0.04/0.24 WORST_CASE(?,O(n^1)) 0.04/0.24 0.04/0.24 Preprocessing Cost Relations 0.04/0.24 ===================================== 0.04/0.24 0.04/0.24 #### Computed strongly connected components 0.04/0.24 0. recursive : [eval_start_bb1_in/6,eval_start_bb2_in/6,eval_start_bb3_in/6,eval_start_bb4_in/6] 0.04/0.24 1. non_recursive : [eval_start_stop/4] 0.04/0.24 2. non_recursive : [eval_start_bb5_in/4] 0.04/0.24 3. non_recursive : [exit_location/1] 0.04/0.24 4. non_recursive : [eval_start_bb1_in_loop_cont/5] 0.04/0.24 5. non_recursive : [eval_start_6/4] 0.04/0.24 6. non_recursive : [eval_start_5/4] 0.04/0.24 7. non_recursive : [eval_start_4/4] 0.04/0.24 8. non_recursive : [eval_start_3/4] 0.04/0.24 9. non_recursive : [eval_start_2/4] 0.04/0.24 10. non_recursive : [eval_start_1/4] 0.04/0.24 11. non_recursive : [eval_start_0/4] 0.04/0.24 12. non_recursive : [eval_start_bb0_in/4] 0.04/0.24 13. non_recursive : [eval_start_start/4] 0.04/0.24 0.04/0.24 #### Obtained direct recursion through partial evaluation 0.04/0.24 0. SCC is partially evaluated into eval_start_bb1_in/6 0.04/0.24 1. SCC is completely evaluated into other SCCs 0.04/0.24 2. SCC is completely evaluated into other SCCs 0.04/0.24 3. SCC is completely evaluated into other SCCs 0.04/0.24 4. SCC is partially evaluated into eval_start_bb1_in_loop_cont/5 0.04/0.24 5. SCC is partially evaluated into eval_start_6/4 0.04/0.24 6. SCC is completely evaluated into other SCCs 0.04/0.24 7. SCC is completely evaluated into other SCCs 0.04/0.24 8. SCC is completely evaluated into other SCCs 0.04/0.24 9. SCC is completely evaluated into other SCCs 0.04/0.24 10. SCC is completely evaluated into other SCCs 0.04/0.24 11. SCC is completely evaluated into other SCCs 0.04/0.24 12. SCC is completely evaluated into other SCCs 0.04/0.24 13. SCC is partially evaluated into eval_start_start/4 0.04/0.24 0.04/0.24 Control-Flow Refinement of Cost Relations 0.04/0.24 ===================================== 0.04/0.24 0.04/0.24 ### Specialization of cost equations eval_start_bb1_in/6 0.04/0.24 * CE 3 is refined into CE [9] 0.04/0.24 * CE 6 is refined into CE [10] 0.04/0.24 * CE 4 is refined into CE [11] 0.04/0.24 * CE 5 is refined into CE [12] 0.04/0.24 0.04/0.24 0.04/0.24 ### Cost equations --> "Loop" of eval_start_bb1_in/6 0.04/0.24 * CEs [11] --> Loop 9 0.04/0.24 * CEs [12] --> Loop 10 0.04/0.24 * CEs [10] --> Loop 11 0.04/0.24 * CEs [9] --> Loop 12 0.04/0.24 0.04/0.24 ### Ranking functions of CR eval_start_bb1_in(V_n,V_x_0,V_y_0,B,C,D) 0.04/0.24 * RF of phase [9]: [V_y_0] 0.04/0.24 * RF of phase [10]: [V_n-V_x_0,V_n-V_y_0] 0.04/0.24 0.04/0.24 #### Partial ranking functions of CR eval_start_bb1_in(V_n,V_x_0,V_y_0,B,C,D) 0.04/0.24 * Partial RF of phase [9]: 0.04/0.24 - RF of loop [9:1]: 0.04/0.24 V_y_0 0.04/0.24 * Partial RF of phase [10]: 0.04/0.24 - RF of loop [10:1]: 0.04/0.24 V_n-V_x_0 0.04/0.24 V_n-V_y_0 0.04/0.24 0.04/0.24 0.04/0.24 ### Specialization of cost equations eval_start_bb1_in_loop_cont/5 0.04/0.24 * CE 8 is refined into CE [13] 0.04/0.24 * CE 7 is refined into CE [14] 0.04/0.24 0.04/0.24 0.04/0.24 ### Cost equations --> "Loop" of eval_start_bb1_in_loop_cont/5 0.04/0.24 * CEs [13] --> Loop 13 0.04/0.24 * CEs [14] --> Loop 14 0.04/0.24 0.04/0.24 ### Ranking functions of CR eval_start_bb1_in_loop_cont(A,B,C,D,E) 0.04/0.24 0.04/0.24 #### Partial ranking functions of CR eval_start_bb1_in_loop_cont(A,B,C,D,E) 0.04/0.24 0.04/0.24 0.04/0.24 ### Specialization of cost equations eval_start_6/4 0.04/0.24 * CE 2 is refined into CE [15,16,17,18] 0.04/0.24 0.04/0.24 0.04/0.24 ### Cost equations --> "Loop" of eval_start_6/4 0.04/0.24 * CEs [16,18] --> Loop 15 0.04/0.24 * CEs [15] --> Loop 16 0.04/0.24 * CEs [17] --> Loop 17 0.04/0.24 0.04/0.24 ### Ranking functions of CR eval_start_6(V_n,V_x_0,V_y_0,B) 0.04/0.24 0.04/0.24 #### Partial ranking functions of CR eval_start_6(V_n,V_x_0,V_y_0,B) 0.04/0.24 0.04/0.24 0.04/0.24 ### Specialization of cost equations eval_start_start/4 0.04/0.24 * CE 1 is refined into CE [19,20,21] 0.04/0.24 0.04/0.24 0.04/0.24 ### Cost equations --> "Loop" of eval_start_start/4 0.04/0.24 * CEs [21] --> Loop 18 0.04/0.24 * CEs [20] --> Loop 19 0.04/0.24 * CEs [19] --> Loop 20 0.04/0.24 0.04/0.24 ### Ranking functions of CR eval_start_start(V_n,V_x_0,V_y_0,B) 0.04/0.24 0.04/0.24 #### Partial ranking functions of CR eval_start_start(V_n,V_x_0,V_y_0,B) 0.04/0.24 0.04/0.24 0.04/0.24 Computing Bounds 0.04/0.24 ===================================== 0.04/0.24 0.04/0.24 #### Cost of chains of eval_start_bb1_in(V_n,V_x_0,V_y_0,B,C,D): 0.04/0.24 * Chain [[10],[9],12]: 1*it(9)+1*it(10)+0 0.04/0.24 Such that:it(10) =< -V_x_0+C 0.04/0.24 it(9) =< C 0.04/0.24 0.04/0.24 with precondition: [B=3,D=0,V_x_0=V_y_0,V_n=C,V_x_0>=0,V_n>=V_x_0+1] 0.04/0.24 0.04/0.24 * Chain [[10],[9],11]: 1*it(9)+1*it(10)+0 0.04/0.24 Such that:it(9) =< V_n 0.04/0.24 it(10) =< V_n-V_y_0 0.04/0.24 0.04/0.24 with precondition: [B=2,V_x_0=V_y_0,V_x_0>=0,V_n>=V_x_0+1] 0.04/0.24 0.04/0.24 * Chain [[10],11]: 1*it(10)+0 0.04/0.24 Such that:it(10) =< V_n-V_y_0 0.04/0.24 0.04/0.24 with precondition: [B=2,V_x_0=V_y_0,V_x_0>=0,V_n>=V_x_0+1] 0.04/0.24 0.04/0.24 * Chain [12]: 0 0.04/0.24 with precondition: [V_y_0=0,B=3,D=0,V_x_0=C,V_x_0>=0,V_x_0>=V_n] 0.04/0.24 0.04/0.24 * Chain [11]: 0 0.04/0.24 with precondition: [B=2,V_y_0>=0,V_x_0>=V_y_0] 0.04/0.24 0.04/0.24 0.04/0.24 #### Cost of chains of eval_start_bb1_in_loop_cont(A,B,C,D,E): 0.04/0.24 * Chain [14]: 0 0.04/0.24 with precondition: [A=2] 0.04/0.24 0.04/0.24 * Chain [13]: 0 0.04/0.24 with precondition: [A=3] 0.04/0.24 0.04/0.24 0.04/0.24 #### Cost of chains of eval_start_6(V_n,V_x_0,V_y_0,B): 0.04/0.24 * Chain [17]: 0 0.04/0.24 with precondition: [] 0.04/0.24 0.04/0.24 * Chain [16]: 0 0.04/0.24 with precondition: [0>=V_n] 0.04/0.24 0.04/0.24 * Chain [15]: 5*s(4)+0 0.04/0.24 Such that:aux(4) =< V_n 0.04/0.24 s(4) =< aux(4) 0.04/0.24 0.04/0.24 with precondition: [V_n>=1] 0.04/0.24 0.04/0.24 0.04/0.24 #### Cost of chains of eval_start_start(V_n,V_x_0,V_y_0,B): 0.04/0.24 * Chain [20]: 0 0.04/0.24 with precondition: [] 0.04/0.24 0.04/0.24 * Chain [19]: 0 0.04/0.24 with precondition: [0>=V_n] 0.04/0.24 0.04/0.24 * Chain [18]: 5*s(10)+0 0.04/0.24 Such that:s(9) =< V_n 0.04/0.24 s(10) =< s(9) 0.04/0.24 0.04/0.24 with precondition: [V_n>=1] 0.04/0.24 0.04/0.24 0.04/0.24 Closed-form bounds of eval_start_start(V_n,V_x_0,V_y_0,B): 0.04/0.24 ------------------------------------- 0.04/0.24 * Chain [20] with precondition: [] 0.04/0.24 - Upper bound: 0 0.04/0.24 - Complexity: constant 0.04/0.24 * Chain [19] with precondition: [0>=V_n] 0.04/0.24 - Upper bound: 0 0.04/0.24 - Complexity: constant 0.04/0.24 * Chain [18] with precondition: [V_n>=1] 0.04/0.24 - Upper bound: 5*V_n 0.04/0.24 - Complexity: n 0.04/0.24 0.04/0.24 ### Maximum cost of eval_start_start(V_n,V_x_0,V_y_0,B): nat(V_n)*5 0.04/0.24 Asymptotic class: n 0.04/0.24 * Total analysis performed in 171 ms. 0.04/0.24 0.04/0.34 EOF