### Cost of chains of eval_speedSimpleMultipleDep_7(V_m,V_n,V_x_0,V_y_0,B): 0.03/0.27 * Chain [17]: 0 0.03/0.27 with precondition: [] 0.03/0.27 0.03/0.27 * Chain [16]: 0 0.03/0.27 with precondition: [0>=V_n] 0.03/0.27 0.03/0.27 * Chain [15]: 2*s(3)+2*s(5)+0 0.03/0.27 Such that:aux(16) =< V_m 0.03/0.27 aux(17) =< V_n 0.03/0.27 s(3) =< aux(17) 0.03/0.27 s(4) =< s(3)*aux(16) 0.03/0.27 s(5) =< s(4)+aux(16) 0.03/0.27 0.03/0.27 with precondition: [V_n>=1] 0.03/0.27 0.03/0.27 0.03/0.27 #### Cost of chains of eval_speedSimpleMultipleDep_start(V_m,V_n,V_x_0,V_y_0,B): 0.03/0.27 * Chain [20]: 0 0.03/0.27 with precondition: [] 0.03/0.27 0.03/0.27 * Chain [19]: 0 0.03/0.27 with precondition: [0>=V_n] 0.03/0.27 0.03/0.27 * Chain [18]: 2*s(13)+2*s(15)+0 0.03/0.27 Such that:s(11) =< V_m 0.03/0.27 s(12) =< V_n 0.03/0.27 s(13) =< s(12) 0.03/0.27 s(14) =< s(13)*s(11) 0.03/0.27 s(15) =< s(14)+s(11) 0.03/0.27 0.03/0.27 with precondition: [V_n>=1] 0.03/0.27 0.03/0.27 0.03/0.27 Closed-form bounds of eval_speedSimpleMultipleDep_start(V_m,V_n,V_x_0,V_y_0,B): 0.03/0.27 ------------------------------------- 0.03/0.27 * Chain [20] with precondition: [] 0.03/0.27 - Upper bound: 0 0.03/0.27 - Complexity: constant 0.03/0.27 * Chain [19] with precondition: [0>=V_n] 0.03/0.27 - Upper bound: 0 0.03/0.27 - Complexity: constant 0.03/0.27 * Chain [18] with precondition: [V_n>=1] 0.03/0.27 - Upper bound: nat(V_m)*2*V_n+nat(V_m)*2+2*V_n 0.03/0.27 - Complexity: n^2 0.03/0.27 0.03/0.27 ### Maximum cost of eval_speedSimpleMultipleDep_start(V_m,V_n,V_x_0,V_y_0,B): nat(V_m)*2*nat(V_n)+nat(V_m)*2+nat(V_n)*2 0.03/0.27 Asymptotic class: n^2 0.03/0.27 * Total analysis performed in 197 ms. 0.03/0.27 0.03/0.38 EOF