0.03/0.18 WORST_CASE(?,O(1)) 0.03/0.18 0.03/0.18 Preprocessing Cost Relations 0.03/0.18 ===================================== 0.03/0.18 0.03/0.18 #### Computed strongly connected components 0.03/0.18 0. recursive : [eval_nd_loop_4/5,eval_nd_loop_5/5,eval_nd_loop_bb1_in/5] 0.03/0.18 1. non_recursive : [eval_nd_loop_stop/3] 0.03/0.18 2. non_recursive : [eval_nd_loop_bb2_in/3] 0.03/0.18 3. non_recursive : [exit_location/1] 0.03/0.18 4. non_recursive : [eval_nd_loop_bb1_in_loop_cont/4] 0.03/0.18 5. non_recursive : [eval_nd_loop_3/3] 0.03/0.18 6. non_recursive : [eval_nd_loop_2/3] 0.03/0.18 7. non_recursive : [eval_nd_loop_1/3] 0.03/0.18 8. non_recursive : [eval_nd_loop_0/3] 0.03/0.18 9. non_recursive : [eval_nd_loop_bb0_in/3] 0.03/0.18 10. non_recursive : [eval_nd_loop_start/3] 0.03/0.18 0.03/0.18 #### Obtained direct recursion through partial evaluation 0.03/0.18 0. SCC is partially evaluated into eval_nd_loop_bb1_in/5 0.03/0.18 1. SCC is completely evaluated into other SCCs 0.03/0.18 2. SCC is completely evaluated into other SCCs 0.03/0.18 3. SCC is completely evaluated into other SCCs 0.03/0.18 4. SCC is partially evaluated into eval_nd_loop_bb1_in_loop_cont/4 0.03/0.18 5. SCC is partially evaluated into eval_nd_loop_3/3 0.03/0.18 6. SCC is completely evaluated into other SCCs 0.03/0.18 7. SCC is completely evaluated into other SCCs 0.03/0.18 8. SCC is completely evaluated into other SCCs 0.03/0.18 9. SCC is completely evaluated into other SCCs 0.03/0.18 10. SCC is partially evaluated into eval_nd_loop_start/3 0.03/0.18 0.03/0.18 Control-Flow Refinement of Cost Relations 0.03/0.18 ===================================== 0.03/0.18 0.03/0.18 ### Specialization of cost equations eval_nd_loop_bb1_in/5 0.03/0.18 * CE 7 is refined into CE [10] 0.03/0.18 * CE 4 is refined into CE [11] 0.03/0.18 * CE 5 is refined into CE [12] 0.03/0.18 * CE 3 is refined into CE [13] 0.03/0.18 * CE 6 is refined into CE [14] 0.03/0.18 0.03/0.18 0.03/0.18 ### Cost equations --> "Loop" of eval_nd_loop_bb1_in/5 0.03/0.18 * CEs [14] --> Loop 10 0.03/0.18 * CEs [10] --> Loop 11 0.03/0.18 * CEs [11] --> Loop 12 0.03/0.18 * CEs [12] --> Loop 13 0.03/0.18 * CEs [13] --> Loop 14 0.03/0.18 0.03/0.18 ### Ranking functions of CR eval_nd_loop_bb1_in(V_0,V_x_0,B,C,D) 0.03/0.18 * RF of phase [10]: [-V_x_0+9] 0.03/0.18 0.03/0.18 #### Partial ranking functions of CR eval_nd_loop_bb1_in(V_0,V_x_0,B,C,D) 0.03/0.18 * Partial RF of phase [10]: 0.03/0.18 - RF of loop [10:1]: 0.03/0.18 -V_x_0+9 0.03/0.18 0.03/0.18 0.03/0.18 ### Specialization of cost equations eval_nd_loop_bb1_in_loop_cont/4 0.03/0.18 * CE 9 is refined into CE [15] 0.03/0.18 * CE 8 is refined into CE [16] 0.03/0.18 0.03/0.18 0.03/0.18 ### Cost equations --> "Loop" of eval_nd_loop_bb1_in_loop_cont/4 0.03/0.18 * CEs [15] --> Loop 15 0.03/0.18 * CEs [16] --> Loop 16 0.03/0.18 0.03/0.18 ### Ranking functions of CR eval_nd_loop_bb1_in_loop_cont(A,B,C,D) 0.03/0.18 0.03/0.18 #### Partial ranking functions of CR eval_nd_loop_bb1_in_loop_cont(A,B,C,D) 0.03/0.18 0.03/0.18 0.03/0.18 ### Specialization of cost equations eval_nd_loop_3/3 0.03/0.18 * CE 2 is refined into CE [17,18,19,20,21,22,23,24] 0.03/0.18 0.03/0.18 0.03/0.18 ### Cost equations --> "Loop" of eval_nd_loop_3/3 0.03/0.18 * CEs [17,18,19,20,21,22,23,24] --> Loop 17 0.03/0.18 0.03/0.18 ### Ranking functions of CR eval_nd_loop_3(V_0,V_x_0,B) 0.03/0.18 0.03/0.18 #### Partial ranking functions of CR eval_nd_loop_3(V_0,V_x_0,B) 0.03/0.18 0.03/0.18 0.03/0.18 ### Specialization of cost equations eval_nd_loop_start/3 0.03/0.18 * CE 1 is refined into CE [25] 0.03/0.18 0.03/0.18 0.03/0.18 ### Cost equations --> "Loop" of eval_nd_loop_start/3 0.03/0.18 * CEs [25] --> Loop 18 0.03/0.18 0.03/0.18 ### Ranking functions of CR eval_nd_loop_start(V_0,V_x_0,B) 0.03/0.18 0.03/0.18 #### Partial ranking functions of CR eval_nd_loop_start(V_0,V_x_0,B) 0.03/0.18 0.03/0.18 0.03/0.18 Computing Bounds 0.03/0.18 ===================================== 0.03/0.18 0.03/0.18 #### Cost of chains of eval_nd_loop_bb1_in(V_0,V_x_0,B,C,D): 0.03/0.18 * Chain [[10],14]: 1*it(10)+0 0.03/0.18 Such that:it(10) =< -V_x_0+D 0.03/0.18 0.03/0.18 with precondition: [B=2,9>=D,V_x_0>=0,C>=10,D>=V_x_0+1] 0.03/0.18 0.03/0.18 * Chain [[10],13]: 1*it(10)+0 0.03/0.18 Such that:it(10) =< -V_x_0+D 0.03/0.18 0.03/0.18 with precondition: [B=2,9>=D,V_x_0>=0,D>=V_x_0+1,C>=D+3] 0.03/0.18 0.03/0.18 * Chain [[10],12]: 1*it(10)+0 0.03/0.18 Such that:it(10) =< -V_x_0+D 0.03/0.18 0.03/0.18 with precondition: [B=2,9>=D,V_x_0>=0,D>=V_x_0+1,D>=C] 0.03/0.18 0.03/0.18 * Chain [[10],11]: 1*it(10)+0 0.03/0.18 Such that:it(10) =< -V_x_0+9 0.03/0.18 0.03/0.18 with precondition: [B=3,8>=V_x_0,V_x_0>=0] 0.03/0.18 0.03/0.18 * Chain [14]: 0 0.03/0.18 with precondition: [B=2,V_x_0=D,V_x_0>=0,C>=10] 0.03/0.18 0.03/0.18 * Chain [13]: 0 0.03/0.18 with precondition: [B=2,V_x_0=D,V_x_0>=0,C>=V_x_0+3] 0.03/0.18 0.03/0.18 * Chain [12]: 0 0.03/0.18 with precondition: [B=2,V_x_0=D,V_x_0>=0,V_x_0>=C] 0.03/0.18 0.03/0.18 * Chain [11]: 0 0.03/0.18 with precondition: [B=3,V_x_0>=0] 0.03/0.18 0.03/0.18 0.03/0.18 #### Cost of chains of eval_nd_loop_bb1_in_loop_cont(A,B,C,D): 0.03/0.18 * Chain [16]: 0 0.03/0.18 with precondition: [A=2] 0.03/0.18 0.03/0.18 * Chain [15]: 0 0.03/0.18 with precondition: [A=3] 0.03/0.18 0.03/0.18 0.03/0.18 #### Cost of chains of eval_nd_loop_3(V_0,V_x_0,B): 0.03/0.18 * Chain [17]: 36 0.03/0.18 with precondition: [] 0.03/0.18 0.03/0.18 0.03/0.18 #### Cost of chains of eval_nd_loop_start(V_0,V_x_0,B): 0.03/0.18 * Chain [18]: 36 0.03/0.18 with precondition: [] 0.03/0.18 0.03/0.18 0.03/0.18 Closed-form bounds of eval_nd_loop_start(V_0,V_x_0,B): 0.03/0.18 ------------------------------------- 0.03/0.18 * Chain [18] with precondition: [] 0.03/0.18 - Upper bound: 36 0.03/0.18 - Complexity: constant 0.03/0.18 0.03/0.18 ### Maximum cost of eval_nd_loop_start(V_0,V_x_0,B): 36 0.03/0.18 Asymptotic class: constant 0.03/0.18 * Total analysis performed in 122 ms. 0.03/0.18 0.03/0.29 EOF