0.04/0.35 WORST_CASE(?,O(n^1)) 0.04/0.35 0.04/0.35 Preprocessing Cost Relations 0.04/0.35 ===================================== 0.04/0.35 0.04/0.35 #### Computed strongly connected components 0.04/0.35 0. recursive : [eval_start_bb1_in/7,eval_start_bb2_in/7] 0.04/0.35 1. recursive : [eval_start_bb3_in/5,eval_start_bb4_in/5] 0.04/0.35 2. recursive : [eval_start_bb5_in/3,eval_start_bb6_in/3] 0.04/0.35 3. non_recursive : [eval_start_stop/7] 0.04/0.35 4. non_recursive : [eval_start_bb7_in/7] 0.04/0.35 5. non_recursive : [exit_location/1] 0.04/0.35 6. non_recursive : [eval_start_bb5_in_loop_cont/8] 0.04/0.35 7. non_recursive : [eval_start_bb3_in_loop_cont/8] 0.04/0.35 8. non_recursive : [eval_start_bb1_in_loop_cont/8] 0.04/0.35 9. non_recursive : [eval_start_4/7] 0.04/0.35 10. non_recursive : [eval_start_3/7] 0.04/0.35 11. non_recursive : [eval_start_2/7] 0.04/0.35 12. non_recursive : [eval_start_1/7] 0.04/0.35 13. non_recursive : [eval_start_0/7] 0.04/0.35 14. non_recursive : [eval_start_bb0_in/7] 0.04/0.35 15. non_recursive : [eval_start_start/7] 0.04/0.35 0.04/0.35 #### Obtained direct recursion through partial evaluation 0.04/0.35 0. SCC is partially evaluated into eval_start_bb1_in/7 0.04/0.35 1. SCC is partially evaluated into eval_start_bb3_in/5 0.04/0.35 2. SCC is partially evaluated into eval_start_bb5_in/3 0.04/0.35 3. SCC is completely evaluated into other SCCs 0.04/0.35 4. SCC is completely evaluated into other SCCs 0.04/0.35 5. SCC is completely evaluated into other SCCs 0.04/0.35 6. SCC is partially evaluated into eval_start_bb5_in_loop_cont/8 0.04/0.35 7. SCC is partially evaluated into eval_start_bb3_in_loop_cont/8 0.04/0.35 8. SCC is partially evaluated into eval_start_bb1_in_loop_cont/8 0.04/0.35 9. SCC is partially evaluated into eval_start_4/7 0.04/0.35 10. SCC is completely evaluated into other SCCs 0.04/0.35 11. SCC is completely evaluated into other SCCs 0.04/0.35 12. SCC is completely evaluated into other SCCs 0.04/0.35 13. SCC is completely evaluated into other SCCs 0.04/0.35 14. SCC is completely evaluated into other SCCs 0.04/0.35 15. SCC is partially evaluated into eval_start_start/7 0.04/0.35 0.04/0.35 Control-Flow Refinement of Cost Relations 0.04/0.35 ===================================== 0.04/0.35 0.04/0.35 ### Specialization of cost equations eval_start_bb1_in/7 0.04/0.35 * CE 4 is refined into CE [18] 0.04/0.35 * CE 5 is refined into CE [19] 0.04/0.35 * CE 3 is refined into CE [20] 0.04/0.35 0.04/0.35 0.04/0.35 ### Cost equations --> "Loop" of eval_start_bb1_in/7 0.04/0.35 * CEs [20] --> Loop 18 0.04/0.35 * CEs [18] --> Loop 19 0.04/0.35 * CEs [19] --> Loop 20 0.04/0.35 0.04/0.35 ### Ranking functions of CR eval_start_bb1_in(V__0,V__01,V__1,B,C,D,E) 0.04/0.35 * RF of phase [18]: [V__0] 0.04/0.35 0.04/0.35 #### Partial ranking functions of CR eval_start_bb1_in(V__0,V__01,V__1,B,C,D,E) 0.04/0.35 * Partial RF of phase [18]: 0.04/0.35 - RF of loop [18:1]: 0.04/0.35 V__0 0.04/0.35 0.04/0.35 0.04/0.35 ### Specialization of cost equations eval_start_bb3_in/5 0.04/0.35 * CE 9 is refined into CE [21] 0.04/0.35 * CE 10 is refined into CE [22] 0.04/0.35 * CE 8 is refined into CE [23] 0.04/0.35 0.04/0.35 0.04/0.35 ### Cost equations --> "Loop" of eval_start_bb3_in/5 0.04/0.35 * CEs [23] --> Loop 21 0.04/0.35 * CEs [21] --> Loop 22 0.04/0.35 * CEs [22] --> Loop 23 0.04/0.35 0.04/0.35 ### Ranking functions of CR eval_start_bb3_in(V__1,V__2,B,C,D) 0.04/0.35 * RF of phase [21]: [V__1] 0.04/0.35 0.04/0.35 #### Partial ranking functions of CR eval_start_bb3_in(V__1,V__2,B,C,D) 0.04/0.35 * Partial RF of phase [21]: 0.04/0.35 - RF of loop [21:1]: 0.04/0.35 V__1 0.04/0.35 0.04/0.35 0.04/0.35 ### Specialization of cost equations eval_start_bb5_in/3 0.04/0.35 * CE 15 is refined into CE [24] 0.04/0.35 * CE 14 is refined into CE [25] 0.04/0.35 * CE 13 is refined into CE [26] 0.04/0.35 0.04/0.35 0.04/0.35 ### Cost equations --> "Loop" of eval_start_bb5_in/3 0.04/0.35 * CEs [26] --> Loop 24 0.04/0.35 * CEs [24] --> Loop 25 0.04/0.35 * CEs [25] --> Loop 26 0.04/0.35 0.04/0.35 ### Ranking functions of CR eval_start_bb5_in(V__2,B,C) 0.04/0.35 * RF of phase [24]: [V__2] 0.04/0.35 0.04/0.35 #### Partial ranking functions of CR eval_start_bb5_in(V__2,B,C) 0.04/0.35 * Partial RF of phase [24]: 0.04/0.35 - RF of loop [24:1]: 0.04/0.35 V__2 0.04/0.35 0.04/0.35 0.04/0.35 ### Specialization of cost equations eval_start_bb5_in_loop_cont/8 0.04/0.35 * CE 17 is refined into CE [27] 0.04/0.35 * CE 16 is refined into CE [28] 0.04/0.35 0.04/0.35 0.04/0.35 ### Cost equations --> "Loop" of eval_start_bb5_in_loop_cont/8 0.04/0.35 * CEs [27] --> Loop 27 0.04/0.35 * CEs [28] --> Loop 28 0.04/0.35 0.04/0.35 ### Ranking functions of CR eval_start_bb5_in_loop_cont(A,B,C,D,E,F,G,H) 0.04/0.35 0.04/0.35 #### Partial ranking functions of CR eval_start_bb5_in_loop_cont(A,B,C,D,E,F,G,H) 0.04/0.35 0.04/0.35 0.04/0.35 ### Specialization of cost equations eval_start_bb3_in_loop_cont/8 0.04/0.35 * CE 12 is refined into CE [29,30,31,32] 0.04/0.35 * CE 11 is refined into CE [33] 0.04/0.35 0.04/0.35 0.04/0.35 ### Cost equations --> "Loop" of eval_start_bb3_in_loop_cont/8 0.04/0.35 * CEs [29,32] --> Loop 29 0.04/0.35 * CEs [30] --> Loop 30 0.04/0.35 * CEs [31] --> Loop 31 0.04/0.35 * CEs [33] --> Loop 32 0.04/0.35 0.04/0.35 ### Ranking functions of CR eval_start_bb3_in_loop_cont(A,B,C,D,E,F,G,H) 0.04/0.35 0.04/0.35 #### Partial ranking functions of CR eval_start_bb3_in_loop_cont(A,B,C,D,E,F,G,H) 0.04/0.35 0.04/0.35 0.04/0.35 ### Specialization of cost equations eval_start_bb1_in_loop_cont/8 0.04/0.35 * CE 7 is refined into CE [34,35,36,37,38,39] 0.04/0.35 * CE 6 is refined into CE [40] 0.04/0.35 0.04/0.35 0.04/0.35 ### Cost equations --> "Loop" of eval_start_bb1_in_loop_cont/8 0.04/0.35 * CEs [35,36,37] --> Loop 33 0.04/0.35 * CEs [38,39] --> Loop 34 0.04/0.35 * CEs [34] --> Loop 35 0.04/0.35 * CEs [40] --> Loop 36 0.04/0.35 0.04/0.35 ### Ranking functions of CR eval_start_bb1_in_loop_cont(A,B,C,D,E,F,G,H) 0.04/0.35 0.04/0.35 #### Partial ranking functions of CR eval_start_bb1_in_loop_cont(A,B,C,D,E,F,G,H) 0.04/0.35 0.04/0.35 0.04/0.35 ### Specialization of cost equations eval_start_4/7 0.04/0.35 * CE 2 is refined into CE [41,42,43,44,45,46,47,48] 0.04/0.35 0.04/0.35 0.04/0.35 ### Cost equations --> "Loop" of eval_start_4/7 0.04/0.35 * CEs [45] --> Loop 37 0.04/0.35 * CEs [44] --> Loop 38 0.04/0.35 * CEs [42,43] --> Loop 39 0.04/0.35 * CEs [48] --> Loop 40 0.04/0.35 * CEs [47] --> Loop 41 0.04/0.35 * CEs [46] --> Loop 42 0.04/0.35 * CEs [41] --> Loop 43 0.04/0.35 0.04/0.35 ### Ranking functions of CR eval_start_4(V__0,V__01,V__1,V__2,V_x,V_y,B) 0.04/0.35 0.04/0.35 #### Partial ranking functions of CR eval_start_4(V__0,V__01,V__1,V__2,V_x,V_y,B) 0.04/0.35 0.04/0.35 0.04/0.35 ### Specialization of cost equations eval_start_start/7 0.04/0.35 * CE 1 is refined into CE [49,50,51,52,53,54,55] 0.04/0.35 0.04/0.35 0.04/0.35 ### Cost equations --> "Loop" of eval_start_start/7 0.04/0.35 * CEs [55] --> Loop 44 0.04/0.35 * CEs [54] --> Loop 45 0.04/0.35 * CEs [53] --> Loop 46 0.04/0.35 * CEs [52] --> Loop 47 0.04/0.35 * CEs [51] --> Loop 48 0.04/0.35 * CEs [50] --> Loop 49 0.04/0.35 * CEs [49] --> Loop 50 0.04/0.35 0.04/0.35 ### Ranking functions of CR eval_start_start(V__0,V__01,V__1,V__2,V_x,V_y,B) 0.04/0.35 0.04/0.35 #### Partial ranking functions of CR eval_start_start(V__0,V__01,V__1,V__2,V_x,V_y,B) 0.04/0.35 0.04/0.35 0.04/0.35 Computing Bounds 0.04/0.35 ===================================== 0.04/0.35 0.04/0.35 #### Cost of chains of eval_start_bb1_in(V__0,V__01,V__1,B,C,D,E): 0.04/0.35 * Chain [[18],20]: 1*it(18)+0 0.04/0.35 Such that:it(18) =< V__0 0.04/0.35 0.04/0.35 with precondition: [B=3,V__0>=1] 0.04/0.35 0.04/0.35 * Chain [[18],19]: 1*it(18)+0 0.04/0.35 Such that:it(18) =< V__0 0.04/0.35 0.04/0.35 with precondition: [B=5,C=0,V__01+2*V__0=D,V__01+2*V__0=E,V__0>=1] 0.04/0.35 0.04/0.35 * Chain [20]: 0 0.04/0.35 with precondition: [B=3] 0.04/0.35 0.04/0.35 * Chain [19]: 0 0.04/0.35 with precondition: [B=5,V__0=C,V__01=D,V__01=E,0>=V__0] 0.04/0.35 0.04/0.35 0.04/0.35 #### Cost of chains of eval_start_bb3_in(V__1,V__2,B,C,D): 0.04/0.35 * Chain [[21],23]: 1*it(21)+0 0.04/0.35 Such that:it(21) =< V__1 0.04/0.35 0.04/0.35 with precondition: [B=3,V__1>=1] 0.04/0.35 0.04/0.35 * Chain [[21],22]: 1*it(21)+0 0.04/0.35 Such that:it(21) =< V__1 0.04/0.35 0.04/0.35 with precondition: [B=4,C=0,D=0,V__1>=1] 0.04/0.35 0.04/0.35 * Chain [23]: 0 0.04/0.35 with precondition: [B=3] 0.04/0.35 0.04/0.35 * Chain [22]: 0 0.04/0.35 with precondition: [B=4,V__1=C,V__1=D,0>=V__1] 0.04/0.35 0.04/0.35 0.04/0.35 #### Cost of chains of eval_start_bb5_in(V__2,B,C): 0.04/0.35 * Chain [[24],26]: 1*it(24)+0 0.04/0.35 Such that:it(24) =< V__2 0.04/0.35 0.04/0.35 with precondition: [B=2,C=0,V__2>=1] 0.04/0.35 0.04/0.35 * Chain [[24],25]: 1*it(24)+0 0.04/0.35 Such that:it(24) =< V__2 0.04/0.35 0.04/0.35 with precondition: [B=3,V__2>=1] 0.04/0.35 0.04/0.35 * Chain [26]: 0 0.04/0.35 with precondition: [B=2,V__2=C,0>=V__2] 0.04/0.35 0.04/0.35 * Chain [25]: 0 0.04/0.35 with precondition: [B=3] 0.04/0.35 0.04/0.35 0.04/0.35 #### Cost of chains of eval_start_bb5_in_loop_cont(A,B,C,D,E,F,G,H): 0.04/0.35 * Chain [28]: 0 0.04/0.35 with precondition: [A=2] 0.04/0.35 0.04/0.35 * Chain [27]: 0 0.04/0.35 with precondition: [A=3] 0.04/0.35 0.04/0.35 0.04/0.35 #### Cost of chains of eval_start_bb3_in_loop_cont(A,B,C,D,E,F,G,H): 0.04/0.35 * Chain [32]: 0 0.04/0.35 with precondition: [A=3] 0.04/0.35 0.04/0.35 * Chain [31]: 0 0.04/0.35 with precondition: [A=4] 0.04/0.35 0.04/0.35 * Chain [30]: 0 0.04/0.35 with precondition: [A=4,0>=E] 0.04/0.35 0.04/0.35 * Chain [29]: 2*s(1)+0 0.04/0.35 Such that:aux(1) =< E 0.04/0.35 s(1) =< aux(1) 0.04/0.35 0.04/0.35 with precondition: [A=4,E>=1] 0.04/0.35 0.04/0.35 0.04/0.35 #### Cost of chains of eval_start_bb1_in_loop_cont(A,B,C,D,E,F,G,H): 0.04/0.35 * Chain [36]: 0 0.04/0.35 with precondition: [A=3] 0.04/0.35 0.04/0.35 * Chain [35]: 0 0.04/0.35 with precondition: [A=5] 0.04/0.35 0.04/0.35 * Chain [34]: 0 0.04/0.35 with precondition: [A=5,0>=D] 0.04/0.35 0.04/0.35 * Chain [33]: 3*s(3)+0 0.04/0.35 Such that:aux(2) =< D 0.04/0.35 s(3) =< aux(2) 0.04/0.35 0.04/0.35 with precondition: [A=5,D>=1] 0.04/0.35 0.04/0.35 0.04/0.35 #### Cost of chains of eval_start_4(V__0,V__01,V__1,V__2,V_x,V_y,B): 0.04/0.35 * Chain [43]: 0 0.04/0.35 with precondition: [] 0.04/0.35 0.04/0.35 * Chain [42]: 0 0.04/0.35 with precondition: [0>=V_x] 0.04/0.35 0.04/0.35 * Chain [41]: 0 0.04/0.35 with precondition: [0>=V_x,0>=V_y] 0.04/0.35 0.04/0.35 * Chain [40]: 3*s(7)+0 0.04/0.35 Such that:s(6) =< V_y 0.04/0.35 s(7) =< s(6) 0.04/0.35 0.04/0.35 with precondition: [0>=V_x,V_y>=1] 0.04/0.35 0.04/0.35 * Chain [39]: 2*s(8)+0 0.04/0.35 Such that:aux(3) =< V_x 0.04/0.35 s(8) =< aux(3) 0.04/0.35 0.04/0.35 with precondition: [V_x>=1] 0.04/0.35 0.04/0.35 * Chain [38]: 1*s(10)+0 0.04/0.35 Such that:s(10) =< V_x 0.04/0.35 0.04/0.35 with precondition: [V_x>=1,0>=2*V_x+V_y] 0.04/0.35 0.04/0.35 * Chain [37]: 1*s(11)+3*s(13)+0 0.04/0.35 Such that:s(11) =< V_x 0.04/0.35 s(12) =< 2*V_x+V_y 0.04/0.35 s(13) =< s(12) 0.04/0.35 0.04/0.35 with precondition: [V_x>=1,V_y+2*V_x>=1] 0.04/0.35 0.04/0.35 0.04/0.35 #### Cost of chains of eval_start_start(V__0,V__01,V__1,V__2,V_x,V_y,B): 0.04/0.35 * Chain [50]: 0 0.04/0.35 with precondition: [] 0.04/0.35 0.04/0.35 * Chain [49]: 0 0.04/0.35 with precondition: [0>=V_x] 0.04/0.35 0.04/0.35 * Chain [48]: 0 0.04/0.35 with precondition: [0>=V_x,0>=V_y] 0.04/0.35 0.04/0.35 * Chain [47]: 3*s(15)+0 0.04/0.35 Such that:s(14) =< V_y 0.04/0.35 s(15) =< s(14) 0.04/0.35 0.04/0.35 with precondition: [0>=V_x,V_y>=1] 0.04/0.35 0.04/0.35 * Chain [46]: 2*s(17)+0 0.04/0.35 Such that:s(16) =< V_x 0.04/0.35 s(17) =< s(16) 0.04/0.35 0.04/0.35 with precondition: [V_x>=1] 0.04/0.35 0.04/0.35 * Chain [45]: 1*s(18)+0 0.04/0.35 Such that:s(18) =< V_x 0.04/0.35 0.04/0.35 with precondition: [V_x>=1,0>=2*V_x+V_y] 0.04/0.35 0.04/0.35 * Chain [44]: 1*s(19)+3*s(21)+0 0.04/0.35 Such that:s(19) =< V_x 0.04/0.35 s(20) =< 2*V_x+V_y 0.04/0.35 s(21) =< s(20) 0.04/0.35 0.04/0.35 with precondition: [V_x>=1,V_y+2*V_x>=1] 0.04/0.35 0.04/0.35 0.04/0.35 Closed-form bounds of eval_start_start(V__0,V__01,V__1,V__2,V_x,V_y,B): 0.04/0.35 ------------------------------------- 0.04/0.35 * Chain [50] with precondition: [] 0.04/0.35 - Upper bound: 0 0.04/0.35 - Complexity: constant 0.04/0.35 * Chain [49] with precondition: [0>=V_x] 0.04/0.35 - Upper bound: 0 0.04/0.35 - Complexity: constant 0.04/0.35 * Chain [48] with precondition: [0>=V_x,0>=V_y] 0.04/0.35 - Upper bound: 0 0.04/0.35 - Complexity: constant 0.04/0.35 * Chain [47] with precondition: [0>=V_x,V_y>=1] 0.04/0.35 - Upper bound: 3*V_y 0.04/0.35 - Complexity: n 0.04/0.35 * Chain [46] with precondition: [V_x>=1] 0.04/0.35 - Upper bound: 2*V_x 0.04/0.35 - Complexity: n 0.04/0.35 * Chain [45] with precondition: [V_x>=1,0>=2*V_x+V_y] 0.04/0.35 - Upper bound: V_x 0.04/0.35 - Complexity: n 0.04/0.35 * Chain [44] with precondition: [V_x>=1,V_y+2*V_x>=1] 0.04/0.35 - Upper bound: 7*V_x+3*V_y 0.04/0.35 - Complexity: n 0.04/0.35 0.04/0.35 ### Maximum cost of eval_start_start(V__0,V__01,V__1,V__2,V_x,V_y,B): max([nat(V_y)*3,nat(V_x)+max([nat(V_x),nat(2*V_x+V_y)*3])]) 0.04/0.35 Asymptotic class: n 0.04/0.35 * Total analysis performed in 273 ms. 0.04/0.35 0.04/0.45 EOF