0.05/0.17 WORST_CASE(?,O(n^1)) 0.05/0.17 0.05/0.17 Preprocessing Cost Relations 0.05/0.17 ===================================== 0.05/0.17 0.05/0.17 #### Computed strongly connected components 0.05/0.17 0. recursive : [eval_wise__critedge_in/3,eval_wise_bb1_in/3] 0.05/0.17 1. non_recursive : [eval_wise_stop/1] 0.05/0.17 2. non_recursive : [eval_wise_bb2_in/1] 0.05/0.17 3. non_recursive : [eval_wise_bb1_in_loop_cont/2] 0.05/0.17 4. non_recursive : [eval_wise_bb0_in/3] 0.05/0.17 5. non_recursive : [eval_wise_start/3] 0.05/0.17 0.05/0.17 #### Obtained direct recursion through partial evaluation 0.05/0.17 0. SCC is partially evaluated into eval_wise_bb1_in/3 0.05/0.17 1. SCC is completely evaluated into other SCCs 0.05/0.17 2. SCC is completely evaluated into other SCCs 0.05/0.17 3. SCC is completely evaluated into other SCCs 0.05/0.17 4. SCC is partially evaluated into eval_wise_bb0_in/3 0.05/0.17 5. SCC is partially evaluated into eval_wise_start/3 0.05/0.17 0.05/0.17 Control-Flow Refinement of Cost Relations 0.05/0.17 ===================================== 0.05/0.17 0.05/0.17 ### Specialization of cost equations eval_wise_bb1_in/3 0.05/0.17 * CE 7 is refined into CE [8] 0.05/0.17 * CE 6 is refined into CE [9] 0.05/0.17 * CE 5 is refined into CE [10] 0.05/0.17 0.05/0.17 0.05/0.17 ### Cost equations --> "Loop" of eval_wise_bb1_in/3 0.05/0.17 * CEs [9] --> Loop 8 0.05/0.17 * CEs [10] --> Loop 9 0.05/0.17 * CEs [8] --> Loop 10 0.05/0.17 0.05/0.17 ### Ranking functions of CR eval_wise_bb1_in(V__01,V__0,B) 0.05/0.17 * RF of phase [8]: [V__01-V__0-2] 0.05/0.17 * RF of phase [9]: [-V__01+V__0-2] 0.05/0.17 0.05/0.17 #### Partial ranking functions of CR eval_wise_bb1_in(V__01,V__0,B) 0.05/0.17 * Partial RF of phase [8]: 0.05/0.17 - RF of loop [8:1]: 0.05/0.17 V__01-V__0-2 0.05/0.17 * Partial RF of phase [9]: 0.05/0.17 - RF of loop [9:1]: 0.05/0.17 -V__01+V__0-2 0.05/0.17 0.05/0.17 0.05/0.17 ### Specialization of cost equations eval_wise_bb0_in/3 0.05/0.17 * CE 4 is refined into CE [11,12,13] 0.05/0.17 * CE 3 is refined into CE [14] 0.05/0.17 * CE 2 is refined into CE [15] 0.05/0.17 0.05/0.17 0.05/0.17 ### Cost equations --> "Loop" of eval_wise_bb0_in/3 0.05/0.17 * CEs [12] --> Loop 11 0.05/0.17 * CEs [13] --> Loop 12 0.05/0.17 * CEs [11] --> Loop 13 0.05/0.17 * CEs [14] --> Loop 14 0.05/0.17 * CEs [15] --> Loop 15 0.05/0.17 0.05/0.17 ### Ranking functions of CR eval_wise_bb0_in(V_x,V_y,B) 0.05/0.17 0.05/0.17 #### Partial ranking functions of CR eval_wise_bb0_in(V_x,V_y,B) 0.05/0.17 0.05/0.17 0.05/0.17 ### Specialization of cost equations eval_wise_start/3 0.05/0.17 * CE 1 is refined into CE [16,17,18,19,20] 0.05/0.17 0.05/0.17 0.05/0.17 ### Cost equations --> "Loop" of eval_wise_start/3 0.05/0.17 * CEs [20] --> Loop 16 0.05/0.17 * CEs [19] --> Loop 17 0.05/0.17 * CEs [18] --> Loop 18 0.05/0.17 * CEs [17] --> Loop 19 0.05/0.17 * CEs [16] --> Loop 20 0.05/0.17 0.05/0.17 ### Ranking functions of CR eval_wise_start(V_x,V_y,B) 0.05/0.17 0.05/0.17 #### Partial ranking functions of CR eval_wise_start(V_x,V_y,B) 0.05/0.17 0.05/0.17 0.05/0.17 Computing Bounds 0.05/0.17 ===================================== 0.05/0.17 0.05/0.17 #### Cost of chains of eval_wise_bb1_in(V__01,V__0,B): 0.05/0.17 * Chain [[9],10]: 1*it(9)+0 0.05/0.17 Such that:it(9) =< -V__01+V__0 0.05/0.17 0.05/0.17 with precondition: [B=2,V__01>=0,V__0>=V__01+3] 0.05/0.17 0.05/0.17 * Chain [[8],10]: 1*it(8)+0 0.05/0.17 Such that:it(8) =< V__01-V__0 0.05/0.17 0.05/0.17 with precondition: [B=2,V__0>=0,V__01>=V__0+3] 0.05/0.17 0.05/0.17 * Chain [10]: 0 0.05/0.17 with precondition: [B=2,V__01>=0,V__0>=0,V__0+2>=V__01,V__01+2>=V__0] 0.05/0.17 0.05/0.17 0.05/0.17 #### Cost of chains of eval_wise_bb0_in(V_x,V_y,B): 0.05/0.17 * Chain [15]: 0 0.05/0.17 with precondition: [0>=V_x+1] 0.05/0.17 0.05/0.17 * Chain [14]: 0 0.05/0.17 with precondition: [0>=V_y+1] 0.05/0.17 0.05/0.17 * Chain [13]: 0 0.05/0.17 with precondition: [V_x>=0,V_y>=0,V_y+2>=V_x,V_x+2>=V_y] 0.05/0.17 0.05/0.17 * Chain [12]: 1*s(1)+0 0.05/0.17 Such that:s(1) =< -V_x+V_y 0.05/0.17 0.05/0.17 with precondition: [V_x>=0,V_y>=V_x+3] 0.05/0.17 0.05/0.17 * Chain [11]: 1*s(2)+0 0.05/0.17 Such that:s(2) =< V_x-V_y 0.05/0.17 0.05/0.17 with precondition: [V_y>=0,V_x>=V_y+3] 0.05/0.17 0.05/0.17 0.05/0.17 #### Cost of chains of eval_wise_start(V_x,V_y,B): 0.05/0.17 * Chain [20]: 0 0.05/0.17 with precondition: [0>=V_x+1] 0.05/0.17 0.05/0.17 * Chain [19]: 0 0.05/0.17 with precondition: [0>=V_y+1] 0.05/0.17 0.05/0.17 * Chain [18]: 0 0.05/0.17 with precondition: [V_x>=0,V_y>=0,V_y+2>=V_x,V_x+2>=V_y] 0.05/0.17 0.05/0.17 * Chain [17]: 1*s(3)+0 0.05/0.17 Such that:s(3) =< -V_x+V_y 0.05/0.17 0.05/0.17 with precondition: [V_x>=0,V_y>=V_x+3] 0.05/0.17 0.05/0.17 * Chain [16]: 1*s(4)+0 0.05/0.17 Such that:s(4) =< V_x-V_y 0.05/0.17 0.05/0.17 with precondition: [V_y>=0,V_x>=V_y+3] 0.05/0.17 0.05/0.17 0.05/0.17 Closed-form bounds of eval_wise_start(V_x,V_y,B): 0.05/0.17 ------------------------------------- 0.05/0.17 * Chain [20] with precondition: [0>=V_x+1] 0.05/0.17 - Upper bound: 0 0.05/0.17 - Complexity: constant 0.05/0.17 * Chain [19] with precondition: [0>=V_y+1] 0.05/0.17 - Upper bound: 0 0.05/0.17 - Complexity: constant 0.05/0.17 * Chain [18] with precondition: [V_x>=0,V_y>=0,V_y+2>=V_x,V_x+2>=V_y] 0.05/0.17 - Upper bound: 0 0.05/0.17 - Complexity: constant 0.05/0.17 * Chain [17] with precondition: [V_x>=0,V_y>=V_x+3] 0.05/0.17 - Upper bound: -V_x+V_y 0.05/0.17 - Complexity: n 0.05/0.17 * Chain [16] with precondition: [V_y>=0,V_x>=V_y+3] 0.05/0.17 - Upper bound: V_x-V_y 0.05/0.17 - Complexity: n 0.05/0.17 0.05/0.17 ### Maximum cost of eval_wise_start(V_x,V_y,B): max([nat(-V_x+V_y),nat(V_x-V_y)]) 0.05/0.17 Asymptotic class: n 0.05/0.17 * Total analysis performed in 95 ms. 0.05/0.17 0.05/0.27 EOF