0.04/0.27 WORST_CASE(?,O(n^1)) 0.04/0.27 0.04/0.27 Preprocessing Cost Relations 0.04/0.27 ===================================== 0.04/0.27 0.04/0.27 #### Computed strongly connected components 0.04/0.27 0. recursive : [eval_start_bb1_in/7,eval_start_bb2_in/7] 0.04/0.27 1. non_recursive : [eval_start_stop/7] 0.04/0.27 2. non_recursive : [eval_start_bb3_in/7] 0.04/0.27 3. non_recursive : [exit_location/1] 0.04/0.27 4. non_recursive : [eval_start_bb1_in_loop_cont/8] 0.04/0.27 5. non_recursive : [eval_start_6/7] 0.04/0.27 6. non_recursive : [eval_start_5/7] 0.04/0.27 7. non_recursive : [eval_start_4/7] 0.04/0.27 8. non_recursive : [eval_start_3/7] 0.04/0.27 9. non_recursive : [eval_start_2/7] 0.04/0.27 10. non_recursive : [eval_start_1/7] 0.04/0.27 11. non_recursive : [eval_start_0/7] 0.04/0.27 12. non_recursive : [eval_start_bb0_in/7] 0.04/0.27 13. non_recursive : [eval_start_start/7] 0.04/0.27 0.04/0.27 #### Obtained direct recursion through partial evaluation 0.04/0.27 0. SCC is partially evaluated into eval_start_bb1_in/7 0.04/0.27 1. SCC is completely evaluated into other SCCs 0.04/0.27 2. SCC is completely evaluated into other SCCs 0.04/0.27 3. SCC is completely evaluated into other SCCs 0.04/0.27 4. SCC is partially evaluated into eval_start_bb1_in_loop_cont/8 0.04/0.27 5. SCC is partially evaluated into eval_start_6/7 0.04/0.27 6. SCC is completely evaluated into other SCCs 0.04/0.27 7. SCC is completely evaluated into other SCCs 0.04/0.27 8. SCC is completely evaluated into other SCCs 0.04/0.27 9. SCC is completely evaluated into other SCCs 0.04/0.27 10. SCC is completely evaluated into other SCCs 0.04/0.27 11. SCC is completely evaluated into other SCCs 0.04/0.27 12. SCC is completely evaluated into other SCCs 0.04/0.27 13. SCC is partially evaluated into eval_start_start/7 0.04/0.27 0.04/0.27 Control-Flow Refinement of Cost Relations 0.04/0.27 ===================================== 0.04/0.27 0.04/0.27 ### Specialization of cost equations eval_start_bb1_in/7 0.04/0.27 * CE 6 is refined into CE [9] 0.04/0.27 * CE 5 is refined into CE [10] 0.04/0.27 * CE 4 is refined into CE [11] 0.04/0.27 * CE 3 is refined into CE [12] 0.04/0.27 0.04/0.27 0.04/0.27 ### Cost equations --> "Loop" of eval_start_bb1_in/7 0.04/0.27 * CEs [11] --> Loop 9 0.04/0.27 * CEs [12] --> Loop 10 0.04/0.27 * CEs [9] --> Loop 11 0.04/0.27 * CEs [10] --> Loop 12 0.04/0.27 0.04/0.27 ### Ranking functions of CR eval_start_bb1_in(V__0,V__01,V_m,V_n,B,C,D) 0.04/0.27 * RF of phase [9]: [-V__01+V_m] 0.04/0.27 * RF of phase [10]: [-V__0+V_n] 0.04/0.27 0.04/0.27 #### Partial ranking functions of CR eval_start_bb1_in(V__0,V__01,V_m,V_n,B,C,D) 0.04/0.27 * Partial RF of phase [9]: 0.04/0.27 - RF of loop [9:1]: 0.04/0.27 -V__01+V_m 0.04/0.27 * Partial RF of phase [10]: 0.04/0.27 - RF of loop [10:1]: 0.04/0.27 -V__0+V_n 0.04/0.27 0.04/0.27 0.04/0.27 ### Specialization of cost equations eval_start_bb1_in_loop_cont/8 0.04/0.27 * CE 8 is refined into CE [13] 0.04/0.27 * CE 7 is refined into CE [14] 0.04/0.27 0.04/0.27 0.04/0.27 ### Cost equations --> "Loop" of eval_start_bb1_in_loop_cont/8 0.04/0.27 * CEs [13] --> Loop 13 0.04/0.27 * CEs [14] --> Loop 14 0.04/0.27 0.04/0.27 ### Ranking functions of CR eval_start_bb1_in_loop_cont(A,B,C,D,E,F,G,H) 0.04/0.27 0.04/0.27 #### Partial ranking functions of CR eval_start_bb1_in_loop_cont(A,B,C,D,E,F,G,H) 0.04/0.27 0.04/0.27 0.04/0.27 ### Specialization of cost equations eval_start_6/7 0.04/0.27 * CE 2 is refined into CE [15,16,17,18,19,20] 0.04/0.27 0.04/0.27 0.04/0.27 ### Cost equations --> "Loop" of eval_start_6/7 0.04/0.27 * CEs [17,19] --> Loop 15 0.04/0.27 * CEs [15] --> Loop 16 0.04/0.27 * CEs [16,20] --> Loop 17 0.04/0.27 * CEs [18] --> Loop 18 0.04/0.27 0.04/0.27 ### Ranking functions of CR eval_start_6(V__0,V__01,V_m,V_n,V_x,V_y,B) 0.04/0.27 0.04/0.27 #### Partial ranking functions of CR eval_start_6(V__0,V__01,V_m,V_n,V_x,V_y,B) 0.04/0.27 0.04/0.27 0.04/0.27 ### Specialization of cost equations eval_start_start/7 0.04/0.27 * CE 1 is refined into CE [21,22,23,24] 0.04/0.27 0.04/0.27 0.04/0.27 ### Cost equations --> "Loop" of eval_start_start/7 0.04/0.27 * CEs [24] --> Loop 19 0.04/0.27 * CEs [23] --> Loop 20 0.04/0.27 * CEs [22] --> Loop 21 0.04/0.27 * CEs [21] --> Loop 22 0.04/0.27 0.04/0.27 ### Ranking functions of CR eval_start_start(V__0,V__01,V_m,V_n,V_x,V_y,B) 0.04/0.27 0.04/0.27 #### Partial ranking functions of CR eval_start_start(V__0,V__01,V_m,V_n,V_x,V_y,B) 0.04/0.27 0.04/0.27 0.04/0.27 Computing Bounds 0.04/0.27 ===================================== 0.04/0.27 0.04/0.27 #### Cost of chains of eval_start_bb1_in(V__0,V__01,V_m,V_n,B,C,D): 0.04/0.27 * Chain [[10],12]: 1*it(10)+0 0.04/0.27 Such that:it(10) =< -V__0+V_n 0.04/0.27 0.04/0.27 with precondition: [B=2,V_n=C,V__01=D,V_n>=V__0+1,V__01>=V_m] 0.04/0.27 0.04/0.27 * Chain [[10],11]: 1*it(10)+0 0.04/0.27 Such that:it(10) =< -V__0+V_n 0.04/0.27 0.04/0.27 with precondition: [B=3,V_n>=V__0+1,V__01>=V_m] 0.04/0.27 0.04/0.27 * Chain [[9],[10],12]: 1*it(9)+1*it(10)+0 0.04/0.27 Such that:it(10) =< -V__0+V_n 0.04/0.27 it(9) =< -V__01+V_m 0.04/0.27 0.04/0.27 with precondition: [B=2,V_n=C,V_m=D,V_n>=V__0+1,V_m>=V__01+1] 0.04/0.27 0.04/0.27 * Chain [[9],[10],11]: 1*it(9)+1*it(10)+0 0.04/0.27 Such that:it(10) =< -V__0+V_n 0.04/0.27 it(9) =< -V__01+V_m 0.04/0.27 0.04/0.27 with precondition: [B=3,V_n>=V__0+1,V_m>=V__01+1] 0.04/0.27 0.04/0.27 * Chain [[9],11]: 1*it(9)+0 0.04/0.27 Such that:it(9) =< -V__01+V_m 0.04/0.27 0.04/0.27 with precondition: [B=3,V_n>=V__0+1,V_m>=V__01+1] 0.04/0.27 0.04/0.27 * Chain [12]: 0 0.04/0.27 with precondition: [B=2,D=V__01,V__0=C,V__0>=V_n] 0.04/0.27 0.04/0.27 * Chain [11]: 0 0.04/0.27 with precondition: [B=3] 0.04/0.27 0.04/0.27 0.04/0.27 #### Cost of chains of eval_start_bb1_in_loop_cont(A,B,C,D,E,F,G,H): 0.04/0.27 * Chain [14]: 0 0.04/0.27 with precondition: [A=2] 0.04/0.27 0.04/0.27 * Chain [13]: 0 0.04/0.27 with precondition: [A=3] 0.04/0.27 0.04/0.27 0.04/0.27 #### Cost of chains of eval_start_6(V__0,V__01,V_m,V_n,V_x,V_y,B): 0.04/0.27 * Chain [18]: 0 0.04/0.27 with precondition: [] 0.04/0.27 0.04/0.27 * Chain [17]: 2*s(4)+0 0.04/0.27 Such that:aux(2) =< V_n-V_x 0.04/0.27 s(4) =< aux(2) 0.04/0.27 0.04/0.27 with precondition: [V_y>=V_m,V_n>=V_x+1] 0.04/0.27 0.04/0.27 * Chain [16]: 0 0.04/0.27 with precondition: [V_x>=V_n] 0.04/0.27 0.04/0.27 * Chain [15]: 2*s(6)+3*s(7)+0 0.04/0.27 Such that:aux(3) =< V_m-V_y 0.04/0.27 aux(4) =< V_n-V_x 0.04/0.27 s(7) =< aux(3) 0.04/0.27 s(6) =< aux(4) 0.04/0.27 0.04/0.27 with precondition: [V_n>=V_x+1,V_m>=V_y+1] 0.04/0.27 0.04/0.27 0.04/0.27 #### Cost of chains of eval_start_start(V__0,V__01,V_m,V_n,V_x,V_y,B): 0.04/0.27 * Chain [22]: 0 0.04/0.27 with precondition: [] 0.04/0.27 0.04/0.27 * Chain [21]: 2*s(12)+0 0.04/0.27 Such that:s(11) =< V_n-V_x 0.04/0.27 s(12) =< s(11) 0.04/0.27 0.04/0.27 with precondition: [V_y>=V_m,V_n>=V_x+1] 0.04/0.27 0.04/0.27 * Chain [20]: 0 0.04/0.27 with precondition: [V_x>=V_n] 0.04/0.27 0.04/0.27 * Chain [19]: 3*s(15)+2*s(16)+0 0.04/0.27 Such that:s(13) =< V_m-V_y 0.04/0.27 s(14) =< V_n-V_x 0.04/0.27 s(15) =< s(13) 0.04/0.27 s(16) =< s(14) 0.04/0.27 0.04/0.27 with precondition: [V_n>=V_x+1,V_m>=V_y+1] 0.04/0.27 0.04/0.27 0.04/0.27 Closed-form bounds of eval_start_start(V__0,V__01,V_m,V_n,V_x,V_y,B): 0.04/0.27 ------------------------------------- 0.04/0.27 * Chain [22] with precondition: [] 0.04/0.27 - Upper bound: 0 0.04/0.27 - Complexity: constant 0.04/0.27 * Chain [21] with precondition: [V_y>=V_m,V_n>=V_x+1] 0.04/0.27 - Upper bound: 2*V_n-2*V_x 0.04/0.27 - Complexity: n 0.04/0.27 * Chain [20] with precondition: [V_x>=V_n] 0.04/0.27 - Upper bound: 0 0.04/0.27 - Complexity: constant 0.04/0.27 * Chain [19] with precondition: [V_n>=V_x+1,V_m>=V_y+1] 0.04/0.27 - Upper bound: 3*V_m+2*V_n-2*V_x-3*V_y 0.04/0.27 - Complexity: n 0.04/0.27 0.04/0.27 ### Maximum cost of eval_start_start(V__0,V__01,V_m,V_n,V_x,V_y,B): nat(V_n-V_x)*2+nat(V_m-V_y)*3 0.04/0.27 Asymptotic class: n 0.04/0.27 * Total analysis performed in 198 ms. 0.04/0.27 0.04/0.37 EOF