0.03/0.30 WORST_CASE(?,O(n^1)) 0.03/0.30 0.03/0.30 Preprocessing Cost Relations 0.03/0.30 ===================================== 0.03/0.30 0.03/0.30 #### Computed strongly connected components 0.03/0.30 0. recursive : [eval_start_4/8,eval_start_5/8,eval_start_bb1_in/8,eval_start_bb2_in/8,eval_start_bb3_in/8] 0.03/0.30 1. recursive : [eval_start_bb4_in/4,eval_start_bb5_in/4] 0.03/0.30 2. non_recursive : [eval_start_stop/5] 0.03/0.30 3. non_recursive : [eval_start_bb6_in/5] 0.03/0.30 4. non_recursive : [exit_location/1] 0.03/0.30 5. non_recursive : [eval_start_bb4_in_loop_cont/6] 0.03/0.30 6. non_recursive : [eval_start_bb1_in_loop_cont/6] 0.03/0.30 7. non_recursive : [eval_start_3/5] 0.03/0.30 8. non_recursive : [eval_start_2/5] 0.03/0.30 9. non_recursive : [eval_start_1/5] 0.03/0.30 10. non_recursive : [eval_start_0/5] 0.03/0.30 11. non_recursive : [eval_start_bb0_in/5] 0.03/0.30 12. non_recursive : [eval_start_start/5] 0.03/0.30 0.03/0.30 #### Obtained direct recursion through partial evaluation 0.03/0.30 0. SCC is partially evaluated into eval_start_bb1_in/8 0.03/0.30 1. SCC is partially evaluated into eval_start_bb4_in/4 0.03/0.30 2. SCC is completely evaluated into other SCCs 0.03/0.30 3. SCC is completely evaluated into other SCCs 0.03/0.30 4. SCC is completely evaluated into other SCCs 0.03/0.30 5. SCC is partially evaluated into eval_start_bb4_in_loop_cont/6 0.03/0.30 6. SCC is partially evaluated into eval_start_bb1_in_loop_cont/6 0.03/0.30 7. SCC is partially evaluated into eval_start_3/5 0.03/0.30 8. SCC is completely evaluated into other SCCs 0.03/0.30 9. SCC is completely evaluated into other SCCs 0.03/0.30 10. SCC is completely evaluated into other SCCs 0.03/0.30 11. SCC is completely evaluated into other SCCs 0.03/0.30 12. SCC is partially evaluated into eval_start_start/5 0.03/0.30 0.03/0.30 Control-Flow Refinement of Cost Relations 0.03/0.30 ===================================== 0.03/0.30 0.03/0.30 ### Specialization of cost equations eval_start_bb1_in/8 0.03/0.30 * CE 3 is refined into CE [14] 0.03/0.30 * CE 5 is refined into CE [15] 0.03/0.30 * CE 6 is refined into CE [16] 0.03/0.30 * CE 4 is refined into CE [17] 0.03/0.30 0.03/0.30 0.03/0.30 ### Cost equations --> "Loop" of eval_start_bb1_in/8 0.03/0.30 * CEs [17] --> Loop 14 0.03/0.30 * CEs [14] --> Loop 15 0.03/0.30 * CEs [15] --> Loop 16 0.03/0.30 * CEs [16] --> Loop 17 0.03/0.30 0.03/0.30 ### Ranking functions of CR eval_start_bb1_in(V_1,V_n,V_x_0,V_x_1,B,C,D,E) 0.03/0.30 * RF of phase [14]: [V_n-V_x_0] 0.03/0.30 0.03/0.30 #### Partial ranking functions of CR eval_start_bb1_in(V_1,V_n,V_x_0,V_x_1,B,C,D,E) 0.03/0.30 * Partial RF of phase [14]: 0.03/0.30 - RF of loop [14:1]: 0.03/0.30 V_n-V_x_0 0.03/0.30 0.03/0.30 0.03/0.30 ### Specialization of cost equations eval_start_bb4_in/4 0.03/0.30 * CE 11 is refined into CE [18] 0.03/0.30 * CE 10 is refined into CE [19] 0.03/0.30 * CE 9 is refined into CE [20] 0.03/0.30 0.03/0.30 0.03/0.30 ### Cost equations --> "Loop" of eval_start_bb4_in/4 0.03/0.30 * CEs [20] --> Loop 18 0.03/0.30 * CEs [18] --> Loop 19 0.03/0.30 * CEs [19] --> Loop 20 0.03/0.30 0.03/0.30 ### Ranking functions of CR eval_start_bb4_in(V_n,V_x_1,B,C) 0.03/0.30 * RF of phase [18]: [V_n-V_x_1] 0.03/0.30 0.03/0.30 #### Partial ranking functions of CR eval_start_bb4_in(V_n,V_x_1,B,C) 0.03/0.30 * Partial RF of phase [18]: 0.03/0.30 - RF of loop [18:1]: 0.03/0.30 V_n-V_x_1 0.03/0.30 0.03/0.30 0.03/0.30 ### Specialization of cost equations eval_start_bb4_in_loop_cont/6 0.03/0.30 * CE 13 is refined into CE [21] 0.03/0.30 * CE 12 is refined into CE [22] 0.03/0.30 0.03/0.30 0.03/0.30 ### Cost equations --> "Loop" of eval_start_bb4_in_loop_cont/6 0.03/0.30 * CEs [21] --> Loop 21 0.03/0.30 * CEs [22] --> Loop 22 0.03/0.30 0.03/0.30 ### Ranking functions of CR eval_start_bb4_in_loop_cont(A,B,C,D,E,F) 0.03/0.30 0.03/0.30 #### Partial ranking functions of CR eval_start_bb4_in_loop_cont(A,B,C,D,E,F) 0.03/0.30 0.03/0.30 0.03/0.30 ### Specialization of cost equations eval_start_bb1_in_loop_cont/6 0.03/0.30 * CE 8 is refined into CE [23,24,25,26] 0.03/0.30 * CE 7 is refined into CE [27] 0.03/0.30 0.03/0.30 0.03/0.30 ### Cost equations --> "Loop" of eval_start_bb1_in_loop_cont/6 0.03/0.30 * CEs [23,26] --> Loop 23 0.03/0.30 * CEs [24] --> Loop 24 0.03/0.30 * CEs [25] --> Loop 25 0.03/0.30 * CEs [27] --> Loop 26 0.03/0.30 0.03/0.30 ### Ranking functions of CR eval_start_bb1_in_loop_cont(A,B,C,D,E,F) 0.03/0.30 0.03/0.30 #### Partial ranking functions of CR eval_start_bb1_in_loop_cont(A,B,C,D,E,F) 0.03/0.30 0.03/0.30 0.03/0.30 ### Specialization of cost equations eval_start_3/5 0.03/0.30 * CE 2 is refined into CE [28,29,30,31,32,33,34,35,36,37] 0.03/0.30 0.03/0.30 0.03/0.30 ### Cost equations --> "Loop" of eval_start_3/5 0.03/0.30 * CEs [36,37] --> Loop 27 0.03/0.30 * CEs [29,32,33,34,35] --> Loop 28 0.03/0.30 * CEs [30,31] --> Loop 29 0.03/0.30 * CEs [28] --> Loop 30 0.03/0.30 0.03/0.30 ### Ranking functions of CR eval_start_3(V_1,V_n,V_x_0,V_x_1,B) 0.03/0.30 0.03/0.30 #### Partial ranking functions of CR eval_start_3(V_1,V_n,V_x_0,V_x_1,B) 0.03/0.30 0.03/0.30 0.03/0.30 ### Specialization of cost equations eval_start_start/5 0.03/0.30 * CE 1 is refined into CE [38,39,40,41] 0.03/0.30 0.03/0.30 0.03/0.30 ### Cost equations --> "Loop" of eval_start_start/5 0.03/0.30 * CEs [41] --> Loop 31 0.03/0.30 * CEs [40] --> Loop 32 0.03/0.30 * CEs [39] --> Loop 33 0.03/0.30 * CEs [38] --> Loop 34 0.03/0.30 0.03/0.30 ### Ranking functions of CR eval_start_start(V_1,V_n,V_x_0,V_x_1,B) 0.03/0.30 0.03/0.30 #### Partial ranking functions of CR eval_start_start(V_1,V_n,V_x_0,V_x_1,B) 0.03/0.30 0.03/0.30 0.03/0.30 Computing Bounds 0.03/0.30 ===================================== 0.03/0.30 0.03/0.30 #### Cost of chains of eval_start_bb1_in(V_1,V_n,V_x_0,V_x_1,B,C,D,E): 0.03/0.30 * Chain [[14],17]: 1*it(14)+0 0.03/0.30 Such that:it(14) =< V_n-V_x_0 0.03/0.30 0.03/0.30 with precondition: [B=3,V_x_0>=0,V_n>=V_x_0+1] 0.03/0.30 0.03/0.30 * Chain [[14],16]: 1*it(14)+0 0.03/0.30 Such that:it(14) =< -V_x_0+D 0.03/0.30 0.03/0.30 with precondition: [B=4,V_n=D,V_n=E,0>=C,V_x_0>=0,V_n>=V_x_0+1] 0.03/0.30 0.03/0.30 * Chain [[14],15]: 1*it(14)+0 0.03/0.30 Such that:it(14) =< -V_x_0+D 0.03/0.30 0.03/0.30 with precondition: [B=4,D=E,V_x_0>=0,C>=1,D>=V_x_0+1,V_n>=D+1] 0.03/0.30 0.03/0.30 * Chain [17]: 0 0.03/0.30 with precondition: [B=3,V_x_0>=0] 0.03/0.30 0.03/0.30 * Chain [16]: 0 0.03/0.30 with precondition: [B=4,C=V_1,V_x_0=D,V_x_0=E,V_x_0>=0,V_x_0>=V_n] 0.03/0.30 0.03/0.30 * Chain [15]: 0 0.03/0.30 with precondition: [B=4,V_x_0=D,V_x_0=E,V_x_0>=0,C>=1,V_n>=V_x_0+1] 0.03/0.30 0.03/0.30 0.03/0.30 #### Cost of chains of eval_start_bb4_in(V_n,V_x_1,B,C): 0.03/0.30 * Chain [[18],20]: 1*it(18)+0 0.03/0.30 Such that:it(18) =< V_n-V_x_1 0.03/0.30 0.03/0.30 with precondition: [B=2,V_n=C,V_n>=V_x_1+1] 0.03/0.30 0.03/0.30 * Chain [[18],19]: 1*it(18)+0 0.03/0.30 Such that:it(18) =< V_n-V_x_1 0.03/0.30 0.03/0.30 with precondition: [B=3,V_n>=V_x_1+1] 0.03/0.30 0.03/0.30 * Chain [20]: 0 0.03/0.30 with precondition: [B=2,V_x_1=C,V_x_1>=V_n] 0.03/0.30 0.03/0.30 * Chain [19]: 0 0.03/0.30 with precondition: [B=3] 0.03/0.30 0.03/0.30 0.03/0.30 #### Cost of chains of eval_start_bb4_in_loop_cont(A,B,C,D,E,F): 0.03/0.30 * Chain [22]: 0 0.03/0.30 with precondition: [A=2] 0.03/0.30 0.03/0.30 * Chain [21]: 0 0.03/0.30 with precondition: [A=3] 0.03/0.30 0.03/0.30 0.03/0.30 #### Cost of chains of eval_start_bb1_in_loop_cont(A,B,C,D,E,F): 0.03/0.30 * Chain [26]: 0 0.03/0.30 with precondition: [A=3] 0.03/0.30 0.03/0.30 * Chain [25]: 0 0.03/0.30 with precondition: [A=4] 0.03/0.30 0.03/0.30 * Chain [24]: 0 0.03/0.30 with precondition: [A=4,E>=C] 0.03/0.30 0.03/0.30 * Chain [23]: 2*s(1)+0 0.03/0.30 Such that:aux(1) =< C-E 0.03/0.30 s(1) =< aux(1) 0.03/0.30 0.03/0.30 with precondition: [A=4,C>=E+1] 0.03/0.30 0.03/0.30 0.03/0.30 #### Cost of chains of eval_start_3(V_1,V_n,V_x_0,V_x_1,B): 0.03/0.30 * Chain [30]: 0 0.03/0.30 with precondition: [] 0.03/0.30 0.03/0.30 * Chain [29]: 0 0.03/0.30 with precondition: [0>=V_n] 0.03/0.30 0.03/0.30 * Chain [28]: 5*s(3)+0 0.03/0.30 Such that:aux(2) =< V_n 0.03/0.30 s(3) =< aux(2) 0.03/0.30 0.03/0.30 with precondition: [V_n>=1] 0.03/0.30 0.03/0.30 * Chain [27]: 4*s(8)+0 0.03/0.30 Such that:aux(4) =< V_n 0.03/0.30 s(8) =< aux(4) 0.03/0.30 0.03/0.30 with precondition: [V_n>=2] 0.03/0.30 0.03/0.30 0.03/0.30 #### Cost of chains of eval_start_start(V_1,V_n,V_x_0,V_x_1,B): 0.03/0.30 * Chain [34]: 0 0.03/0.30 with precondition: [] 0.03/0.30 0.03/0.30 * Chain [33]: 0 0.03/0.30 with precondition: [0>=V_n] 0.03/0.30 0.03/0.30 * Chain [32]: 5*s(13)+0 0.03/0.30 Such that:s(12) =< V_n 0.03/0.30 s(13) =< s(12) 0.03/0.30 0.03/0.30 with precondition: [V_n>=1] 0.03/0.30 0.03/0.30 * Chain [31]: 4*s(15)+0 0.03/0.30 Such that:s(14) =< V_n 0.03/0.30 s(15) =< s(14) 0.03/0.30 0.03/0.30 with precondition: [V_n>=2] 0.03/0.30 0.03/0.30 0.03/0.30 Closed-form bounds of eval_start_start(V_1,V_n,V_x_0,V_x_1,B): 0.03/0.30 ------------------------------------- 0.03/0.30 * Chain [34] with precondition: [] 0.03/0.30 - Upper bound: 0 0.03/0.30 - Complexity: constant 0.03/0.30 * Chain [33] with precondition: [0>=V_n] 0.03/0.30 - Upper bound: 0 0.03/0.30 - Complexity: constant 0.03/0.30 * Chain [32] with precondition: [V_n>=1] 0.03/0.30 - Upper bound: 5*V_n 0.03/0.30 - Complexity: n 0.03/0.30 * Chain [31] with precondition: [V_n>=2] 0.03/0.30 - Upper bound: 4*V_n 0.03/0.30 - Complexity: n 0.03/0.30 0.03/0.30 ### Maximum cost of eval_start_start(V_1,V_n,V_x_0,V_x_1,B): nat(V_n)*5 0.03/0.30 Asymptotic class: n 0.03/0.30 * Total analysis performed in 229 ms. 0.03/0.30 0.03/0.40 EOF