0.04/0.21 WORST_CASE(?,O(n^1)) 0.04/0.21 0.04/0.21 Preprocessing Cost Relations 0.04/0.21 ===================================== 0.04/0.21 0.04/0.21 #### Computed strongly connected components 0.04/0.21 0. recursive : [eval_start_5/7,eval_start_6/7,eval_start_bb1_in/7,eval_start_bb2_in/7] 0.04/0.21 1. non_recursive : [eval_start_stop/6] 0.04/0.21 2. non_recursive : [eval_start_bb3_in/6] 0.04/0.21 3. non_recursive : [exit_location/1] 0.04/0.21 4. non_recursive : [eval_start_bb1_in_loop_cont/7] 0.04/0.21 5. non_recursive : [eval_start_4/6] 0.04/0.21 6. non_recursive : [eval_start_3/6] 0.04/0.21 7. non_recursive : [eval_start_2/6] 0.04/0.21 8. non_recursive : [eval_start_1/6] 0.04/0.21 9. non_recursive : [eval_start_0/6] 0.04/0.21 10. non_recursive : [eval_start_bb0_in/6] 0.04/0.21 11. non_recursive : [eval_start_start/6] 0.04/0.21 0.04/0.21 #### Obtained direct recursion through partial evaluation 0.04/0.21 0. SCC is partially evaluated into eval_start_bb1_in/7 0.04/0.21 1. SCC is completely evaluated into other SCCs 0.04/0.21 2. SCC is completely evaluated into other SCCs 0.04/0.21 3. SCC is completely evaluated into other SCCs 0.04/0.21 4. SCC is partially evaluated into eval_start_bb1_in_loop_cont/7 0.04/0.21 5. SCC is partially evaluated into eval_start_4/6 0.04/0.21 6. SCC is completely evaluated into other SCCs 0.04/0.21 7. SCC is completely evaluated into other SCCs 0.04/0.21 8. SCC is completely evaluated into other SCCs 0.04/0.21 9. SCC is completely evaluated into other SCCs 0.04/0.21 10. SCC is completely evaluated into other SCCs 0.04/0.21 11. SCC is partially evaluated into eval_start_start/6 0.04/0.21 0.04/0.21 Control-Flow Refinement of Cost Relations 0.04/0.21 ===================================== 0.04/0.21 0.04/0.21 ### Specialization of cost equations eval_start_bb1_in/7 0.04/0.21 * CE 6 is refined into CE [9] 0.04/0.21 * CE 5 is refined into CE [10] 0.04/0.21 * CE 3 is refined into CE [11] 0.04/0.21 * CE 4 is refined into CE [12] 0.04/0.21 0.04/0.21 0.04/0.21 ### Cost equations --> "Loop" of eval_start_bb1_in/7 0.04/0.21 * CEs [11] --> Loop 9 0.04/0.21 * CEs [12] --> Loop 10 0.04/0.21 * CEs [9] --> Loop 11 0.04/0.21 * CEs [10] --> Loop 12 0.04/0.21 0.04/0.21 ### Ranking functions of CR eval_start_bb1_in(V__0,V__01,V_1,B,C,D,E) 0.04/0.21 * RF of phase [9,10]: [V__0-V__01] 0.04/0.21 0.04/0.21 #### Partial ranking functions of CR eval_start_bb1_in(V__0,V__01,V_1,B,C,D,E) 0.04/0.21 * Partial RF of phase [9,10]: 0.04/0.21 - RF of loop [9:1,10:1]: 0.04/0.21 V__0-V__01 0.04/0.21 0.04/0.21 0.04/0.21 ### Specialization of cost equations eval_start_bb1_in_loop_cont/7 0.04/0.21 * CE 8 is refined into CE [13] 0.04/0.21 * CE 7 is refined into CE [14] 0.04/0.21 0.04/0.21 0.04/0.21 ### Cost equations --> "Loop" of eval_start_bb1_in_loop_cont/7 0.04/0.21 * CEs [13] --> Loop 13 0.04/0.21 * CEs [14] --> Loop 14 0.04/0.21 0.04/0.21 ### Ranking functions of CR eval_start_bb1_in_loop_cont(A,B,C,D,E,F,G) 0.04/0.21 0.04/0.21 #### Partial ranking functions of CR eval_start_bb1_in_loop_cont(A,B,C,D,E,F,G) 0.04/0.21 0.04/0.21 0.04/0.21 ### Specialization of cost equations eval_start_4/6 0.04/0.21 * CE 2 is refined into CE [15,16,17,18] 0.04/0.21 0.04/0.21 0.04/0.21 ### Cost equations --> "Loop" of eval_start_4/6 0.04/0.21 * CEs [16,18] --> Loop 15 0.04/0.21 * CEs [15] --> Loop 16 0.04/0.21 * CEs [17] --> Loop 17 0.04/0.21 0.04/0.21 ### Ranking functions of CR eval_start_4(V__0,V__01,V_1,V_x,V_y,B) 0.04/0.21 0.04/0.21 #### Partial ranking functions of CR eval_start_4(V__0,V__01,V_1,V_x,V_y,B) 0.04/0.21 0.04/0.21 0.04/0.21 ### Specialization of cost equations eval_start_start/6 0.04/0.21 * CE 1 is refined into CE [19,20,21] 0.04/0.21 0.04/0.21 0.04/0.21 ### Cost equations --> "Loop" of eval_start_start/6 0.04/0.21 * CEs [21] --> Loop 18 0.04/0.21 * CEs [20] --> Loop 19 0.04/0.21 * CEs [19] --> Loop 20 0.04/0.21 0.04/0.21 ### Ranking functions of CR eval_start_start(V__0,V__01,V_1,V_x,V_y,B) 0.04/0.21 0.04/0.21 #### Partial ranking functions of CR eval_start_start(V__0,V__01,V_1,V_x,V_y,B) 0.04/0.21 0.04/0.21 0.04/0.21 Computing Bounds 0.04/0.21 ===================================== 0.04/0.21 0.04/0.21 #### Cost of chains of eval_start_bb1_in(V__0,V__01,V_1,B,C,D,E): 0.04/0.21 * Chain [[9,10],12]: 2*it(9)+0 0.04/0.21 Such that:aux(3) =< V__0-V__01 0.04/0.21 it(9) =< aux(3) 0.04/0.21 0.04/0.21 with precondition: [B=2,C=D,V__0>=V__01+1,C>=V__01,V__0>=C] 0.04/0.21 0.04/0.21 * Chain [[9,10],11]: 2*it(9)+0 0.04/0.21 Such that:aux(4) =< V__0-V__01 0.04/0.21 it(9) =< aux(4) 0.04/0.21 0.04/0.21 with precondition: [B=3,V__0>=V__01+1] 0.04/0.21 0.04/0.21 * Chain [12]: 0 0.04/0.21 with precondition: [B=2,E=V_1,V__0=C,V__01=D,V__01>=V__0] 0.04/0.21 0.04/0.21 * Chain [11]: 0 0.04/0.21 with precondition: [B=3] 0.04/0.21 0.04/0.21 0.04/0.21 #### Cost of chains of eval_start_bb1_in_loop_cont(A,B,C,D,E,F,G): 0.04/0.21 * Chain [14]: 0 0.04/0.21 with precondition: [A=2] 0.04/0.21 0.04/0.21 * Chain [13]: 0 0.04/0.21 with precondition: [A=3] 0.04/0.21 0.04/0.21 0.04/0.21 #### Cost of chains of eval_start_4(V__0,V__01,V_1,V_x,V_y,B): 0.04/0.21 * Chain [17]: 0 0.04/0.21 with precondition: [] 0.04/0.21 0.04/0.21 * Chain [16]: 0 0.04/0.21 with precondition: [V_y>=V_x] 0.04/0.21 0.04/0.21 * Chain [15]: 4*s(2)+0 0.04/0.21 Such that:aux(5) =< V_x-V_y 0.04/0.21 s(2) =< aux(5) 0.04/0.21 0.04/0.21 with precondition: [V_x>=V_y+1] 0.04/0.21 0.04/0.21 0.04/0.21 #### Cost of chains of eval_start_start(V__0,V__01,V_1,V_x,V_y,B): 0.04/0.21 * Chain [20]: 0 0.04/0.21 with precondition: [] 0.04/0.21 0.04/0.21 * Chain [19]: 0 0.04/0.21 with precondition: [V_y>=V_x] 0.04/0.21 0.04/0.21 * Chain [18]: 4*s(6)+0 0.04/0.21 Such that:s(5) =< V_x-V_y 0.04/0.21 s(6) =< s(5) 0.04/0.21 0.04/0.21 with precondition: [V_x>=V_y+1] 0.04/0.21 0.04/0.21 0.04/0.21 Closed-form bounds of eval_start_start(V__0,V__01,V_1,V_x,V_y,B): 0.04/0.21 ------------------------------------- 0.04/0.21 * Chain [20] with precondition: [] 0.04/0.21 - Upper bound: 0 0.04/0.21 - Complexity: constant 0.04/0.21 * Chain [19] with precondition: [V_y>=V_x] 0.04/0.21 - Upper bound: 0 0.04/0.21 - Complexity: constant 0.04/0.21 * Chain [18] with precondition: [V_x>=V_y+1] 0.04/0.21 - Upper bound: 4*V_x-4*V_y 0.04/0.21 - Complexity: n 0.04/0.21 0.04/0.21 ### Maximum cost of eval_start_start(V__0,V__01,V_1,V_x,V_y,B): nat(V_x-V_y)*4 0.04/0.21 Asymptotic class: n 0.04/0.21 * Total analysis performed in 137 ms. 0.04/0.21 0.04/0.31 EOF