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_start_bb1_in/6,eval_start_bb2_in/6] 0.03/0.24 1. recursive : [eval_start_bb3_in/3,eval_start_bb4_in/3] 0.03/0.24 2. non_recursive : [eval_start_stop/5] 0.03/0.24 3. non_recursive : [eval_start_bb5_in/5] 0.03/0.24 4. non_recursive : [exit_location/1] 0.03/0.24 5. non_recursive : [eval_start_bb3_in_loop_cont/6] 0.03/0.24 6. non_recursive : [eval_start_bb1_in_loop_cont/6] 0.03/0.24 7. non_recursive : [eval_start_3/5] 0.03/0.24 8. non_recursive : [eval_start_2/5] 0.03/0.24 9. non_recursive : [eval_start_1/5] 0.03/0.24 10. non_recursive : [eval_start_0/5] 0.03/0.24 11. non_recursive : [eval_start_bb0_in/5] 0.03/0.24 12. non_recursive : [eval_start_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_start_bb1_in/6 0.03/0.24 1. SCC is partially evaluated into eval_start_bb3_in/3 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 completely evaluated into other SCCs 0.03/0.24 5. SCC is partially evaluated into eval_start_bb3_in_loop_cont/6 0.03/0.24 6. SCC is partially evaluated into eval_start_bb1_in_loop_cont/6 0.03/0.24 7. SCC is partially evaluated into eval_start_3/5 0.03/0.24 8. SCC is completely evaluated into other SCCs 0.03/0.24 9. SCC is completely evaluated into other SCCs 0.03/0.24 10. SCC is completely evaluated into other SCCs 0.03/0.24 11. SCC is completely evaluated into other SCCs 0.03/0.24 12. SCC is partially evaluated into eval_start_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_start_bb1_in/6 0.03/0.24 * CE 4 is refined into CE [13] 0.03/0.24 * CE 5 is refined into CE [14] 0.03/0.24 * CE 3 is refined into CE [15] 0.03/0.24 0.03/0.24 0.03/0.24 ### Cost equations --> "Loop" of eval_start_bb1_in/6 0.03/0.24 * CEs [15] --> Loop 13 0.03/0.24 * CEs [13] --> Loop 14 0.03/0.24 * CEs [14] --> Loop 15 0.03/0.24 0.03/0.24 ### Ranking functions of CR eval_start_bb1_in(V__0,V__1,V_z,B,C,D) 0.03/0.24 * RF of phase [13]: [-V__0+V_z] 0.03/0.24 0.03/0.24 #### Partial ranking functions of CR eval_start_bb1_in(V__0,V__1,V_z,B,C,D) 0.03/0.24 * Partial RF of phase [13]: 0.03/0.24 - RF of loop [13:1]: 0.03/0.24 -V__0+V_z 0.03/0.24 0.03/0.24 0.03/0.24 ### Specialization of cost equations eval_start_bb3_in/3 0.03/0.24 * CE 10 is refined into CE [16] 0.03/0.24 * CE 9 is refined into CE [17] 0.03/0.24 * CE 8 is refined into CE [18] 0.03/0.24 0.03/0.24 0.03/0.24 ### Cost equations --> "Loop" of eval_start_bb3_in/3 0.03/0.24 * CEs [18] --> Loop 16 0.03/0.24 * CEs [16] --> Loop 17 0.03/0.24 * CEs [17] --> Loop 18 0.03/0.24 0.03/0.24 ### Ranking functions of CR eval_start_bb3_in(V__1,B,C) 0.03/0.24 * RF of phase [16]: [V__1-2] 0.03/0.24 0.03/0.24 #### Partial ranking functions of CR eval_start_bb3_in(V__1,B,C) 0.03/0.24 * Partial RF of phase [16]: 0.03/0.24 - RF of loop [16:1]: 0.03/0.24 V__1-2 0.03/0.24 0.03/0.24 0.03/0.24 ### Specialization of cost equations eval_start_bb3_in_loop_cont/6 0.03/0.24 * CE 12 is refined into CE [19] 0.03/0.24 * CE 11 is refined into CE [20] 0.03/0.24 0.03/0.24 0.03/0.24 ### Cost equations --> "Loop" of eval_start_bb3_in_loop_cont/6 0.03/0.24 * CEs [19] --> Loop 19 0.03/0.24 * CEs [20] --> Loop 20 0.03/0.24 0.03/0.24 ### Ranking functions of CR eval_start_bb3_in_loop_cont(A,B,C,D,E,F) 0.03/0.24 0.03/0.24 #### Partial ranking functions of CR eval_start_bb3_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_start_bb1_in_loop_cont/6 0.03/0.24 * CE 7 is refined into CE [21,22,23,24] 0.03/0.24 * CE 6 is refined into CE [25] 0.03/0.24 0.03/0.24 0.03/0.24 ### Cost equations --> "Loop" of eval_start_bb1_in_loop_cont/6 0.03/0.24 * CEs [22,24] --> Loop 21 0.03/0.24 * CEs [21] --> Loop 22 0.03/0.24 * CEs [23] --> Loop 23 0.03/0.24 * CEs [25] --> Loop 24 0.03/0.24 0.03/0.24 ### Ranking functions of CR eval_start_bb1_in_loop_cont(A,B,C,D,E,F) 0.03/0.24 0.03/0.24 #### Partial ranking functions of CR eval_start_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_start_3/5 0.03/0.24 * CE 2 is refined into CE [26,27,28,29,30,31,32,33] 0.03/0.24 0.03/0.24 0.03/0.24 ### Cost equations --> "Loop" of eval_start_3/5 0.03/0.24 * CEs [28] --> Loop 25 0.03/0.24 * CEs [27,31] --> Loop 26 0.03/0.24 * CEs [33] --> Loop 27 0.03/0.24 * CEs [30] --> Loop 28 0.03/0.24 * CEs [32] --> Loop 29 0.03/0.24 * CEs [29] --> Loop 30 0.03/0.24 * CEs [26] --> Loop 31 0.03/0.24 0.03/0.24 ### Ranking functions of CR eval_start_3(V__0,V__1,V_y,V_z,B) 0.03/0.24 0.03/0.24 #### Partial ranking functions of CR eval_start_3(V__0,V__1,V_y,V_z,B) 0.03/0.24 0.03/0.24 0.03/0.24 ### Specialization of cost equations eval_start_start/5 0.03/0.24 * CE 1 is refined into CE [34,35,36,37,38,39,40] 0.03/0.24 0.03/0.24 0.03/0.24 ### Cost equations --> "Loop" of eval_start_start/5 0.03/0.24 * CEs [40] --> Loop 32 0.03/0.24 * CEs [39] --> Loop 33 0.03/0.24 * CEs [38] --> Loop 34 0.03/0.24 * CEs [37] --> Loop 35 0.03/0.24 * CEs [36] --> Loop 36 0.03/0.24 * CEs [35] --> Loop 37 0.03/0.24 * CEs [34] --> Loop 38 0.03/0.24 0.03/0.24 ### Ranking functions of CR eval_start_start(V__0,V__1,V_y,V_z,B) 0.03/0.24 0.03/0.24 #### Partial ranking functions of CR eval_start_start(V__0,V__1,V_y,V_z,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_start_bb1_in(V__0,V__1,V_z,B,C,D): 0.03/0.24 * Chain [[13],15]: 1*it(13)+0 0.03/0.24 Such that:it(13) =< -V__0+V_z 0.03/0.24 0.03/0.24 with precondition: [B=3,V_z>=V__0+1] 0.03/0.24 0.03/0.24 * Chain [[13],14]: 1*it(13)+0 0.03/0.24 Such that:it(13) =< -V__0+C 0.03/0.24 0.03/0.24 with precondition: [B=4,V_z=C,V_z=D,V_z>=V__0+1] 0.03/0.24 0.03/0.24 * Chain [15]: 0 0.03/0.24 with precondition: [B=3] 0.03/0.24 0.03/0.24 * Chain [14]: 0 0.03/0.24 with precondition: [B=4,V__0=C,V__0=D,V__0>=V_z] 0.03/0.24 0.03/0.24 0.03/0.24 #### Cost of chains of eval_start_bb3_in(V__1,B,C): 0.03/0.24 * Chain [[16],18]: 1*it(16)+0 0.03/0.24 Such that:it(16) =< V__1-C 0.03/0.24 0.03/0.24 with precondition: [B=2,2>=C,C>=0,V__1>=C+3] 0.03/0.24 0.03/0.24 * Chain [[16],17]: 1*it(16)+0 0.03/0.24 Such that:it(16) =< V__1 0.03/0.24 0.03/0.24 with precondition: [B=3,V__1>=3] 0.03/0.24 0.03/0.24 * Chain [18]: 0 0.03/0.24 with precondition: [B=2,V__1=C,2>=V__1] 0.03/0.24 0.03/0.24 * Chain [17]: 0 0.03/0.24 with precondition: [B=3] 0.03/0.24 0.03/0.24 0.03/0.24 #### Cost of chains of eval_start_bb3_in_loop_cont(A,B,C,D,E,F): 0.03/0.24 * Chain [20]: 0 0.03/0.24 with precondition: [A=2] 0.03/0.24 0.03/0.24 * Chain [19]: 0 0.03/0.24 with precondition: [A=3] 0.03/0.24 0.03/0.24 0.03/0.24 #### Cost of chains of eval_start_bb1_in_loop_cont(A,B,C,D,E,F): 0.03/0.24 * Chain [24]: 0 0.03/0.24 with precondition: [A=3] 0.03/0.24 0.03/0.24 * Chain [23]: 0 0.03/0.24 with precondition: [A=4] 0.03/0.24 0.03/0.24 * Chain [22]: 0 0.03/0.24 with precondition: [A=4,2>=C] 0.03/0.24 0.03/0.24 * Chain [21]: 2*s(1)+0 0.03/0.24 Such that:aux(1) =< C 0.03/0.24 s(1) =< aux(1) 0.03/0.24 0.03/0.24 with precondition: [A=4,C>=3] 0.03/0.24 0.03/0.24 0.03/0.24 #### Cost of chains of eval_start_3(V__0,V__1,V_y,V_z,B): 0.03/0.24 * Chain [31]: 0 0.03/0.24 with precondition: [] 0.03/0.24 0.03/0.24 * Chain [30]: 0 0.03/0.24 with precondition: [2>=V_y,V_y>=V_z] 0.03/0.24 0.03/0.24 * Chain [29]: 1*s(3)+0 0.03/0.24 Such that:s(3) =< -V_y+V_z 0.03/0.24 0.03/0.24 with precondition: [2>=V_z,V_z>=V_y+1] 0.03/0.24 0.03/0.24 * Chain [28]: 2*s(5)+0 0.03/0.24 Such that:s(4) =< V_y 0.03/0.24 s(5) =< s(4) 0.03/0.24 0.03/0.24 with precondition: [V_y>=3,V_y>=V_z] 0.03/0.24 0.03/0.24 * Chain [27]: 1*s(6)+2*s(8)+0 0.03/0.24 Such that:s(6) =< -V_y+V_z 0.03/0.24 s(7) =< V_z 0.03/0.24 s(8) =< s(7) 0.03/0.24 0.03/0.24 with precondition: [V_z>=3,V_z>=V_y+1] 0.03/0.24 0.03/0.24 * Chain [26]: 2*s(9)+0 0.03/0.24 Such that:aux(2) =< -V_y+V_z 0.03/0.24 s(9) =< aux(2) 0.03/0.24 0.03/0.24 with precondition: [V_z>=V_y+1] 0.03/0.24 0.03/0.24 * Chain [25]: 0 0.03/0.24 with precondition: [V_y>=V_z] 0.03/0.24 0.03/0.24 0.03/0.24 #### Cost of chains of eval_start_start(V__0,V__1,V_y,V_z,B): 0.03/0.24 * Chain [38]: 0 0.03/0.24 with precondition: [] 0.03/0.24 0.03/0.24 * Chain [37]: 0 0.03/0.24 with precondition: [2>=V_y,V_y>=V_z] 0.03/0.24 0.03/0.24 * Chain [36]: 1*s(11)+0 0.03/0.24 Such that:s(11) =< -V_y+V_z 0.03/0.24 0.03/0.24 with precondition: [2>=V_z,V_z>=V_y+1] 0.03/0.24 0.03/0.24 * Chain [35]: 2*s(13)+0 0.03/0.24 Such that:s(12) =< V_y 0.03/0.24 s(13) =< s(12) 0.03/0.24 0.03/0.24 with precondition: [V_y>=3,V_y>=V_z] 0.03/0.24 0.03/0.24 * Chain [34]: 1*s(14)+2*s(16)+0 0.03/0.24 Such that:s(14) =< -V_y+V_z 0.03/0.24 s(15) =< V_z 0.03/0.24 s(16) =< s(15) 0.03/0.24 0.03/0.24 with precondition: [V_z>=3,V_z>=V_y+1] 0.03/0.24 0.03/0.24 * Chain [33]: 2*s(18)+0 0.03/0.24 Such that:s(17) =< -V_y+V_z 0.03/0.24 s(18) =< s(17) 0.03/0.24 0.03/0.24 with precondition: [V_z>=V_y+1] 0.03/0.24 0.03/0.24 * Chain [32]: 0 0.03/0.24 with precondition: [V_y>=V_z] 0.03/0.24 0.03/0.24 0.03/0.24 Closed-form bounds of eval_start_start(V__0,V__1,V_y,V_z,B): 0.03/0.24 ------------------------------------- 0.03/0.24 * Chain [38] with precondition: [] 0.03/0.24 - Upper bound: 0 0.03/0.24 - Complexity: constant 0.03/0.24 * Chain [37] with precondition: [2>=V_y,V_y>=V_z] 0.03/0.24 - Upper bound: 0 0.03/0.24 - Complexity: constant 0.03/0.24 * Chain [36] with precondition: [2>=V_z,V_z>=V_y+1] 0.03/0.24 - Upper bound: -V_y+V_z 0.03/0.24 - Complexity: n 0.03/0.24 * Chain [35] with precondition: [V_y>=3,V_y>=V_z] 0.03/0.24 - Upper bound: 2*V_y 0.03/0.24 - Complexity: n 0.03/0.24 * Chain [34] with precondition: [V_z>=3,V_z>=V_y+1] 0.03/0.24 - Upper bound: -V_y+3*V_z 0.03/0.24 - Complexity: n 0.03/0.24 * Chain [33] with precondition: [V_z>=V_y+1] 0.03/0.24 - Upper bound: -2*V_y+2*V_z 0.03/0.24 - Complexity: n 0.03/0.24 * Chain [32] with precondition: [V_y>=V_z] 0.03/0.24 - Upper bound: 0 0.03/0.24 - Complexity: constant 0.03/0.24 0.03/0.24 ### Maximum cost of eval_start_start(V__0,V__1,V_y,V_z,B): max([nat(V_y)*2,nat(-V_y+V_z)+max([nat(-V_y+V_z),nat(V_z)*2])]) 0.03/0.24 Asymptotic class: n 0.03/0.24 * Total analysis performed in 178 ms. 0.03/0.24 0.03/0.35 EOF