0.05/0.27 WORST_CASE(?,O(n^2)) 0.05/0.27 0.05/0.27 Preprocessing Cost Relations 0.05/0.27 ===================================== 0.05/0.27 0.05/0.27 #### Computed strongly connected components 0.05/0.27 0. recursive : [eval_perfect_bb2_in/4,eval_perfect_bb3_in/4] 0.05/0.27 1. recursive : [eval_perfect_bb1_in/5,eval_perfect_bb2_in_loop_cont/8,eval_perfect_bb4_in/7] 0.05/0.27 2. non_recursive : [eval_perfect_stop/1] 0.05/0.27 3. non_recursive : [eval_perfect_bb6_in/1] 0.05/0.27 4. non_recursive : [eval_perfect_bb5_in/2] 0.05/0.27 5. non_recursive : [eval_perfect_bb1_in_loop_cont/3] 0.05/0.27 6. non_recursive : [eval_perfect_bb0_in/2] 0.05/0.27 7. non_recursive : [eval_perfect_start/2] 0.05/0.27 0.05/0.27 #### Obtained direct recursion through partial evaluation 0.05/0.27 0. SCC is partially evaluated into eval_perfect_bb2_in/4 0.05/0.27 1. SCC is partially evaluated into eval_perfect_bb1_in/5 0.05/0.27 2. SCC is completely evaluated into other SCCs 0.05/0.27 3. SCC is completely evaluated into other SCCs 0.05/0.27 4. SCC is partially evaluated into eval_perfect_bb5_in/2 0.05/0.27 5. SCC is completely evaluated into other SCCs 0.05/0.27 6. SCC is partially evaluated into eval_perfect_bb0_in/2 0.05/0.27 7. SCC is partially evaluated into eval_perfect_start/2 0.05/0.27 0.05/0.27 Control-Flow Refinement of Cost Relations 0.05/0.27 ===================================== 0.05/0.27 0.05/0.27 ### Specialization of cost equations eval_perfect_bb2_in/4 0.05/0.27 * CE 12 is refined into CE [13] 0.05/0.27 * CE 11 is refined into CE [14] 0.05/0.27 0.05/0.27 0.05/0.27 ### Cost equations --> "Loop" of eval_perfect_bb2_in/4 0.05/0.27 * CEs [14] --> Loop 12 0.05/0.27 * CEs [13] --> Loop 13 0.05/0.27 0.05/0.27 ### Ranking functions of CR eval_perfect_bb2_in(V_1,V_y2_1,B,C) 0.05/0.27 * RF of phase [12]: [-V_1+V_y2_1+1,V_y2_1] 0.05/0.27 0.05/0.27 #### Partial ranking functions of CR eval_perfect_bb2_in(V_1,V_y2_1,B,C) 0.05/0.27 * Partial RF of phase [12]: 0.05/0.27 - RF of loop [12:1]: 0.05/0.27 -V_1+V_y2_1+1 0.05/0.27 V_y2_1 0.05/0.27 0.05/0.27 0.05/0.27 ### Specialization of cost equations eval_perfect_bb1_in/5 0.05/0.27 * CE 7 is refined into CE [15] 0.05/0.27 * CE 6 is refined into CE [16] 0.05/0.27 * CE 4 is refined into CE [17] 0.05/0.27 * CE 5 is discarded (unfeasible) 0.05/0.27 0.05/0.27 0.05/0.27 ### Cost equations --> "Loop" of eval_perfect_bb1_in/5 0.05/0.27 * CEs [16] --> Loop 14 0.05/0.27 * CEs [17] --> Loop 15 0.05/0.27 * CEs [15] --> Loop 16 0.05/0.27 0.05/0.27 ### Ranking functions of CR eval_perfect_bb1_in(V_x,V_y1_0_sink,V_y3_0,B,C) 0.05/0.27 * RF of phase [14,15]: [V_y1_0_sink-1] 0.05/0.27 0.05/0.27 #### Partial ranking functions of CR eval_perfect_bb1_in(V_x,V_y1_0_sink,V_y3_0,B,C) 0.05/0.27 * Partial RF of phase [14,15]: 0.05/0.27 - RF of loop [14:1]: 0.05/0.27 V_y1_0_sink-1 0.05/0.27 - RF of loop [15:1]: 0.05/0.27 V_y1_0_sink-2 0.05/0.27 0.05/0.27 0.05/0.27 ### Specialization of cost equations eval_perfect_bb5_in/2 0.05/0.27 * CE 9 is refined into CE [18] 0.05/0.27 * CE 8 is refined into CE [19] 0.05/0.27 * CE 10 is refined into CE [20] 0.05/0.27 0.05/0.27 0.05/0.27 ### Cost equations --> "Loop" of eval_perfect_bb5_in/2 0.05/0.27 * CEs [18] --> Loop 17 0.05/0.27 * CEs [19] --> Loop 18 0.05/0.27 * CEs [20] --> Loop 19 0.05/0.27 0.05/0.27 ### Ranking functions of CR eval_perfect_bb5_in(V_y3_0,B) 0.05/0.27 0.05/0.27 #### Partial ranking functions of CR eval_perfect_bb5_in(V_y3_0,B) 0.05/0.27 0.05/0.27 0.05/0.27 ### Specialization of cost equations eval_perfect_bb0_in/2 0.05/0.27 * CE 3 is refined into CE [21,22,23] 0.05/0.27 * CE 2 is refined into CE [24] 0.05/0.27 0.05/0.27 0.05/0.27 ### Cost equations --> "Loop" of eval_perfect_bb0_in/2 0.05/0.27 * CEs [21,22,23] --> Loop 20 0.05/0.27 * CEs [24] --> Loop 21 0.05/0.27 0.05/0.27 ### Ranking functions of CR eval_perfect_bb0_in(V_x,B) 0.05/0.27 0.05/0.27 #### Partial ranking functions of CR eval_perfect_bb0_in(V_x,B) 0.05/0.27 0.05/0.27 0.05/0.27 ### Specialization of cost equations eval_perfect_start/2 0.05/0.27 * CE 1 is refined into CE [25,26] 0.05/0.27 0.05/0.27 0.05/0.27 ### Cost equations --> "Loop" of eval_perfect_start/2 0.05/0.27 * CEs [26] --> Loop 22 0.05/0.27 * CEs [25] --> Loop 23 0.05/0.27 0.05/0.27 ### Ranking functions of CR eval_perfect_start(V_x,B) 0.05/0.27 0.05/0.27 #### Partial ranking functions of CR eval_perfect_start(V_x,B) 0.05/0.27 0.05/0.27 0.05/0.27 Computing Bounds 0.05/0.27 ===================================== 0.05/0.27 0.05/0.27 #### Cost of chains of eval_perfect_bb2_in(V_1,V_y2_1,B,C): 0.05/0.27 * Chain [[12],13]: 1*it(12)+0 0.05/0.27 Such that:it(12) =< -V_1+V_y2_1+1 0.05/0.27 0.05/0.27 with precondition: [B=2,C>=0,V_1>=C+1,V_y2_1>=V_1+C] 0.05/0.27 0.05/0.27 0.05/0.27 #### Cost of chains of eval_perfect_bb1_in(V_x,V_y1_0_sink,V_y3_0,B,C): 0.05/0.27 * Chain [[14,15],16]: 2*it(14)+1*s(5)+1*s(6)+0 0.05/0.27 Such that:aux(1) =< V_x 0.05/0.27 aux(5) =< V_y1_0_sink 0.05/0.27 it(14) =< aux(5) 0.05/0.27 aux(2) =< aux(1) 0.05/0.27 s(5) =< it(14)*aux(1) 0.05/0.27 s(6) =< it(14)*aux(2) 0.05/0.27 0.05/0.27 with precondition: [B=3,V_y1_0_sink>=2,V_x>=V_y1_0_sink,V_x>=V_y3_0,V_y3_0>=C+1] 0.05/0.27 0.05/0.27 0.05/0.27 #### Cost of chains of eval_perfect_bb5_in(V_y3_0,B): 0.05/0.27 * Chain [19]: 0 0.05/0.27 with precondition: [V_y3_0=0] 0.05/0.27 0.05/0.27 * Chain [18]: 0 0.05/0.27 with precondition: [0>=V_y3_0+1] 0.05/0.27 0.05/0.27 * Chain [17]: 0 0.05/0.27 with precondition: [V_y3_0>=1] 0.05/0.27 0.05/0.27 0.05/0.27 #### Cost of chains of eval_perfect_bb0_in(V_x,B): 0.05/0.27 * Chain [21]: 0 0.05/0.27 with precondition: [1>=V_x] 0.05/0.27 0.05/0.27 * Chain [20]: 6*s(9)+3*s(11)+3*s(12)+0 0.05/0.27 Such that:aux(9) =< V_x 0.05/0.27 s(9) =< aux(9) 0.05/0.27 s(10) =< aux(9) 0.05/0.27 s(11) =< s(9)*aux(9) 0.05/0.27 s(12) =< s(9)*s(10) 0.05/0.27 0.05/0.27 with precondition: [V_x>=2] 0.05/0.27 0.05/0.27 0.05/0.27 #### Cost of chains of eval_perfect_start(V_x,B): 0.05/0.27 * Chain [23]: 0 0.05/0.27 with precondition: [1>=V_x] 0.05/0.27 0.05/0.27 * Chain [22]: 6*s(26)+3*s(28)+3*s(29)+0 0.05/0.27 Such that:s(25) =< V_x 0.05/0.27 s(26) =< s(25) 0.05/0.27 s(27) =< s(25) 0.05/0.27 s(28) =< s(26)*s(25) 0.05/0.27 s(29) =< s(26)*s(27) 0.05/0.27 0.05/0.27 with precondition: [V_x>=2] 0.05/0.27 0.05/0.27 0.05/0.27 Closed-form bounds of eval_perfect_start(V_x,B): 0.05/0.27 ------------------------------------- 0.05/0.27 * Chain [23] with precondition: [1>=V_x] 0.05/0.27 - Upper bound: 0 0.05/0.27 - Complexity: constant 0.05/0.27 * Chain [22] with precondition: [V_x>=2] 0.05/0.27 - Upper bound: 6*V_x*V_x+6*V_x 0.05/0.27 - Complexity: n^2 0.05/0.27 0.05/0.27 ### Maximum cost of eval_perfect_start(V_x,B): nat(V_x)*6*nat(V_x)+nat(V_x)*6 0.05/0.27 Asymptotic class: n^2 0.05/0.27 * Total analysis performed in 190 ms. 0.05/0.27 0.05/0.37 EOF