0.04/0.24 WORST_CASE(?,O(n^1)) 0.04/0.24 0.04/0.24 Preprocessing Cost Relations 0.04/0.24 ===================================== 0.04/0.24 0.04/0.24 #### Computed strongly connected components 0.04/0.24 0. recursive : [eval_start_bb1_in/5,eval_start_bb2_in/5] 0.04/0.24 1. recursive : [eval_start_bb3_in/4,eval_start_bb4_in/4] 0.04/0.24 2. non_recursive : [eval_start_stop/5] 0.04/0.24 3. non_recursive : [eval_start_bb5_in/5] 0.04/0.24 4. non_recursive : [exit_location/1] 0.04/0.24 5. non_recursive : [eval_start_bb3_in_loop_cont/6] 0.04/0.24 6. non_recursive : [eval_start_bb1_in_loop_cont/6] 0.04/0.24 7. non_recursive : [eval_start_3/5] 0.04/0.24 8. non_recursive : [eval_start_2/5] 0.04/0.24 9. non_recursive : [eval_start_1/5] 0.04/0.24 10. non_recursive : [eval_start_0/5] 0.04/0.24 11. non_recursive : [eval_start_bb0_in/5] 0.04/0.24 12. non_recursive : [eval_start_start/5] 0.04/0.24 0.04/0.24 #### Obtained direct recursion through partial evaluation 0.04/0.24 0. SCC is partially evaluated into eval_start_bb1_in/5 0.04/0.24 1. SCC is partially evaluated into eval_start_bb3_in/4 0.04/0.24 2. SCC is completely evaluated into other SCCs 0.04/0.24 3. SCC is completely evaluated into other SCCs 0.04/0.24 4. SCC is completely evaluated into other SCCs 0.04/0.24 5. SCC is partially evaluated into eval_start_bb3_in_loop_cont/6 0.04/0.24 6. SCC is partially evaluated into eval_start_bb1_in_loop_cont/6 0.04/0.24 7. SCC is partially evaluated into eval_start_3/5 0.04/0.24 8. SCC is completely evaluated into other SCCs 0.04/0.24 9. SCC is completely evaluated into other SCCs 0.04/0.24 10. SCC is completely evaluated into other SCCs 0.04/0.24 11. SCC is completely evaluated into other SCCs 0.04/0.24 12. SCC is partially evaluated into eval_start_start/5 0.04/0.24 0.04/0.24 Control-Flow Refinement of Cost Relations 0.04/0.24 ===================================== 0.04/0.24 0.04/0.24 ### Specialization of cost equations eval_start_bb1_in/5 0.04/0.24 * CE 4 is refined into CE [13] 0.04/0.24 * CE 5 is refined into CE [14] 0.04/0.24 * CE 3 is refined into CE [15] 0.04/0.24 0.04/0.24 0.04/0.24 ### Cost equations --> "Loop" of eval_start_bb1_in/5 0.04/0.24 * CEs [15] --> Loop 13 0.04/0.24 * CEs [13] --> Loop 14 0.04/0.24 * CEs [14] --> Loop 15 0.04/0.24 0.04/0.24 ### Ranking functions of CR eval_start_bb1_in(V__0,V__01,V_y,B,C) 0.04/0.24 * RF of phase [13]: [-V__0+V_y] 0.04/0.24 0.04/0.24 #### Partial ranking functions of CR eval_start_bb1_in(V__0,V__01,V_y,B,C) 0.04/0.24 * Partial RF of phase [13]: 0.04/0.24 - RF of loop [13:1]: 0.04/0.24 -V__0+V_y 0.04/0.24 0.04/0.24 0.04/0.24 ### Specialization of cost equations eval_start_bb3_in/4 0.04/0.24 * CE 10 is refined into CE [16] 0.04/0.24 * CE 9 is refined into CE [17] 0.04/0.24 * CE 8 is refined into CE [18] 0.04/0.24 0.04/0.24 0.04/0.24 ### Cost equations --> "Loop" of eval_start_bb3_in/4 0.04/0.24 * CEs [18] --> Loop 16 0.04/0.24 * CEs [16] --> Loop 17 0.04/0.24 * CEs [17] --> Loop 18 0.04/0.24 0.04/0.24 ### Ranking functions of CR eval_start_bb3_in(V__0,V__01,B,C) 0.04/0.24 * RF of phase [16]: [V__0-V__01] 0.04/0.24 0.04/0.24 #### Partial ranking functions of CR eval_start_bb3_in(V__0,V__01,B,C) 0.04/0.24 * Partial RF of phase [16]: 0.04/0.24 - RF of loop [16:1]: 0.04/0.24 V__0-V__01 0.04/0.24 0.04/0.24 0.04/0.24 ### Specialization of cost equations eval_start_bb3_in_loop_cont/6 0.04/0.24 * CE 12 is refined into CE [19] 0.04/0.24 * CE 11 is refined into CE [20] 0.04/0.24 0.04/0.24 0.04/0.24 ### Cost equations --> "Loop" of eval_start_bb3_in_loop_cont/6 0.04/0.24 * CEs [19] --> Loop 19 0.04/0.24 * CEs [20] --> Loop 20 0.04/0.24 0.04/0.24 ### Ranking functions of CR eval_start_bb3_in_loop_cont(A,B,C,D,E,F) 0.04/0.24 0.04/0.24 #### Partial ranking functions of CR eval_start_bb3_in_loop_cont(A,B,C,D,E,F) 0.04/0.24 0.04/0.24 0.04/0.24 ### Specialization of cost equations eval_start_bb1_in_loop_cont/6 0.04/0.24 * CE 7 is refined into CE [21,22,23,24] 0.04/0.24 * CE 6 is refined into CE [25] 0.04/0.24 0.04/0.24 0.04/0.24 ### Cost equations --> "Loop" of eval_start_bb1_in_loop_cont/6 0.04/0.24 * CEs [21,24] --> Loop 21 0.04/0.24 * CEs [22] --> Loop 22 0.04/0.24 * CEs [23] --> Loop 23 0.04/0.24 * CEs [25] --> Loop 24 0.04/0.24 0.04/0.24 ### Ranking functions of CR eval_start_bb1_in_loop_cont(A,B,C,D,E,F) 0.04/0.24 0.04/0.24 #### Partial ranking functions of CR eval_start_bb1_in_loop_cont(A,B,C,D,E,F) 0.04/0.24 0.04/0.24 0.04/0.24 ### Specialization of cost equations eval_start_3/5 0.04/0.24 * CE 2 is refined into CE [26,27,28,29,30,31,32] 0.04/0.24 0.04/0.24 0.04/0.24 ### Cost equations --> "Loop" of eval_start_3/5 0.04/0.24 * CEs [30] --> Loop 25 0.04/0.24 * CEs [28] --> Loop 26 0.04/0.24 * CEs [27,31,32] --> Loop 27 0.04/0.24 * CEs [29] --> Loop 28 0.04/0.24 * CEs [26] --> Loop 29 0.04/0.24 0.04/0.24 ### Ranking functions of CR eval_start_3(V__0,V__01,V_x,V_y,B) 0.04/0.24 0.04/0.24 #### Partial ranking functions of CR eval_start_3(V__0,V__01,V_x,V_y,B) 0.04/0.24 0.04/0.24 0.04/0.24 ### Specialization of cost equations eval_start_start/5 0.04/0.24 * CE 1 is refined into CE [33,34,35,36,37] 0.04/0.24 0.04/0.24 0.04/0.24 ### Cost equations --> "Loop" of eval_start_start/5 0.04/0.24 * CEs [37] --> Loop 30 0.04/0.24 * CEs [36] --> Loop 31 0.04/0.24 * CEs [35] --> Loop 32 0.04/0.24 * CEs [34] --> Loop 33 0.04/0.24 * CEs [33] --> Loop 34 0.04/0.24 0.04/0.24 ### Ranking functions of CR eval_start_start(V__0,V__01,V_x,V_y,B) 0.04/0.24 0.04/0.24 #### Partial ranking functions of CR eval_start_start(V__0,V__01,V_x,V_y,B) 0.04/0.24 0.04/0.24 0.04/0.24 Computing Bounds 0.04/0.24 ===================================== 0.04/0.24 0.04/0.24 #### Cost of chains of eval_start_bb1_in(V__0,V__01,V_y,B,C): 0.04/0.24 * Chain [[13],15]: 1*it(13)+0 0.04/0.24 Such that:it(13) =< -V__0+V_y 0.04/0.24 0.04/0.24 with precondition: [B=3,V_y>=V__0+1] 0.04/0.24 0.04/0.24 * Chain [[13],14]: 1*it(13)+0 0.04/0.24 Such that:it(13) =< -V__0+V_y 0.04/0.24 0.04/0.24 with precondition: [B=4,V_y=C,V_y>=V__0+1] 0.04/0.24 0.04/0.24 * Chain [15]: 0 0.04/0.24 with precondition: [B=3] 0.04/0.24 0.04/0.24 * Chain [14]: 0 0.04/0.24 with precondition: [B=4,V__0=C,V__0>=V_y] 0.04/0.24 0.04/0.24 0.04/0.24 #### Cost of chains of eval_start_bb3_in(V__0,V__01,B,C): 0.04/0.24 * Chain [[16],18]: 1*it(16)+0 0.04/0.24 Such that:it(16) =< V__0-V__01 0.04/0.24 0.04/0.24 with precondition: [B=2,V__0=C,V__0>=V__01+1] 0.04/0.24 0.04/0.24 * Chain [[16],17]: 1*it(16)+0 0.04/0.24 Such that:it(16) =< V__0-V__01 0.04/0.24 0.04/0.24 with precondition: [B=3,V__0>=V__01+1] 0.04/0.24 0.04/0.24 * Chain [18]: 0 0.04/0.24 with precondition: [B=2,V__01=C,V__01>=V__0] 0.04/0.24 0.04/0.24 * Chain [17]: 0 0.04/0.24 with precondition: [B=3] 0.04/0.24 0.04/0.24 0.04/0.24 #### Cost of chains of eval_start_bb3_in_loop_cont(A,B,C,D,E,F): 0.04/0.24 * Chain [20]: 0 0.04/0.24 with precondition: [A=2] 0.04/0.24 0.04/0.24 * Chain [19]: 0 0.04/0.24 with precondition: [A=3] 0.04/0.24 0.04/0.24 0.04/0.24 #### Cost of chains of eval_start_bb1_in_loop_cont(A,B,C,D,E,F): 0.04/0.24 * Chain [24]: 0 0.04/0.24 with precondition: [A=3,E=C] 0.04/0.24 0.04/0.24 * Chain [23]: 0 0.04/0.24 with precondition: [A=4,E=C] 0.04/0.24 0.04/0.24 * Chain [22]: 0 0.04/0.24 with precondition: [A=4,E=C,E>=B] 0.04/0.24 0.04/0.24 * Chain [21]: 2*s(1)+0 0.04/0.24 Such that:aux(1) =< B-C 0.04/0.24 s(1) =< aux(1) 0.04/0.24 0.04/0.24 with precondition: [A=4,E=C,B>=E+1] 0.04/0.24 0.04/0.24 0.04/0.24 #### Cost of chains of eval_start_3(V__0,V__01,V_x,V_y,B): 0.04/0.24 * Chain [29]: 0 0.04/0.24 with precondition: [] 0.04/0.24 0.04/0.24 * Chain [28]: 0 0.04/0.24 with precondition: [V_y=V_x] 0.04/0.24 0.04/0.24 * Chain [27]: 3*s(3)+0 0.04/0.24 Such that:aux(2) =< -V_x+V_y 0.04/0.24 s(3) =< aux(2) 0.04/0.24 0.04/0.24 with precondition: [V_y>=V_x+1] 0.04/0.24 0.04/0.24 * Chain [26]: 0 0.04/0.24 with precondition: [V_x>=V_y] 0.04/0.24 0.04/0.24 * Chain [25]: 2*s(7)+0 0.04/0.24 Such that:s(6) =< V_x-V_y 0.04/0.24 s(7) =< s(6) 0.04/0.24 0.04/0.24 with precondition: [V_x>=V_y+1] 0.04/0.24 0.04/0.24 0.04/0.24 #### Cost of chains of eval_start_start(V__0,V__01,V_x,V_y,B): 0.04/0.24 * Chain [34]: 0 0.04/0.24 with precondition: [] 0.04/0.24 0.04/0.24 * Chain [33]: 0 0.04/0.24 with precondition: [V_y=V_x] 0.04/0.24 0.04/0.24 * Chain [32]: 3*s(9)+0 0.04/0.24 Such that:s(8) =< -V_x+V_y 0.04/0.24 s(9) =< s(8) 0.04/0.24 0.04/0.24 with precondition: [V_y>=V_x+1] 0.04/0.24 0.04/0.24 * Chain [31]: 0 0.04/0.24 with precondition: [V_x>=V_y] 0.04/0.24 0.04/0.24 * Chain [30]: 2*s(11)+0 0.04/0.24 Such that:s(10) =< V_x-V_y 0.04/0.24 s(11) =< s(10) 0.04/0.24 0.04/0.24 with precondition: [V_x>=V_y+1] 0.04/0.24 0.04/0.24 0.04/0.24 Closed-form bounds of eval_start_start(V__0,V__01,V_x,V_y,B): 0.04/0.24 ------------------------------------- 0.04/0.24 * Chain [34] with precondition: [] 0.04/0.24 - Upper bound: 0 0.04/0.24 - Complexity: constant 0.04/0.24 * Chain [33] with precondition: [V_y=V_x] 0.04/0.24 - Upper bound: 0 0.04/0.24 - Complexity: constant 0.04/0.24 * Chain [32] with precondition: [V_y>=V_x+1] 0.04/0.24 - Upper bound: -3*V_x+3*V_y 0.04/0.24 - Complexity: n 0.04/0.24 * Chain [31] with precondition: [V_x>=V_y] 0.04/0.24 - Upper bound: 0 0.04/0.24 - Complexity: constant 0.04/0.24 * Chain [30] with precondition: [V_x>=V_y+1] 0.04/0.24 - Upper bound: 2*V_x-2*V_y 0.04/0.24 - Complexity: n 0.04/0.24 0.04/0.24 ### Maximum cost of eval_start_start(V__0,V__01,V_x,V_y,B): max([nat(-V_x+V_y)*3,nat(V_x-V_y)*2]) 0.04/0.24 Asymptotic class: n 0.04/0.24 * Total analysis performed in 171 ms. 0.04/0.24 0.04/0.34 EOF