0.04/0.32 WORST_CASE(?,O(n^1)) 0.04/0.32 0.04/0.32 Preprocessing Cost Relations 0.04/0.32 ===================================== 0.04/0.32 0.04/0.32 #### Computed strongly connected components 0.04/0.32 0. recursive : [eval_start_bb2_in/9,eval_start_bb3_in/9] 0.04/0.32 1. recursive : [eval_start_bb1_in/9,eval_start_bb2_in_loop_cont/10] 0.04/0.32 2. non_recursive : [eval_start_stop/6] 0.04/0.32 3. non_recursive : [eval_start_bb4_in/6] 0.04/0.32 4. non_recursive : [exit_location/1] 0.04/0.32 5. non_recursive : [eval_start_bb1_in_loop_cont/7] 0.04/0.32 6. non_recursive : [eval_start_5/6] 0.04/0.32 7. non_recursive : [eval_start_4/6] 0.04/0.32 8. non_recursive : [eval_start_3/6] 0.04/0.32 9. non_recursive : [eval_start_2/6] 0.04/0.32 10. non_recursive : [eval_start_1/6] 0.04/0.32 11. non_recursive : [eval_start_0/6] 0.04/0.32 12. non_recursive : [eval_start_bb0_in/6] 0.04/0.32 13. non_recursive : [eval_start_start/6] 0.04/0.32 0.04/0.32 #### Obtained direct recursion through partial evaluation 0.04/0.32 0. SCC is partially evaluated into eval_start_bb2_in/9 0.04/0.32 1. SCC is partially evaluated into eval_start_bb1_in/9 0.04/0.32 2. SCC is completely evaluated into other SCCs 0.04/0.32 3. SCC is completely evaluated into other SCCs 0.04/0.32 4. SCC is completely evaluated into other SCCs 0.04/0.32 5. SCC is partially evaluated into eval_start_bb1_in_loop_cont/7 0.04/0.32 6. SCC is partially evaluated into eval_start_5/6 0.04/0.32 7. SCC is completely evaluated into other SCCs 0.04/0.32 8. SCC is completely evaluated into other SCCs 0.04/0.32 9. SCC is completely evaluated into other SCCs 0.04/0.32 10. SCC is completely evaluated into other SCCs 0.04/0.32 11. SCC is completely evaluated into other SCCs 0.04/0.32 12. SCC is completely evaluated into other SCCs 0.04/0.32 13. SCC is partially evaluated into eval_start_start/6 0.04/0.32 0.04/0.32 Control-Flow Refinement of Cost Relations 0.04/0.32 ===================================== 0.04/0.32 0.04/0.32 ### Specialization of cost equations eval_start_bb2_in/9 0.04/0.32 * CE 11 is refined into CE [12] 0.04/0.32 * CE 10 is refined into CE [13] 0.04/0.32 * CE 9 is refined into CE [14] 0.04/0.32 0.04/0.32 0.04/0.32 ### Cost equations --> "Loop" of eval_start_bb2_in/9 0.04/0.32 * CEs [14] --> Loop 12 0.04/0.32 * CEs [12] --> Loop 13 0.04/0.32 * CEs [13] --> Loop 14 0.04/0.32 0.04/0.32 ### Ranking functions of CR eval_start_bb2_in(V__0,V__1,V_flag_0,V_flag_1,B,C,D,E,F) 0.04/0.32 * RF of phase [12]: [V__1] 0.04/0.32 0.04/0.32 #### Partial ranking functions of CR eval_start_bb2_in(V__0,V__1,V_flag_0,V_flag_1,B,C,D,E,F) 0.04/0.32 * Partial RF of phase [12]: 0.04/0.32 - RF of loop [12:1]: 0.04/0.32 V__1 0.04/0.32 0.04/0.32 0.04/0.32 ### Specialization of cost equations eval_start_bb1_in/9 0.04/0.32 * CE 5 is refined into CE [15] 0.04/0.32 * CE 3 is refined into CE [16,17] 0.04/0.32 * CE 6 is refined into CE [18] 0.04/0.32 * CE 4 is refined into CE [19,20] 0.04/0.32 0.04/0.32 0.04/0.32 ### Cost equations --> "Loop" of eval_start_bb1_in/9 0.04/0.32 * CEs [20] --> Loop 15 0.04/0.32 * CEs [19] --> Loop 16 0.04/0.32 * CEs [15] --> Loop 17 0.04/0.32 * CEs [17] --> Loop 18 0.04/0.32 * CEs [16] --> Loop 19 0.04/0.32 * CEs [18] --> Loop 20 0.04/0.32 0.04/0.32 ### Ranking functions of CR eval_start_bb1_in(V__0,V__1,V_flag_0,V_flag_1,B,C,D,E,F) 0.04/0.32 0.04/0.32 #### Partial ranking functions of CR eval_start_bb1_in(V__0,V__1,V_flag_0,V_flag_1,B,C,D,E,F) 0.04/0.32 0.04/0.32 0.04/0.32 ### Specialization of cost equations eval_start_bb1_in_loop_cont/7 0.04/0.32 * CE 7 is refined into CE [21] 0.04/0.32 * CE 8 is refined into CE [22] 0.04/0.32 0.04/0.32 0.04/0.32 ### Cost equations --> "Loop" of eval_start_bb1_in_loop_cont/7 0.04/0.32 * CEs [21] --> Loop 21 0.04/0.32 * CEs [22] --> Loop 22 0.04/0.32 0.04/0.32 ### Ranking functions of CR eval_start_bb1_in_loop_cont(A,B,C,D,E,F,G) 0.04/0.32 0.04/0.32 #### Partial ranking functions of CR eval_start_bb1_in_loop_cont(A,B,C,D,E,F,G) 0.04/0.32 0.04/0.32 0.04/0.32 ### Specialization of cost equations eval_start_5/6 0.04/0.32 * CE 2 is refined into CE [23,24,25,26,27,28] 0.04/0.32 0.04/0.32 0.04/0.32 ### Cost equations --> "Loop" of eval_start_5/6 0.04/0.32 * CEs [25,26] --> Loop 23 0.04/0.32 * CEs [24,27] --> Loop 24 0.04/0.32 * CEs [23,28] --> Loop 25 0.04/0.32 0.04/0.32 ### Ranking functions of CR eval_start_5(V__0,V__1,V_flag_0,V_flag_1,V_n,B) 0.04/0.32 0.04/0.32 #### Partial ranking functions of CR eval_start_5(V__0,V__1,V_flag_0,V_flag_1,V_n,B) 0.04/0.32 0.04/0.32 0.04/0.32 ### Specialization of cost equations eval_start_start/6 0.04/0.32 * CE 1 is refined into CE [29,30,31] 0.04/0.32 0.04/0.32 0.04/0.32 ### Cost equations --> "Loop" of eval_start_start/6 0.04/0.32 * CEs [31] --> Loop 26 0.04/0.32 * CEs [30] --> Loop 27 0.04/0.32 * CEs [29] --> Loop 28 0.04/0.32 0.04/0.32 ### Ranking functions of CR eval_start_start(V__0,V__1,V_flag_0,V_flag_1,V_n,B) 0.04/0.32 0.04/0.32 #### Partial ranking functions of CR eval_start_start(V__0,V__1,V_flag_0,V_flag_1,V_n,B) 0.04/0.32 0.04/0.32 0.04/0.32 Computing Bounds 0.04/0.32 ===================================== 0.04/0.32 0.04/0.32 #### Cost of chains of eval_start_bb2_in(V__0,V__1,V_flag_0,V_flag_1,B,C,D,E,F): 0.04/0.32 * Chain [[12],14]: 1*it(12)+0 0.04/0.32 Such that:it(12) =< V__1 0.04/0.32 0.04/0.32 with precondition: [B=2,C=0,D=0,E=1,F=1,1>=V_flag_1,V__1>=1,V_flag_0>=1] 0.04/0.32 0.04/0.32 * Chain [[12],13]: 1*it(12)+0 0.04/0.32 Such that:it(12) =< V__1 0.04/0.32 0.04/0.32 with precondition: [B=3,1>=V_flag_1,V__1>=1,V_flag_0>=1] 0.04/0.32 0.04/0.32 * Chain [14]: 0 0.04/0.32 with precondition: [B=2,V__1=C,V__1=D,V_flag_1=E,V_flag_1=F,0>=V__1,1>=V_flag_1,V_flag_0>=1] 0.04/0.32 0.04/0.32 * Chain [13]: 0 0.04/0.32 with precondition: [B=3,1>=V_flag_1,V_flag_0>=1] 0.04/0.32 0.04/0.32 0.04/0.32 #### Cost of chains of eval_start_bb1_in(V__0,V__1,V_flag_0,V_flag_1,B,C,D,E,F): 0.04/0.32 * Chain [20]: 0 0.04/0.32 with precondition: [B=3,1>=V_flag_0,V_flag_0>=0] 0.04/0.32 0.04/0.32 * Chain [19]: 1*s(1)+0 0.04/0.32 Such that:s(1) =< V__0 0.04/0.32 0.04/0.32 with precondition: [V_flag_0=1,B=3,V__0>=1] 0.04/0.32 0.04/0.32 * Chain [18]: 0 0.04/0.32 with precondition: [V_flag_0=1,B=3] 0.04/0.32 0.04/0.32 * Chain [16,20]: 1*s(2)+1 0.04/0.32 Such that:s(2) =< V__0 0.04/0.32 0.04/0.32 with precondition: [V_flag_0=1,B=3,V__0>=1] 0.04/0.32 0.04/0.32 * Chain [16,18]: 1*s(2)+1 0.04/0.32 Such that:s(2) =< V__0 0.04/0.32 0.04/0.32 with precondition: [V_flag_0=1,B=3,V__0>=1] 0.04/0.32 0.04/0.32 * Chain [16,15,20]: 1*s(2)+2 0.04/0.32 Such that:s(2) =< V__0 0.04/0.32 0.04/0.32 with precondition: [V_flag_0=1,B=3,V__0>=1] 0.04/0.32 0.04/0.32 * Chain [16,15,17]: 1*s(2)+2 0.04/0.32 Such that:s(2) =< V__0 0.04/0.32 0.04/0.32 with precondition: [V_flag_0=1,B=4,C=0,D=0,E=0,F=0,V__0>=1] 0.04/0.32 0.04/0.32 * Chain [15,20]: 1 0.04/0.32 with precondition: [V_flag_0=1,B=3,0>=V__0] 0.04/0.32 0.04/0.32 * Chain [15,17]: 1 0.04/0.32 with precondition: [V_flag_0=1,B=4,E=0,F=0,V__0=C,V__0=D,0>=V__0] 0.04/0.32 0.04/0.32 0.04/0.32 #### Cost of chains of eval_start_bb1_in_loop_cont(A,B,C,D,E,F,G): 0.04/0.32 * Chain [22]: 0 0.04/0.32 with precondition: [A=3] 0.04/0.32 0.04/0.32 * Chain [21]: 0 0.04/0.32 with precondition: [A=4] 0.04/0.32 0.04/0.32 0.04/0.32 #### Cost of chains of eval_start_5(V__0,V__1,V_flag_0,V_flag_1,V_n,B): 0.04/0.32 * Chain [25]: 0 0.04/0.32 with precondition: [] 0.04/0.32 0.04/0.32 * Chain [24]: 1 0.04/0.32 with precondition: [0>=V_n] 0.04/0.32 0.04/0.32 * Chain [23]: 5*s(8)+2 0.04/0.32 Such that:aux(2) =< V_n 0.04/0.32 s(8) =< aux(2) 0.04/0.32 0.04/0.32 with precondition: [V_n>=1] 0.04/0.32 0.04/0.32 0.04/0.32 #### Cost of chains of eval_start_start(V__0,V__1,V_flag_0,V_flag_1,V_n,B): 0.04/0.32 * Chain [28]: 0 0.04/0.32 with precondition: [] 0.04/0.32 0.04/0.32 * Chain [27]: 1 0.04/0.32 with precondition: [0>=V_n] 0.04/0.32 0.04/0.32 * Chain [26]: 5*s(11)+2 0.04/0.32 Such that:s(10) =< V_n 0.04/0.32 s(11) =< s(10) 0.04/0.32 0.04/0.32 with precondition: [V_n>=1] 0.04/0.32 0.04/0.32 0.04/0.32 Closed-form bounds of eval_start_start(V__0,V__1,V_flag_0,V_flag_1,V_n,B): 0.04/0.32 ------------------------------------- 0.04/0.32 * Chain [28] with precondition: [] 0.04/0.32 - Upper bound: 0 0.04/0.32 - Complexity: constant 0.04/0.32 * Chain [27] with precondition: [0>=V_n] 0.04/0.32 - Upper bound: 1 0.04/0.32 - Complexity: constant 0.04/0.32 * Chain [26] with precondition: [V_n>=1] 0.04/0.32 - Upper bound: 5*V_n+2 0.04/0.32 - Complexity: n 0.04/0.32 0.04/0.32 ### Maximum cost of eval_start_start(V__0,V__1,V_flag_0,V_flag_1,V_n,B): max([1,nat(V_n)*5+2]) 0.04/0.32 Asymptotic class: n 0.04/0.32 * Total analysis performed in 247 ms. 0.04/0.32 0.04/0.42 EOF