0.03/0.24 WORST_CASE(?,O(n^1)) 0.03/0.24 0.03/0.24 Preprocessing Cost Relations 0.03/0.24 ===================================== 0.03/0.24 0.03/0.24 #### Computed strongly connected components 0.03/0.24 0. recursive : [eval_wise__critedge_in/5,eval_wise_bb1_in/5] 0.03/0.24 1. non_recursive : [eval_wise_stop/5] 0.03/0.24 2. non_recursive : [eval_wise_bb2_in/5] 0.03/0.24 3. non_recursive : [exit_location/1] 0.03/0.24 4. non_recursive : [eval_wise_bb1_in_loop_cont/6] 0.03/0.24 5. non_recursive : [eval_wise_2/5] 0.03/0.24 6. non_recursive : [eval_wise_1/5] 0.03/0.24 7. non_recursive : [eval_wise_0/5] 0.03/0.24 8. non_recursive : [eval_wise_bb0_in/5] 0.03/0.24 9. non_recursive : [eval_wise_start/5] 0.03/0.24 0.03/0.24 #### Obtained direct recursion through partial evaluation 0.03/0.24 0. SCC is partially evaluated into eval_wise_bb1_in/5 0.03/0.24 1. SCC is completely evaluated into other SCCs 0.03/0.24 2. SCC is completely evaluated into other SCCs 0.03/0.24 3. SCC is completely evaluated into other SCCs 0.03/0.24 4. SCC is partially evaluated into eval_wise_bb1_in_loop_cont/6 0.03/0.24 5. SCC is partially evaluated into eval_wise_2/5 0.03/0.24 6. SCC is completely evaluated into other SCCs 0.03/0.24 7. SCC is completely evaluated into other SCCs 0.03/0.24 8. SCC is completely evaluated into other SCCs 0.03/0.24 9. SCC is partially evaluated into eval_wise_start/5 0.03/0.24 0.03/0.24 Control-Flow Refinement of Cost Relations 0.03/0.24 ===================================== 0.03/0.24 0.03/0.24 ### Specialization of cost equations eval_wise_bb1_in/5 0.03/0.24 * CE 8 is refined into CE [11] 0.03/0.24 * CE 7 is refined into CE [12] 0.03/0.24 * CE 5 is refined into CE [13] 0.03/0.24 * CE 6 is refined into CE [14] 0.03/0.24 0.03/0.24 0.03/0.24 ### Cost equations --> "Loop" of eval_wise_bb1_in/5 0.03/0.24 * CEs [13] --> Loop 11 0.03/0.24 * CEs [14] --> Loop 12 0.03/0.24 * CEs [11] --> Loop 13 0.03/0.24 * CEs [12] --> Loop 14 0.03/0.24 0.03/0.24 ### Ranking functions of CR eval_wise_bb1_in(V__0,V__01,B,C,D) 0.03/0.24 * RF of phase [11]: [V__0-V__01-2] 0.03/0.24 * RF of phase [12]: [-V__0+V__01-2] 0.03/0.24 0.03/0.24 #### Partial ranking functions of CR eval_wise_bb1_in(V__0,V__01,B,C,D) 0.03/0.24 * Partial RF of phase [11]: 0.03/0.24 - RF of loop [11:1]: 0.03/0.24 V__0-V__01-2 0.03/0.24 * Partial RF of phase [12]: 0.03/0.24 - RF of loop [12:1]: 0.03/0.24 -V__0+V__01-2 0.03/0.24 0.03/0.24 0.03/0.24 ### Specialization of cost equations eval_wise_bb1_in_loop_cont/6 0.03/0.24 * CE 10 is refined into CE [15] 0.03/0.24 * CE 9 is refined into CE [16] 0.03/0.24 0.03/0.24 0.03/0.24 ### Cost equations --> "Loop" of eval_wise_bb1_in_loop_cont/6 0.03/0.24 * CEs [15] --> Loop 15 0.03/0.24 * CEs [16] --> Loop 16 0.03/0.24 0.03/0.24 ### Ranking functions of CR eval_wise_bb1_in_loop_cont(A,B,C,D,E,F) 0.03/0.24 0.03/0.24 #### Partial ranking functions of CR eval_wise_bb1_in_loop_cont(A,B,C,D,E,F) 0.03/0.24 0.03/0.24 0.03/0.24 ### Specialization of cost equations eval_wise_2/5 0.03/0.24 * CE 4 is refined into CE [17,18,19,20,21,22] 0.03/0.24 * CE 3 is refined into CE [23] 0.03/0.24 * CE 2 is refined into CE [24] 0.03/0.24 0.03/0.24 0.03/0.24 ### Cost equations --> "Loop" of eval_wise_2/5 0.03/0.24 * CEs [17,22] --> Loop 17 0.03/0.24 * CEs [19,21] --> Loop 18 0.03/0.24 * CEs [18] --> Loop 19 0.03/0.24 * CEs [20] --> Loop 20 0.03/0.24 * CEs [23] --> Loop 21 0.03/0.24 * CEs [24] --> Loop 22 0.03/0.24 0.03/0.24 ### Ranking functions of CR eval_wise_2(V__0,V__01,V_x,V_y,B) 0.03/0.24 0.03/0.24 #### Partial ranking functions of CR eval_wise_2(V__0,V__01,V_x,V_y,B) 0.03/0.24 0.03/0.24 0.03/0.24 ### Specialization of cost equations eval_wise_start/5 0.03/0.24 * CE 1 is refined into CE [25,26,27,28,29,30] 0.03/0.24 0.03/0.24 0.03/0.24 ### Cost equations --> "Loop" of eval_wise_start/5 0.03/0.24 * CEs [30] --> Loop 23 0.03/0.24 * CEs [29] --> Loop 24 0.03/0.24 * CEs [28] --> Loop 25 0.03/0.24 * CEs [27] --> Loop 26 0.03/0.24 * CEs [26] --> Loop 27 0.03/0.24 * CEs [25] --> Loop 28 0.03/0.24 0.03/0.24 ### Ranking functions of CR eval_wise_start(V__0,V__01,V_x,V_y,B) 0.03/0.24 0.03/0.24 #### Partial ranking functions of CR eval_wise_start(V__0,V__01,V_x,V_y,B) 0.03/0.24 0.03/0.24 0.03/0.24 Computing Bounds 0.03/0.24 ===================================== 0.03/0.24 0.03/0.24 #### Cost of chains of eval_wise_bb1_in(V__0,V__01,B,C,D): 0.03/0.24 * Chain [[12],14]: 1*it(12)+0 0.03/0.24 Such that:it(12) =< -V__0+D 0.03/0.24 0.03/0.24 with precondition: [B=2,V__01=C+2,V__01=D,V__0>=0,V__01>=V__0+3] 0.03/0.24 0.03/0.24 * Chain [[12],13]: 1*it(12)+0 0.03/0.24 Such that:it(12) =< -V__0+V__01 0.03/0.24 0.03/0.24 with precondition: [B=3,V__0>=0,V__01>=V__0+3] 0.03/0.24 0.03/0.24 * Chain [[11],14]: 1*it(11)+0 0.03/0.24 Such that:it(11) =< -V__01+D 0.03/0.24 0.03/0.24 with precondition: [B=2,V__0=C,V__0=D+2,V__01>=0,V__0>=V__01+3] 0.03/0.24 0.03/0.24 * Chain [[11],13]: 1*it(11)+0 0.03/0.24 Such that:it(11) =< V__0-V__01 0.03/0.24 0.03/0.24 with precondition: [B=3,V__01>=0,V__0>=V__01+3] 0.03/0.24 0.03/0.24 * Chain [14]: 0 0.03/0.24 with precondition: [B=2,V__0=C,V__01=D,V__0>=0,V__01>=0,V__01+2>=V__0,V__0+2>=V__01] 0.03/0.24 0.03/0.24 * Chain [13]: 0 0.03/0.25 with precondition: [B=3,V__0>=0,V__01>=0] 0.03/0.25 0.03/0.25 0.03/0.25 #### Cost of chains of eval_wise_bb1_in_loop_cont(A,B,C,D,E,F): 0.03/0.25 * Chain [16]: 0 0.03/0.25 with precondition: [A=2,D>=0,E>=0] 0.03/0.25 0.03/0.25 * Chain [15]: 0 0.03/0.25 with precondition: [A=3,D>=0,E>=0] 0.03/0.25 0.03/0.25 0.03/0.25 #### Cost of chains of eval_wise_2(V__0,V__01,V_x,V_y,B): 0.03/0.25 * Chain [22]: 0 0.03/0.25 with precondition: [0>=V_x+1] 0.03/0.25 0.03/0.25 * Chain [21]: 0 0.03/0.25 with precondition: [0>=V_y+1] 0.03/0.25 0.03/0.25 * Chain [20]: 0 0.03/0.25 with precondition: [V_x>=0,V_y>=0] 0.03/0.25 0.03/0.25 * Chain [19]: 0 0.03/0.25 with precondition: [V_x>=0,V_y>=0,V_y+2>=V_x,V_x+2>=V_y] 0.03/0.25 0.03/0.25 * Chain [18]: 2*s(1)+0 0.03/0.25 Such that:aux(1) =< -V_x+V_y 0.03/0.25 s(1) =< aux(1) 0.03/0.25 0.03/0.25 with precondition: [V_x>=0,V_y>=V_x+3] 0.03/0.25 0.03/0.25 * Chain [17]: 2*s(3)+0 0.03/0.25 Such that:aux(2) =< V_x-V_y 0.03/0.25 s(3) =< aux(2) 0.03/0.25 0.03/0.25 with precondition: [V_y>=0,V_x>=V_y+3] 0.03/0.25 0.03/0.25 0.03/0.25 #### Cost of chains of eval_wise_start(V__0,V__01,V_x,V_y,B): 0.03/0.25 * Chain [28]: 0 0.03/0.25 with precondition: [0>=V_x+1] 0.03/0.25 0.03/0.25 * Chain [27]: 0 0.03/0.25 with precondition: [0>=V_y+1] 0.03/0.25 0.03/0.25 * Chain [26]: 0 0.03/0.25 with precondition: [V_x>=0,V_y>=0] 0.03/0.25 0.03/0.25 * Chain [25]: 0 0.03/0.25 with precondition: [V_x>=0,V_y>=0,V_y+2>=V_x,V_x+2>=V_y] 0.03/0.25 0.03/0.25 * Chain [24]: 2*s(6)+0 0.03/0.25 Such that:s(5) =< -V_x+V_y 0.03/0.25 s(6) =< s(5) 0.03/0.25 0.03/0.25 with precondition: [V_x>=0,V_y>=V_x+3] 0.03/0.25 0.03/0.25 * Chain [23]: 2*s(8)+0 0.03/0.25 Such that:s(7) =< V_x-V_y 0.03/0.25 s(8) =< s(7) 0.03/0.25 0.03/0.25 with precondition: [V_y>=0,V_x>=V_y+3] 0.03/0.25 0.03/0.25 0.03/0.25 Closed-form bounds of eval_wise_start(V__0,V__01,V_x,V_y,B): 0.03/0.25 ------------------------------------- 0.03/0.25 * Chain [28] with precondition: [0>=V_x+1] 0.03/0.25 - Upper bound: 0 0.03/0.25 - Complexity: constant 0.03/0.25 * Chain [27] with precondition: [0>=V_y+1] 0.03/0.25 - Upper bound: 0 0.03/0.25 - Complexity: constant 0.03/0.25 * Chain [26] with precondition: [V_x>=0,V_y>=0] 0.03/0.25 - Upper bound: 0 0.03/0.25 - Complexity: constant 0.03/0.25 * Chain [25] with precondition: [V_x>=0,V_y>=0,V_y+2>=V_x,V_x+2>=V_y] 0.03/0.25 - Upper bound: 0 0.03/0.25 - Complexity: constant 0.03/0.25 * Chain [24] with precondition: [V_x>=0,V_y>=V_x+3] 0.03/0.25 - Upper bound: -2*V_x+2*V_y 0.03/0.25 - Complexity: n 0.03/0.25 * Chain [23] with precondition: [V_y>=0,V_x>=V_y+3] 0.03/0.25 - Upper bound: 2*V_x-2*V_y 0.03/0.25 - Complexity: n 0.03/0.25 0.03/0.25 ### Maximum cost of eval_wise_start(V__0,V__01,V_x,V_y,B): max([nat(-V_x+V_y)*2,nat(V_x-V_y)*2]) 0.03/0.25 Asymptotic class: n 0.03/0.25 * Total analysis performed in 179 ms. 0.03/0.25 0.03/0.35 EOF