0.20/0.26 WORST_CASE(?,O(n^1)) 0.20/0.26 0.20/0.26 Preprocessing Cost Relations 0.20/0.26 ===================================== 0.20/0.26 0.20/0.26 #### Computed strongly connected components 0.20/0.26 0. recursive : [eval_start_bb1_in/3,eval_start_bb2_in/3] 0.20/0.26 1. recursive : [eval_start_bb4_in/3,eval_start_bb5_in/3] 0.20/0.26 2. non_recursive : [eval_start_stop/6] 0.20/0.26 3. non_recursive : [eval_start_bb6_in/6] 0.20/0.26 4. non_recursive : [exit_location/1] 0.20/0.26 5. non_recursive : [eval_start_bb4_in_loop_cont/7] 0.20/0.26 6. non_recursive : [eval_start_10/6] 0.20/0.26 7. non_recursive : [eval_start_9/6] 0.20/0.26 8. non_recursive : [eval_start_8/6] 0.20/0.26 9. non_recursive : [eval_start_bb3_in/6] 0.20/0.26 10. non_recursive : [eval_start_bb1_in_loop_cont/7] 0.20/0.26 11. non_recursive : [eval_start_3/6] 0.20/0.26 12. non_recursive : [eval_start_2/6] 0.20/0.26 13. non_recursive : [eval_start_1/6] 0.20/0.26 14. non_recursive : [eval_start_0/6] 0.20/0.26 15. non_recursive : [eval_start_bb0_in/6] 0.20/0.26 16. non_recursive : [eval_start_start/6] 0.20/0.26 0.20/0.26 #### Obtained direct recursion through partial evaluation 0.20/0.26 0. SCC is partially evaluated into eval_start_bb1_in/3 0.20/0.26 1. SCC is partially evaluated into eval_start_bb4_in/3 0.20/0.26 2. SCC is completely evaluated into other SCCs 0.20/0.26 3. SCC is completely evaluated into other SCCs 0.20/0.26 4. SCC is completely evaluated into other SCCs 0.20/0.26 5. SCC is partially evaluated into eval_start_bb4_in_loop_cont/7 0.20/0.26 6. SCC is partially evaluated into eval_start_10/6 0.20/0.26 7. SCC is completely evaluated into other SCCs 0.20/0.26 8. SCC is completely evaluated into other SCCs 0.20/0.26 9. SCC is completely evaluated into other SCCs 0.20/0.26 10. SCC is partially evaluated into eval_start_bb1_in_loop_cont/7 0.20/0.26 11. SCC is partially evaluated into eval_start_3/6 0.20/0.26 12. SCC is completely evaluated into other SCCs 0.20/0.26 13. SCC is completely evaluated into other SCCs 0.20/0.26 14. SCC is completely evaluated into other SCCs 0.20/0.26 15. SCC is completely evaluated into other SCCs 0.20/0.26 16. SCC is partially evaluated into eval_start_start/6 0.20/0.26 0.20/0.26 Control-Flow Refinement of Cost Relations 0.20/0.26 ===================================== 0.20/0.26 0.20/0.26 ### Specialization of cost equations eval_start_bb1_in/3 0.20/0.26 * CE 5 is refined into CE [14] 0.20/0.26 * CE 4 is refined into CE [15] 0.20/0.26 * CE 3 is refined into CE [16] 0.20/0.26 0.20/0.26 0.20/0.26 ### Cost equations --> "Loop" of eval_start_bb1_in/3 0.20/0.26 * CEs [16] --> Loop 14 0.20/0.26 * CEs [14] --> Loop 15 0.20/0.26 * CEs [15] --> Loop 16 0.20/0.26 0.20/0.26 ### Ranking functions of CR eval_start_bb1_in(V__0,B,C) 0.20/0.26 * RF of phase [14]: [V__0-100] 0.20/0.26 0.20/0.26 #### Partial ranking functions of CR eval_start_bb1_in(V__0,B,C) 0.20/0.26 * Partial RF of phase [14]: 0.20/0.26 - RF of loop [14:1]: 0.20/0.26 V__0-100 0.20/0.26 0.20/0.26 0.20/0.26 ### Specialization of cost equations eval_start_bb4_in/3 0.20/0.26 * CE 10 is refined into CE [17] 0.20/0.26 * CE 11 is refined into CE [18] 0.20/0.26 * CE 9 is refined into CE [19] 0.20/0.26 0.20/0.26 0.20/0.26 ### Cost equations --> "Loop" of eval_start_bb4_in/3 0.20/0.26 * CEs [19] --> Loop 17 0.20/0.26 * CEs [17] --> Loop 18 0.20/0.26 * CEs [18] --> Loop 19 0.20/0.26 0.20/0.26 ### Ranking functions of CR eval_start_bb4_in(V__1,B,C) 0.20/0.26 * RF of phase [17]: [V__1+1] 0.20/0.26 0.20/0.26 #### Partial ranking functions of CR eval_start_bb4_in(V__1,B,C) 0.20/0.26 * Partial RF of phase [17]: 0.20/0.26 - RF of loop [17:1]: 0.20/0.26 V__1+1 0.20/0.26 0.20/0.26 0.20/0.26 ### Specialization of cost equations eval_start_bb4_in_loop_cont/7 0.20/0.26 * CE 12 is refined into CE [20] 0.20/0.26 * CE 13 is refined into CE [21] 0.20/0.26 0.20/0.26 0.20/0.26 ### Cost equations --> "Loop" of eval_start_bb4_in_loop_cont/7 0.20/0.26 * CEs [20] --> Loop 20 0.20/0.26 * CEs [21] --> Loop 21 0.20/0.26 0.20/0.26 ### Ranking functions of CR eval_start_bb4_in_loop_cont(A,B,C,D,E,F,G) 0.20/0.26 0.20/0.26 #### Partial ranking functions of CR eval_start_bb4_in_loop_cont(A,B,C,D,E,F,G) 0.20/0.26 0.20/0.26 0.20/0.26 ### Specialization of cost equations eval_start_10/6 0.20/0.26 * CE 8 is refined into CE [22,23,24,25] 0.20/0.26 0.20/0.26 0.20/0.26 ### Cost equations --> "Loop" of eval_start_10/6 0.20/0.26 * CEs [22] --> Loop 22 0.20/0.26 * CEs [23,24] --> Loop 23 0.20/0.26 * CEs [25] --> Loop 24 0.20/0.26 0.20/0.26 ### Ranking functions of CR eval_start_10(V__0,V__1,V_3,V_i,V_k,B) 0.20/0.26 0.20/0.26 #### Partial ranking functions of CR eval_start_10(V__0,V__1,V_3,V_i,V_k,B) 0.20/0.26 0.20/0.26 0.20/0.26 ### Specialization of cost equations eval_start_bb1_in_loop_cont/7 0.20/0.26 * CE 7 is refined into CE [26] 0.20/0.26 * CE 6 is refined into CE [27,28,29] 0.20/0.26 0.20/0.26 0.20/0.26 ### Cost equations --> "Loop" of eval_start_bb1_in_loop_cont/7 0.20/0.26 * CEs [26] --> Loop 25 0.20/0.26 * CEs [29] --> Loop 26 0.20/0.26 * CEs [28] --> Loop 27 0.20/0.26 * CEs [27] --> Loop 28 0.20/0.26 0.20/0.26 ### Ranking functions of CR eval_start_bb1_in_loop_cont(A,B,C,D,E,F,G) 0.20/0.26 0.20/0.26 #### Partial ranking functions of CR eval_start_bb1_in_loop_cont(A,B,C,D,E,F,G) 0.20/0.26 0.20/0.26 0.20/0.26 ### Specialization of cost equations eval_start_3/6 0.20/0.26 * CE 2 is refined into CE [30,31,32,33,34,35,36,37] 0.20/0.26 0.20/0.26 0.20/0.26 ### Cost equations --> "Loop" of eval_start_3/6 0.20/0.26 * CEs [32] --> Loop 29 0.20/0.26 * CEs [30,37] --> Loop 30 0.20/0.26 * CEs [31] --> Loop 31 0.20/0.26 * CEs [35] --> Loop 32 0.20/0.26 * CEs [34] --> Loop 33 0.20/0.26 * CEs [33] --> Loop 34 0.20/0.26 * CEs [36] --> Loop 35 0.20/0.26 0.20/0.26 ### Ranking functions of CR eval_start_3(V__0,V__1,V_3,V_i,V_k,B) 0.20/0.26 0.20/0.26 #### Partial ranking functions of CR eval_start_3(V__0,V__1,V_3,V_i,V_k,B) 0.20/0.26 0.20/0.26 0.20/0.26 ### Specialization of cost equations eval_start_start/6 0.20/0.26 * CE 1 is refined into CE [38,39,40,41,42,43,44] 0.20/0.26 0.20/0.26 0.20/0.26 ### Cost equations --> "Loop" of eval_start_start/6 0.20/0.26 * CEs [44] --> Loop 36 0.20/0.26 * CEs [43] --> Loop 37 0.20/0.26 * CEs [42] --> Loop 38 0.20/0.26 * CEs [41] --> Loop 39 0.20/0.26 * CEs [40] --> Loop 40 0.20/0.26 * CEs [39] --> Loop 41 0.20/0.26 * CEs [38] --> Loop 42 0.20/0.26 0.20/0.26 ### Ranking functions of CR eval_start_start(V__0,V__1,V_3,V_i,V_k,B) 0.20/0.26 0.20/0.26 #### Partial ranking functions of CR eval_start_start(V__0,V__1,V_3,V_i,V_k,B) 0.20/0.26 0.20/0.26 0.20/0.26 Computing Bounds 0.20/0.26 ===================================== 0.20/0.26 0.20/0.26 #### Cost of chains of eval_start_bb1_in(V__0,B,C): 0.20/0.26 * Chain [[14],16]: 1*it(14)+0 0.20/0.26 Such that:it(14) =< V__0 0.20/0.26 0.20/0.26 with precondition: [B=2,C=100,V__0>=101] 0.20/0.26 0.20/0.26 * Chain [[14],15]: 1*it(14)+0 0.20/0.26 Such that:it(14) =< V__0 0.20/0.26 0.20/0.26 with precondition: [B=3,V__0>=101] 0.20/0.26 0.20/0.26 * Chain [16]: 0 0.20/0.26 with precondition: [B=2,V__0=C,100>=V__0] 0.20/0.26 0.20/0.26 * Chain [15]: 0 0.20/0.26 with precondition: [B=3] 0.20/0.26 0.20/0.26 0.20/0.26 #### Cost of chains of eval_start_bb4_in(V__1,B,C): 0.20/0.26 * Chain [[17],19]: 1*it(17)+0 0.20/0.26 Such that:it(17) =< V__1+1 0.20/0.26 0.20/0.26 with precondition: [B=3,V__1>=0] 0.20/0.26 0.20/0.26 * Chain [[17],18]: 1*it(17)+0 0.20/0.26 Such that:it(17) =< V__1+1 0.20/0.26 0.20/0.26 with precondition: [B=4,C+1=0,V__1>=0] 0.20/0.26 0.20/0.26 * Chain [19]: 0 0.20/0.26 with precondition: [B=3] 0.20/0.26 0.20/0.26 * Chain [18]: 0 0.20/0.26 with precondition: [B=4,V__1=C,0>=V__1+1] 0.20/0.26 0.20/0.26 0.20/0.26 #### Cost of chains of eval_start_bb4_in_loop_cont(A,B,C,D,E,F,G): 0.20/0.26 * Chain [21]: 0 0.20/0.26 with precondition: [A=3,D=B+F+50] 0.20/0.26 0.20/0.26 * Chain [20]: 0 0.20/0.26 with precondition: [A=4,D=B+F+50] 0.20/0.26 0.20/0.26 0.20/0.26 #### Cost of chains of eval_start_10(V__0,V__1,V_3,V_i,V_k,B): 0.20/0.26 * Chain [24]: 0 0.20/0.26 with precondition: [V__0+V_k+50=V_3,0>=V__0+V_k+51] 0.20/0.26 0.20/0.26 * Chain [23]: 2*s(1)+0 0.20/0.26 Such that:aux(1) =< V_3+1 0.20/0.26 s(1) =< aux(1) 0.20/0.26 0.20/0.26 with precondition: [V__0+V_k+50=V_3,V__0+V_k+50>=0] 0.20/0.26 0.20/0.26 * Chain [22]: 0 0.20/0.26 with precondition: [V_3=V__0+V_k+50] 0.20/0.26 0.20/0.26 0.20/0.26 #### Cost of chains of eval_start_bb1_in_loop_cont(A,B,C,D,E,F,G): 0.20/0.26 * Chain [28]: 0 0.20/0.26 with precondition: [A=2] 0.20/0.26 0.20/0.26 * Chain [27]: 0 0.20/0.26 with precondition: [A=2,0>=B+F+51] 0.20/0.26 0.20/0.26 * Chain [26]: 2*s(4)+0 0.20/0.26 Such that:s(3) =< B+F+51 0.20/0.26 s(4) =< s(3) 0.20/0.26 0.20/0.26 with precondition: [A=2,B+F+50>=0] 0.20/0.26 0.20/0.26 * Chain [25]: 0 0.20/0.26 with precondition: [A=3] 0.20/0.26 0.20/0.26 0.20/0.26 #### Cost of chains of eval_start_3(V__0,V__1,V_3,V_i,V_k,B): 0.20/0.26 * Chain [35]: 0 0.20/0.26 with precondition: [] 0.20/0.26 0.20/0.26 * Chain [34]: 0 0.20/0.26 with precondition: [100>=V_i] 0.20/0.26 0.20/0.26 * Chain [33]: 0 0.20/0.26 with precondition: [100>=V_i,0>=V_i+V_k+51] 0.20/0.26 0.20/0.26 * Chain [32]: 2*s(6)+0 0.20/0.26 Such that:s(5) =< V_i+V_k+51 0.20/0.26 s(6) =< s(5) 0.20/0.26 0.20/0.26 with precondition: [100>=V_i,V_i+V_k+50>=0] 0.20/0.26 0.20/0.26 * Chain [31]: 1*s(7)+0 0.20/0.26 Such that:s(7) =< V_i 0.20/0.26 0.20/0.26 with precondition: [0>=V_k+151,V_i>=101] 0.20/0.26 0.20/0.26 * Chain [30]: 2*s(8)+0 0.20/0.26 Such that:aux(2) =< V_i 0.20/0.26 s(8) =< aux(2) 0.20/0.26 0.20/0.26 with precondition: [V_i>=101] 0.20/0.26 0.20/0.26 * Chain [29]: 1*s(10)+2*s(12)+0 0.20/0.26 Such that:s(10) =< V_i 0.20/0.26 s(11) =< V_k+151 0.20/0.26 s(12) =< s(11) 0.20/0.26 0.20/0.26 with precondition: [V_i>=101,V_k+150>=0] 0.20/0.26 0.20/0.26 0.20/0.26 #### Cost of chains of eval_start_start(V__0,V__1,V_3,V_i,V_k,B): 0.20/0.26 * Chain [42]: 0 0.20/0.26 with precondition: [] 0.20/0.26 0.20/0.26 * Chain [41]: 0 0.20/0.26 with precondition: [100>=V_i] 0.20/0.26 0.20/0.26 * Chain [40]: 0 0.20/0.26 with precondition: [100>=V_i,0>=V_i+V_k+51] 0.20/0.26 0.20/0.26 * Chain [39]: 2*s(14)+0 0.20/0.26 Such that:s(13) =< V_i+V_k+51 0.20/0.26 s(14) =< s(13) 0.20/0.26 0.20/0.26 with precondition: [100>=V_i,V_i+V_k+50>=0] 0.20/0.26 0.20/0.26 * Chain [38]: 1*s(15)+0 0.20/0.26 Such that:s(15) =< V_i 0.20/0.26 0.20/0.26 with precondition: [0>=V_k+151,V_i>=101] 0.20/0.26 0.20/0.26 * Chain [37]: 2*s(17)+0 0.20/0.26 Such that:s(16) =< V_i 0.20/0.26 s(17) =< s(16) 0.20/0.26 0.20/0.26 with precondition: [V_i>=101] 0.20/0.26 0.20/0.26 * Chain [36]: 1*s(18)+2*s(20)+0 0.20/0.26 Such that:s(18) =< V_i 0.20/0.26 s(19) =< V_k+151 0.20/0.26 s(20) =< s(19) 0.20/0.26 0.20/0.26 with precondition: [V_i>=101,V_k+150>=0] 0.20/0.26 0.20/0.26 0.20/0.26 Closed-form bounds of eval_start_start(V__0,V__1,V_3,V_i,V_k,B): 0.20/0.26 ------------------------------------- 0.20/0.27 * Chain [42] with precondition: [] 0.20/0.27 - Upper bound: 0 0.20/0.27 - Complexity: constant 0.20/0.27 * Chain [41] with precondition: [100>=V_i] 0.20/0.27 - Upper bound: 0 0.20/0.27 - Complexity: constant 0.20/0.27 * Chain [40] with precondition: [100>=V_i,0>=V_i+V_k+51] 0.20/0.27 - Upper bound: 0 0.20/0.27 - Complexity: constant 0.20/0.27 * Chain [39] with precondition: [100>=V_i,V_i+V_k+50>=0] 0.20/0.27 - Upper bound: 2*V_i+2*V_k+102 0.20/0.27 - Complexity: n 0.20/0.27 * Chain [38] with precondition: [0>=V_k+151,V_i>=101] 0.20/0.27 - Upper bound: V_i 0.20/0.27 - Complexity: n 0.20/0.27 * Chain [37] with precondition: [V_i>=101] 0.20/0.27 - Upper bound: 2*V_i 0.20/0.27 - Complexity: n 0.20/0.27 * Chain [36] with precondition: [V_i>=101,V_k+150>=0] 0.20/0.27 - Upper bound: V_i+2*V_k+302 0.20/0.27 - Complexity: n 0.20/0.27 0.20/0.27 ### Maximum cost of eval_start_start(V__0,V__1,V_3,V_i,V_k,B): max([nat(V_i+V_k+51)*2,nat(V_i)+max([nat(V_i),nat(V_k+151)*2])]) 0.20/0.27 Asymptotic class: n 0.20/0.27 * Total analysis performed in 193 ms. 0.20/0.27 0.27/0.37 EOF