0.03/0.27 WORST_CASE(?,O(n^1)) 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_start_bb1_in/6,eval_start_bb2_in/6,eval_start_bb3_in/6] 0.03/0.27 1. non_recursive : [eval_start_stop/5] 0.03/0.27 2. non_recursive : [eval_start_bb4_in/5] 0.03/0.27 3. non_recursive : [exit_location/1] 0.03/0.27 4. non_recursive : [eval_start_bb1_in_loop_cont/6] 0.03/0.27 5. non_recursive : [eval_start_9/5] 0.03/0.27 6. non_recursive : [eval_start_8/5] 0.03/0.27 7. non_recursive : [eval_start_bb5_in/5] 0.03/0.27 8. non_recursive : [eval_start_4/5] 0.03/0.27 9. non_recursive : [eval_start_3/5] 0.03/0.27 10. non_recursive : [eval_start_2/5] 0.03/0.27 11. non_recursive : [eval_start_1/5] 0.03/0.27 12. non_recursive : [eval_start_0/5] 0.03/0.27 13. non_recursive : [eval_start_bb0_in/5] 0.03/0.27 14. non_recursive : [eval_start_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_start_bb1_in/6 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_start_bb1_in_loop_cont/6 0.03/0.27 5. SCC is completely evaluated into other SCCs 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 partially evaluated into eval_start_4/5 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_start_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_start_bb1_in/6 0.03/0.27 * CE 7 is refined into CE [10] 0.03/0.27 * CE 6 is refined into CE [11] 0.03/0.27 * CE 5 is refined into CE [12] 0.03/0.27 * CE 4 is refined into CE [13] 0.03/0.27 0.03/0.27 0.03/0.27 ### Cost equations --> "Loop" of eval_start_bb1_in/6 0.03/0.27 * CEs [12] --> Loop 10 0.03/0.27 * CEs [13] --> Loop 11 0.03/0.27 * CEs [10] --> Loop 12 0.03/0.27 * CEs [11] --> Loop 13 0.03/0.27 0.03/0.27 ### Ranking functions of CR eval_start_bb1_in(V_m,V_va_0,V_vb_0,B,C,D) 0.03/0.27 * RF of phase [10,11]: [2*V_va_0+V_vb_0-1] 0.03/0.27 0.03/0.27 #### Partial ranking functions of CR eval_start_bb1_in(V_m,V_va_0,V_vb_0,B,C,D) 0.03/0.27 * Partial RF of phase [10,11]: 0.03/0.27 - RF of loop [10:1]: 0.03/0.27 V_m-V_vb_0 depends on loops [11:1] 0.03/0.27 V_va_0 0.03/0.27 - RF of loop [11:1]: 0.03/0.27 -V_m+V_vb_0+1 depends on loops [10:1] 0.03/0.27 V_vb_0 depends on loops [10:1] 0.03/0.27 0.03/0.27 0.03/0.27 ### Specialization of cost equations eval_start_bb1_in_loop_cont/6 0.03/0.27 * CE 9 is refined into CE [14] 0.03/0.27 * CE 8 is refined into CE [15] 0.03/0.27 0.03/0.27 0.03/0.27 ### Cost equations --> "Loop" of eval_start_bb1_in_loop_cont/6 0.03/0.27 * CEs [14] --> Loop 14 0.03/0.27 * CEs [15] --> Loop 15 0.03/0.27 0.03/0.27 ### Ranking functions of CR eval_start_bb1_in_loop_cont(A,B,C,D,E,F) 0.03/0.27 0.03/0.27 #### Partial ranking functions of CR eval_start_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_start_4/5 0.03/0.27 * CE 3 is refined into CE [16,17,18,19] 0.03/0.27 * CE 2 is refined into CE [20] 0.03/0.27 0.03/0.27 0.03/0.27 ### Cost equations --> "Loop" of eval_start_4/5 0.03/0.27 * CEs [16,18] --> Loop 16 0.03/0.27 * CEs [19] --> Loop 17 0.03/0.27 * CEs [17] --> Loop 18 0.03/0.27 * CEs [20] --> Loop 19 0.03/0.27 0.03/0.27 ### Ranking functions of CR eval_start_4(V_m,V_n,V_va_0,V_vb_0,B) 0.03/0.27 0.03/0.27 #### Partial ranking functions of CR eval_start_4(V_m,V_n,V_va_0,V_vb_0,B) 0.03/0.27 0.03/0.27 0.03/0.27 ### Specialization of cost equations eval_start_start/5 0.03/0.27 * CE 1 is refined into CE [21,22,23,24] 0.03/0.27 0.03/0.27 0.03/0.27 ### Cost equations --> "Loop" of eval_start_start/5 0.03/0.27 * CEs [24] --> Loop 20 0.03/0.27 * CEs [23] --> Loop 21 0.03/0.27 * CEs [22] --> Loop 22 0.03/0.27 * CEs [21] --> Loop 23 0.03/0.27 0.03/0.27 ### Ranking functions of CR eval_start_start(V_m,V_n,V_va_0,V_vb_0,B) 0.03/0.27 0.03/0.27 #### Partial ranking functions of CR eval_start_start(V_m,V_n,V_va_0,V_vb_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_start_bb1_in(V_m,V_va_0,V_vb_0,B,C,D): 0.03/0.27 * Chain [[10,11],13]: 1*it(10)+1*it(11)+0 0.03/0.27 Such that:it(10) =< V_va_0 0.03/0.27 aux(16) =< 2*V_va_0+V_vb_0 0.03/0.27 aux(17) =< 2*V_va_0+V_vb_0-D 0.03/0.27 it(10) =< aux(16) 0.03/0.27 it(11) =< aux(16) 0.03/0.27 it(10) =< aux(17) 0.03/0.27 it(11) =< aux(17) 0.03/0.27 0.03/0.27 with precondition: [B=2,C=0,V_m>=1,V_va_0>=1,V_vb_0>=0,V_m>=D,V_va_0+V_vb_0>=D] 0.03/0.27 0.03/0.27 * Chain [[10,11],12]: 1*it(10)+1*it(11)+0 0.03/0.27 Such that:it(10) =< V_va_0 0.03/0.27 aux(20) =< 2*V_va_0+V_vb_0 0.03/0.27 it(10) =< aux(20) 0.03/0.27 it(11) =< aux(20) 0.03/0.27 0.03/0.27 with precondition: [B=3,V_m>=1,V_va_0>=1,V_vb_0>=0] 0.03/0.27 0.03/0.27 * Chain [13]: 0 0.03/0.27 with precondition: [B=2,V_va_0=C,V_vb_0=D,0>=V_va_0,V_m>=1,V_vb_0>=0] 0.03/0.27 0.03/0.27 * Chain [12]: 0 0.03/0.27 with precondition: [B=3,V_m>=1,V_vb_0>=0] 0.03/0.27 0.03/0.27 0.03/0.27 #### Cost of chains of eval_start_bb1_in_loop_cont(A,B,C,D,E,F): 0.03/0.27 * Chain [15]: 0 0.03/0.27 with precondition: [A=2,B>=1] 0.03/0.27 0.03/0.27 * Chain [14]: 0 0.03/0.27 with precondition: [A=3,B>=1] 0.03/0.27 0.03/0.27 0.03/0.27 #### Cost of chains of eval_start_4(V_m,V_n,V_va_0,V_vb_0,B): 0.03/0.27 * Chain [19]: 0 0.03/0.27 with precondition: [0>=V_m] 0.03/0.27 0.03/0.27 * Chain [18]: 0 0.03/0.27 with precondition: [0>=V_n,V_m>=1] 0.03/0.27 0.03/0.27 * Chain [17]: 0 0.03/0.27 with precondition: [V_m>=1] 0.03/0.27 0.03/0.27 * Chain [16]: 2*s(1)+2*s(4)+0 0.03/0.27 Such that:aux(21) =< V_n 0.03/0.27 aux(22) =< 2*V_n 0.03/0.27 s(1) =< aux(21) 0.03/0.27 s(1) =< aux(22) 0.03/0.27 s(4) =< aux(22) 0.03/0.27 0.03/0.27 with precondition: [V_m>=1,V_n>=1] 0.03/0.27 0.03/0.27 0.03/0.27 #### Cost of chains of eval_start_start(V_m,V_n,V_va_0,V_vb_0,B): 0.03/0.27 * Chain [23]: 0 0.03/0.27 with precondition: [0>=V_m] 0.03/0.27 0.03/0.27 * Chain [22]: 0 0.03/0.27 with precondition: [0>=V_n,V_m>=1] 0.03/0.27 0.03/0.27 * Chain [21]: 0 0.03/0.27 with precondition: [V_m>=1] 0.03/0.27 0.03/0.27 * Chain [20]: 2*s(10)+2*s(11)+0 0.03/0.27 Such that:s(8) =< V_n 0.03/0.27 s(9) =< 2*V_n 0.03/0.27 s(10) =< s(8) 0.03/0.27 s(10) =< s(9) 0.03/0.27 s(11) =< s(9) 0.03/0.27 0.03/0.27 with precondition: [V_m>=1,V_n>=1] 0.03/0.27 0.03/0.27 0.03/0.27 Closed-form bounds of eval_start_start(V_m,V_n,V_va_0,V_vb_0,B): 0.03/0.27 ------------------------------------- 0.03/0.27 * Chain [23] with precondition: [0>=V_m] 0.03/0.27 - Upper bound: 0 0.03/0.27 - Complexity: constant 0.03/0.27 * Chain [22] with precondition: [0>=V_n,V_m>=1] 0.03/0.27 - Upper bound: 0 0.03/0.27 - Complexity: constant 0.03/0.27 * Chain [21] with precondition: [V_m>=1] 0.03/0.27 - Upper bound: 0 0.03/0.27 - Complexity: constant 0.03/0.27 * Chain [20] with precondition: [V_m>=1,V_n>=1] 0.03/0.27 - Upper bound: 6*V_n 0.03/0.27 - Complexity: n 0.03/0.27 0.03/0.27 ### Maximum cost of eval_start_start(V_m,V_n,V_va_0,V_vb_0,B): nat(2*V_n)*2+nat(V_n)*2 0.03/0.27 Asymptotic class: n 0.03/0.27 * Total analysis performed in 199 ms. 0.03/0.27 0.03/0.38 EOF