0.03/0.20 WORST_CASE(?,O(n^1)) 0.03/0.20 0.03/0.20 Preprocessing Cost Relations 0.03/0.20 ===================================== 0.03/0.20 0.03/0.20 #### Computed strongly connected components 0.03/0.20 0. recursive : [eval_start_bb1_in/5,eval_start_bb2_in/5] 0.03/0.20 1. non_recursive : [eval_start_stop/4] 0.03/0.20 2. non_recursive : [eval_start_bb3_in/4] 0.03/0.20 3. non_recursive : [exit_location/1] 0.03/0.20 4. non_recursive : [eval_start_bb1_in_loop_cont/5] 0.03/0.20 5. non_recursive : [eval_start_5/4] 0.03/0.20 6. non_recursive : [eval_start_4/4] 0.03/0.20 7. non_recursive : [eval_start_3/4] 0.03/0.20 8. non_recursive : [eval_start_2/4] 0.03/0.20 9. non_recursive : [eval_start_1/4] 0.03/0.20 10. non_recursive : [eval_start_0/4] 0.03/0.20 11. non_recursive : [eval_start_bb0_in/4] 0.03/0.20 12. non_recursive : [eval_start_start/4] 0.03/0.20 0.03/0.20 #### Obtained direct recursion through partial evaluation 0.03/0.20 0. SCC is partially evaluated into eval_start_bb1_in/5 0.03/0.20 1. SCC is completely evaluated into other SCCs 0.03/0.20 2. SCC is completely evaluated into other SCCs 0.03/0.20 3. SCC is completely evaluated into other SCCs 0.03/0.20 4. SCC is partially evaluated into eval_start_bb1_in_loop_cont/5 0.03/0.20 5. SCC is partially evaluated into eval_start_5/4 0.03/0.20 6. SCC is completely evaluated into other SCCs 0.03/0.20 7. SCC is completely evaluated into other SCCs 0.03/0.20 8. SCC is completely evaluated into other SCCs 0.03/0.20 9. SCC is completely evaluated into other SCCs 0.03/0.20 10. SCC is completely evaluated into other SCCs 0.03/0.20 11. SCC is completely evaluated into other SCCs 0.03/0.20 12. SCC is partially evaluated into eval_start_start/4 0.03/0.20 0.03/0.20 Control-Flow Refinement of Cost Relations 0.03/0.20 ===================================== 0.03/0.20 0.03/0.20 ### Specialization of cost equations eval_start_bb1_in/5 0.03/0.20 * CE 6 is refined into CE [9] 0.03/0.20 * CE 5 is refined into CE [10] 0.03/0.20 * CE 4 is refined into CE [11] 0.03/0.20 * CE 3 is refined into CE [12] 0.03/0.20 0.03/0.20 0.03/0.20 ### Cost equations --> "Loop" of eval_start_bb1_in/5 0.03/0.20 * CEs [11] --> Loop 9 0.03/0.20 * CEs [12] --> Loop 10 0.03/0.20 * CEs [9] --> Loop 11 0.03/0.20 * CEs [10] --> Loop 12 0.03/0.20 0.03/0.20 ### Ranking functions of CR eval_start_bb1_in(V__0,V_flag_0,B,C,D) 0.03/0.20 * RF of phase [9]: [V__0] 0.03/0.20 0.03/0.20 #### Partial ranking functions of CR eval_start_bb1_in(V__0,V_flag_0,B,C,D) 0.03/0.20 * Partial RF of phase [9]: 0.03/0.20 - RF of loop [9:1]: 0.03/0.20 V__0 0.03/0.20 0.03/0.20 0.03/0.20 ### Specialization of cost equations eval_start_bb1_in_loop_cont/5 0.03/0.20 * CE 8 is refined into CE [13] 0.03/0.20 * CE 7 is refined into CE [14] 0.03/0.20 0.03/0.20 0.03/0.20 ### Cost equations --> "Loop" of eval_start_bb1_in_loop_cont/5 0.03/0.20 * CEs [13] --> Loop 13 0.03/0.20 * CEs [14] --> Loop 14 0.03/0.20 0.03/0.20 ### Ranking functions of CR eval_start_bb1_in_loop_cont(A,B,C,D,E) 0.03/0.20 0.03/0.20 #### Partial ranking functions of CR eval_start_bb1_in_loop_cont(A,B,C,D,E) 0.03/0.20 0.03/0.20 0.03/0.20 ### Specialization of cost equations eval_start_5/4 0.03/0.20 * CE 2 is refined into CE [15,16,17,18,19] 0.03/0.20 0.03/0.20 0.03/0.20 ### Cost equations --> "Loop" of eval_start_5/4 0.03/0.20 * CEs [15,18] --> Loop 15 0.03/0.20 * CEs [16,17] --> Loop 16 0.03/0.20 * CEs [19] --> Loop 17 0.03/0.20 0.03/0.20 ### Ranking functions of CR eval_start_5(V__0,V_flag_0,V_n,B) 0.03/0.20 0.03/0.20 #### Partial ranking functions of CR eval_start_5(V__0,V_flag_0,V_n,B) 0.03/0.20 0.03/0.20 0.03/0.20 ### Specialization of cost equations eval_start_start/4 0.03/0.20 * CE 1 is refined into CE [20,21,22] 0.03/0.20 0.03/0.20 0.03/0.20 ### Cost equations --> "Loop" of eval_start_start/4 0.03/0.20 * CEs [22] --> Loop 18 0.03/0.20 * CEs [21] --> Loop 19 0.03/0.20 * CEs [20] --> Loop 20 0.03/0.20 0.03/0.20 ### Ranking functions of CR eval_start_start(V__0,V_flag_0,V_n,B) 0.03/0.20 0.03/0.20 #### Partial ranking functions of CR eval_start_start(V__0,V_flag_0,V_n,B) 0.03/0.20 0.03/0.20 0.03/0.20 Computing Bounds 0.03/0.20 ===================================== 0.03/0.20 0.03/0.20 #### Cost of chains of eval_start_bb1_in(V__0,V_flag_0,B,C,D): 0.03/0.20 * Chain [[9],11]: 1*it(9)+0 0.03/0.20 Such that:it(9) =< V__0 0.03/0.20 0.03/0.20 with precondition: [V_flag_0=1,B=3,V__0>=1] 0.03/0.20 0.03/0.20 * Chain [[9],10,12]: 1*it(9)+1 0.03/0.20 Such that:it(9) =< V__0 0.03/0.20 0.03/0.20 with precondition: [V_flag_0=1,B=2,C=0,D=0,V__0>=1] 0.03/0.20 0.03/0.20 * Chain [[9],10,11]: 1*it(9)+1 0.03/0.20 Such that:it(9) =< V__0 0.03/0.20 0.03/0.20 with precondition: [V_flag_0=1,B=3,V__0>=1] 0.03/0.20 0.03/0.20 * Chain [11]: 0 0.03/0.20 with precondition: [B=3,1>=V_flag_0,V_flag_0>=0] 0.03/0.20 0.03/0.20 * Chain [10,12]: 1 0.03/0.20 with precondition: [V_flag_0=1,B=2,D=0,V__0=C,0>=V__0] 0.03/0.20 0.03/0.20 * Chain [10,11]: 1 0.03/0.20 with precondition: [V_flag_0=1,B=3,0>=V__0] 0.03/0.20 0.03/0.20 0.03/0.20 #### Cost of chains of eval_start_bb1_in_loop_cont(A,B,C,D,E): 0.03/0.20 * Chain [14]: 0 0.03/0.20 with precondition: [A=2] 0.03/0.20 0.03/0.20 * Chain [13]: 0 0.03/0.20 with precondition: [A=3] 0.03/0.20 0.03/0.20 0.03/0.20 #### Cost of chains of eval_start_5(V__0,V_flag_0,V_n,B): 0.03/0.20 * Chain [17]: 0 0.03/0.20 with precondition: [] 0.03/0.20 0.03/0.20 * Chain [16]: 1 0.03/0.20 with precondition: [0>=V_n] 0.03/0.20 0.03/0.20 * Chain [15]: 3*s(3)+1 0.03/0.20 Such that:aux(2) =< V_n 0.03/0.20 s(3) =< aux(2) 0.03/0.20 0.03/0.20 with precondition: [V_n>=1] 0.03/0.20 0.03/0.20 0.03/0.20 #### Cost of chains of eval_start_start(V__0,V_flag_0,V_n,B): 0.03/0.20 * Chain [20]: 0 0.03/0.20 with precondition: [] 0.03/0.20 0.03/0.20 * Chain [19]: 1 0.03/0.20 with precondition: [0>=V_n] 0.03/0.20 0.03/0.20 * Chain [18]: 3*s(7)+1 0.03/0.20 Such that:s(6) =< V_n 0.03/0.20 s(7) =< s(6) 0.03/0.20 0.03/0.20 with precondition: [V_n>=1] 0.03/0.20 0.03/0.20 0.03/0.20 Closed-form bounds of eval_start_start(V__0,V_flag_0,V_n,B): 0.03/0.20 ------------------------------------- 0.03/0.20 * Chain [20] with precondition: [] 0.03/0.20 - Upper bound: 0 0.03/0.20 - Complexity: constant 0.03/0.20 * Chain [19] with precondition: [0>=V_n] 0.03/0.20 - Upper bound: 1 0.03/0.20 - Complexity: constant 0.03/0.20 * Chain [18] with precondition: [V_n>=1] 0.03/0.20 - Upper bound: 3*V_n+1 0.03/0.20 - Complexity: n 0.03/0.20 0.03/0.20 ### Maximum cost of eval_start_start(V__0,V_flag_0,V_n,B): max([1,nat(V_n)*3+1]) 0.03/0.20 Asymptotic class: n 0.03/0.20 * Total analysis performed in 121 ms. 0.03/0.20 0.03/0.30 EOF