0.06/0.24 WORST_CASE(?,O(n^1)) 0.06/0.24 0.06/0.24 Preprocessing Cost Relations 0.06/0.24 ===================================== 0.06/0.24 0.06/0.24 #### Computed strongly connected components 0.06/0.24 0. recursive : [eval_rank2_3/4,eval_rank2_4/5,eval_rank2_bb3_in/4,eval_rank2_bb4_in/4,eval_rank2_bb5_in/5] 0.06/0.24 1. recursive : [eval_rank2__critedge_in/5,eval_rank2_bb1_in/3,eval_rank2_bb2_in/3,eval_rank2_bb3_in_loop_cont/6] 0.06/0.24 2. non_recursive : [eval_rank2_stop/1] 0.06/0.24 3. non_recursive : [eval_rank2_bb6_in/1] 0.06/0.24 4. non_recursive : [eval_rank2_bb1_in_loop_cont/2] 0.06/0.24 5. non_recursive : [eval_rank2_bb0_in/2] 0.06/0.24 6. non_recursive : [eval_rank2_start/2] 0.06/0.24 0.06/0.24 #### Obtained direct recursion through partial evaluation 0.06/0.24 0. SCC is partially evaluated into eval_rank2_bb3_in/4 0.06/0.24 1. SCC is partially evaluated into eval_rank2_bb1_in/3 0.06/0.24 2. SCC is completely evaluated into other SCCs 0.06/0.24 3. SCC is completely evaluated into other SCCs 0.06/0.24 4. SCC is completely evaluated into other SCCs 0.06/0.24 5. SCC is partially evaluated into eval_rank2_bb0_in/2 0.06/0.24 6. SCC is partially evaluated into eval_rank2_start/2 0.06/0.24 0.06/0.24 Control-Flow Refinement of Cost Relations 0.06/0.24 ===================================== 0.06/0.24 0.06/0.24 ### Specialization of cost equations eval_rank2_bb3_in/4 0.06/0.24 * CE 7 is refined into CE [8] 0.06/0.24 * CE 5 is refined into CE [9] 0.06/0.24 * CE 6 is refined into CE [10] 0.06/0.24 0.06/0.24 0.06/0.24 ### Cost equations --> "Loop" of eval_rank2_bb3_in/4 0.06/0.24 * CEs [10] --> Loop 8 0.06/0.24 * CEs [8] --> Loop 9 0.06/0.24 * CEs [9] --> Loop 10 0.06/0.24 0.06/0.24 ### Ranking functions of CR eval_rank2_bb3_in(V_1,V_y_1,B,C) 0.06/0.24 * RF of phase [8]: [-V_1+V_y_1+1,V_y_1] 0.06/0.24 0.06/0.24 #### Partial ranking functions of CR eval_rank2_bb3_in(V_1,V_y_1,B,C) 0.06/0.24 * Partial RF of phase [8]: 0.06/0.24 - RF of loop [8:1]: 0.06/0.24 -V_1+V_y_1+1 0.06/0.24 V_y_1 0.06/0.24 0.06/0.24 0.06/0.24 ### Specialization of cost equations eval_rank2_bb1_in/3 0.06/0.24 * CE 4 is refined into CE [11] 0.06/0.24 * CE 3 is refined into CE [12,13,14,15] 0.06/0.24 0.06/0.24 0.06/0.24 ### Cost equations --> "Loop" of eval_rank2_bb1_in/3 0.06/0.24 * CEs [15] --> Loop 11 0.06/0.24 * CEs [13] --> Loop 12 0.06/0.24 * CEs [14] --> Loop 13 0.06/0.24 * CEs [12] --> Loop 14 0.06/0.24 * CEs [11] --> Loop 15 0.06/0.24 0.06/0.24 ### Ranking functions of CR eval_rank2_bb1_in(V_x_0,V_y_0,B) 0.06/0.24 * RF of phase [11,12,14]: [V_x_0/2-1/2] 0.06/0.24 0.06/0.24 #### Partial ranking functions of CR eval_rank2_bb1_in(V_x_0,V_y_0,B) 0.06/0.24 * Partial RF of phase [11,12,14]: 0.06/0.24 - RF of loop [11:1,12:1]: 0.06/0.24 V_x_0/2-1/2 0.06/0.24 - RF of loop [14:1]: 0.06/0.24 V_x_0-1 0.06/0.24 0.06/0.24 0.06/0.24 ### Specialization of cost equations eval_rank2_bb0_in/2 0.06/0.24 * CE 2 is refined into CE [16,17] 0.06/0.24 0.06/0.24 0.06/0.24 ### Cost equations --> "Loop" of eval_rank2_bb0_in/2 0.06/0.24 * CEs [17] --> Loop 16 0.06/0.24 * CEs [16] --> Loop 17 0.06/0.24 0.06/0.24 ### Ranking functions of CR eval_rank2_bb0_in(V_m,B) 0.06/0.24 0.06/0.24 #### Partial ranking functions of CR eval_rank2_bb0_in(V_m,B) 0.06/0.24 0.06/0.24 0.06/0.24 ### Specialization of cost equations eval_rank2_start/2 0.06/0.24 * CE 1 is refined into CE [18,19] 0.06/0.24 0.06/0.24 0.06/0.24 ### Cost equations --> "Loop" of eval_rank2_start/2 0.06/0.24 * CEs [19] --> Loop 18 0.06/0.24 * CEs [18] --> Loop 19 0.06/0.24 0.06/0.24 ### Ranking functions of CR eval_rank2_start(V_m,B) 0.06/0.24 0.06/0.24 #### Partial ranking functions of CR eval_rank2_start(V_m,B) 0.06/0.24 0.06/0.24 0.06/0.24 Computing Bounds 0.06/0.24 ===================================== 0.06/0.24 0.06/0.24 #### Cost of chains of eval_rank2_bb3_in(V_1,V_y_1,B,C): 0.06/0.24 * Chain [[8],10]: 1*it(8)+0 0.06/0.24 Such that:it(8) =< V_y_1-C 0.06/0.24 0.06/0.24 with precondition: [B=2,V_1>=1,C>=V_1,V_y_1>=C+1] 0.06/0.24 0.06/0.24 * Chain [[8],9]: 1*it(8)+0 0.06/0.24 Such that:it(8) =< V_y_1-C 0.06/0.24 0.06/0.24 with precondition: [B=2,V_1=C+1,V_1>=1,V_y_1>=V_1] 0.06/0.24 0.06/0.24 * Chain [10]: 0 0.06/0.24 with precondition: [B=2,V_y_1=C,V_1>=1,V_y_1>=V_1] 0.06/0.24 0.06/0.24 * Chain [9]: 0 0.06/0.24 with precondition: [B=2,V_y_1=C,V_1>=1,V_1>=V_y_1+1] 0.06/0.24 0.06/0.24 0.06/0.24 #### Cost of chains of eval_rank2_bb1_in(V_x_0,V_y_0,B): 0.06/0.24 * Chain [[11,12,14],15]: 2*it(11)+1*it(14)+2*s(5)+0 0.06/0.24 Such that:it(14) =< V_x_0 0.06/0.24 aux(5) =< V_x_0/2 0.06/0.24 aux(6) =< V_x_0/2+V_y_0 0.06/0.24 it(11) =< aux(5) 0.06/0.24 it(14) =< aux(5) 0.06/0.24 s(5) =< aux(6) 0.06/0.24 it(14) =< aux(6) 0.06/0.24 0.06/0.24 with precondition: [B=3,V_x_0>=2,V_y_0>=0] 0.06/0.24 0.06/0.24 * Chain [15]: 0 0.06/0.24 with precondition: [B=3,1>=V_x_0] 0.06/0.24 0.06/0.24 0.06/0.24 #### Cost of chains of eval_rank2_bb0_in(V_m,B): 0.06/0.24 * Chain [17]: 0 0.06/0.24 with precondition: [1>=V_m] 0.06/0.24 0.06/0.24 * Chain [16]: 1*s(7)+2*s(10)+2*s(11)+0 0.06/0.24 Such that:s(7) =< V_m 0.06/0.24 s(8) =< V_m/2 0.06/0.24 s(9) =< 3/2*V_m 0.06/0.24 s(10) =< s(8) 0.06/0.24 s(7) =< s(8) 0.06/0.24 s(11) =< s(9) 0.06/0.24 s(7) =< s(9) 0.06/0.24 0.06/0.24 with precondition: [V_m>=2] 0.06/0.24 0.06/0.24 0.06/0.24 #### Cost of chains of eval_rank2_start(V_m,B): 0.06/0.24 * Chain [19]: 0 0.06/0.24 with precondition: [1>=V_m] 0.06/0.24 0.06/0.24 * Chain [18]: 1*s(12)+2*s(15)+2*s(16)+0 0.06/0.24 Such that:s(12) =< V_m 0.06/0.24 s(13) =< V_m/2 0.06/0.24 s(14) =< 3/2*V_m 0.06/0.24 s(15) =< s(13) 0.06/0.24 s(12) =< s(13) 0.06/0.24 s(16) =< s(14) 0.06/0.24 s(12) =< s(14) 0.06/0.24 0.06/0.24 with precondition: [V_m>=2] 0.06/0.24 0.06/0.24 0.06/0.24 Closed-form bounds of eval_rank2_start(V_m,B): 0.06/0.24 ------------------------------------- 0.06/0.24 * Chain [19] with precondition: [1>=V_m] 0.06/0.24 - Upper bound: 0 0.06/0.24 - Complexity: constant 0.06/0.24 * Chain [18] with precondition: [V_m>=2] 0.06/0.24 - Upper bound: 5*V_m 0.06/0.24 - Complexity: n 0.06/0.24 0.06/0.24 ### Maximum cost of eval_rank2_start(V_m,B): nat(3/2*V_m)*2+nat(V_m)+nat(V_m/2)*2 0.06/0.24 Asymptotic class: n 0.06/0.24 * Total analysis performed in 158 ms. 0.06/0.24 0.06/0.34 EOF