0.05/0.31 WORST_CASE(?,O(n^2)) 0.05/0.31 0.05/0.31 Preprocessing Cost Relations 0.05/0.31 ===================================== 0.05/0.31 0.05/0.31 #### Computed strongly connected components 0.05/0.31 0. recursive : [eval_perfect2_bb4_in/4,eval_perfect2_bb5_in/4] 0.05/0.31 1. recursive : [eval_perfect2_bb1_in/5,eval_perfect2_bb4_in_loop_cont/8,eval_perfect2_bb6_in/7] 0.05/0.31 2. non_recursive : [eval_perfect2_stop/1] 0.05/0.31 3. non_recursive : [eval_perfect2_bb3_in/1] 0.05/0.31 4. non_recursive : [eval_perfect2_bb2_in/2] 0.05/0.31 5. non_recursive : [eval_perfect2_bb1_in_loop_cont/3] 0.05/0.31 6. non_recursive : [eval_perfect2_bb0_in/2] 0.05/0.31 7. non_recursive : [eval_perfect2_start/2] 0.05/0.31 0.05/0.31 #### Obtained direct recursion through partial evaluation 0.05/0.31 0. SCC is partially evaluated into eval_perfect2_bb4_in/4 0.05/0.31 1. SCC is partially evaluated into eval_perfect2_bb1_in/5 0.05/0.31 2. SCC is completely evaluated into other SCCs 0.05/0.31 3. SCC is completely evaluated into other SCCs 0.05/0.31 4. SCC is partially evaluated into eval_perfect2_bb2_in/2 0.05/0.31 5. SCC is completely evaluated into other SCCs 0.05/0.31 6. SCC is partially evaluated into eval_perfect2_bb0_in/2 0.05/0.31 7. SCC is partially evaluated into eval_perfect2_start/2 0.05/0.31 0.05/0.31 Control-Flow Refinement of Cost Relations 0.05/0.31 ===================================== 0.05/0.31 0.05/0.31 ### Specialization of cost equations eval_perfect2_bb4_in/4 0.05/0.31 * CE 15 is refined into CE [16] 0.05/0.31 * CE 14 is refined into CE [17] 0.05/0.31 0.05/0.31 0.05/0.31 ### Cost equations --> "Loop" of eval_perfect2_bb4_in/4 0.05/0.31 * CEs [17] --> Loop 14 0.05/0.31 * CEs [16] --> Loop 15 0.05/0.31 0.05/0.31 ### Ranking functions of CR eval_perfect2_bb4_in(V_1,V_y2_1,B,C) 0.05/0.31 * RF of phase [14]: [-V_1+V_y2_1+1,V_y2_1] 0.05/0.31 0.05/0.31 #### Partial ranking functions of CR eval_perfect2_bb4_in(V_1,V_y2_1,B,C) 0.05/0.31 * Partial RF of phase [14]: 0.05/0.31 - RF of loop [14:1]: 0.05/0.31 -V_1+V_y2_1+1 0.05/0.31 V_y2_1 0.05/0.31 0.05/0.31 0.05/0.31 ### Specialization of cost equations eval_perfect2_bb1_in/5 0.05/0.31 * CE 10 is refined into CE [18] 0.05/0.31 * CE 4 is refined into CE [19] 0.05/0.31 * CE 6 is discarded (unfeasible) 0.05/0.31 * CE 5 is discarded (unfeasible) 0.05/0.31 * CE 7 is discarded (unfeasible) 0.05/0.31 * CE 8 is refined into CE [20] 0.05/0.31 * CE 9 is discarded (unfeasible) 0.05/0.31 0.05/0.31 0.05/0.31 ### Cost equations --> "Loop" of eval_perfect2_bb1_in/5 0.05/0.31 * CEs [19] --> Loop 16 0.05/0.31 * CEs [20] --> Loop 17 0.05/0.31 * CEs [18] --> Loop 18 0.05/0.31 0.05/0.31 ### Ranking functions of CR eval_perfect2_bb1_in(V_x,V_y3_0,V_y1_0,B,C) 0.05/0.31 * RF of phase [16,17]: [V_y1_0-1] 0.05/0.31 0.05/0.31 #### Partial ranking functions of CR eval_perfect2_bb1_in(V_x,V_y3_0,V_y1_0,B,C) 0.05/0.31 * Partial RF of phase [16,17]: 0.05/0.31 - RF of loop [16:1]: 0.05/0.31 V_y1_0-2 0.05/0.31 - RF of loop [17:1]: 0.05/0.31 V_y1_0-1 0.05/0.31 0.05/0.31 0.05/0.31 ### Specialization of cost equations eval_perfect2_bb2_in/2 0.05/0.31 * CE 12 is refined into CE [21] 0.05/0.31 * CE 11 is refined into CE [22] 0.05/0.31 * CE 13 is refined into CE [23] 0.05/0.31 0.05/0.31 0.05/0.31 ### Cost equations --> "Loop" of eval_perfect2_bb2_in/2 0.05/0.31 * CEs [21] --> Loop 19 0.05/0.31 * CEs [22] --> Loop 20 0.05/0.31 * CEs [23] --> Loop 21 0.05/0.31 0.05/0.31 ### Ranking functions of CR eval_perfect2_bb2_in(V_y3_0,B) 0.05/0.31 0.05/0.31 #### Partial ranking functions of CR eval_perfect2_bb2_in(V_y3_0,B) 0.05/0.31 0.05/0.31 0.05/0.31 ### Specialization of cost equations eval_perfect2_bb0_in/2 0.05/0.31 * CE 3 is refined into CE [24,25,26,27] 0.05/0.31 * CE 2 is refined into CE [28] 0.05/0.31 0.05/0.31 0.05/0.31 ### Cost equations --> "Loop" of eval_perfect2_bb0_in/2 0.05/0.31 * CEs [25,26,27] --> Loop 22 0.05/0.31 * CEs [28] --> Loop 23 0.05/0.31 * CEs [24] --> Loop 24 0.05/0.31 0.05/0.31 ### Ranking functions of CR eval_perfect2_bb0_in(V_x,B) 0.05/0.31 0.05/0.31 #### Partial ranking functions of CR eval_perfect2_bb0_in(V_x,B) 0.05/0.31 0.05/0.31 0.05/0.31 ### Specialization of cost equations eval_perfect2_start/2 0.05/0.31 * CE 1 is refined into CE [29,30,31] 0.05/0.31 0.05/0.31 0.05/0.31 ### Cost equations --> "Loop" of eval_perfect2_start/2 0.05/0.31 * CEs [31] --> Loop 25 0.05/0.31 * CEs [30] --> Loop 26 0.05/0.31 * CEs [29] --> Loop 27 0.05/0.31 0.05/0.31 ### Ranking functions of CR eval_perfect2_start(V_x,B) 0.05/0.31 0.05/0.31 #### Partial ranking functions of CR eval_perfect2_start(V_x,B) 0.05/0.31 0.05/0.31 0.05/0.31 Computing Bounds 0.05/0.31 ===================================== 0.05/0.31 0.05/0.31 #### Cost of chains of eval_perfect2_bb4_in(V_1,V_y2_1,B,C): 0.05/0.31 * Chain [[14],15]: 1*it(14)+0 0.05/0.31 Such that:it(14) =< -V_1+V_y2_1+1 0.05/0.31 0.05/0.31 with precondition: [B=2,C>=0,V_1>=C+1,V_y2_1>=V_1+C] 0.05/0.31 0.05/0.31 0.05/0.31 #### Cost of chains of eval_perfect2_bb1_in(V_x,V_y3_0,V_y1_0,B,C): 0.05/0.31 * Chain [[16,17],18]: 2*it(16)+1*s(5)+1*s(6)+0 0.05/0.31 Such that:aux(1) =< V_x 0.05/0.31 aux(5) =< V_y1_0 0.05/0.31 it(16) =< aux(5) 0.05/0.31 aux(2) =< aux(1) 0.05/0.31 s(5) =< it(16)*aux(1) 0.05/0.31 s(6) =< it(16)*aux(2) 0.05/0.31 0.05/0.31 with precondition: [B=3,V_y1_0>=2,V_x>=V_y3_0,V_x>=V_y1_0,V_y3_0>=C+1] 0.05/0.31 0.05/0.31 * Chain [18]: 0 0.05/0.31 with precondition: [V_y1_0=1,B=3,V_y3_0=C,V_x>=1,V_x>=V_y3_0] 0.05/0.31 0.05/0.31 0.05/0.31 #### Cost of chains of eval_perfect2_bb2_in(V_y3_0,B): 0.05/0.31 * Chain [21]: 0 0.05/0.31 with precondition: [V_y3_0=0] 0.05/0.31 0.05/0.31 * Chain [20]: 0 0.05/0.31 with precondition: [0>=V_y3_0+1] 0.05/0.31 0.05/0.31 * Chain [19]: 0 0.05/0.31 with precondition: [V_y3_0>=1] 0.05/0.31 0.05/0.31 0.05/0.31 #### Cost of chains of eval_perfect2_bb0_in(V_x,B): 0.05/0.31 * Chain [24]: 0 0.05/0.31 with precondition: [V_x=1] 0.05/0.31 0.05/0.31 * Chain [23]: 0 0.05/0.31 with precondition: [0>=V_x] 0.05/0.31 0.05/0.31 * Chain [22]: 6*s(9)+3*s(11)+3*s(12)+0 0.05/0.31 Such that:aux(9) =< V_x 0.05/0.31 s(9) =< aux(9) 0.05/0.31 s(10) =< aux(9) 0.05/0.31 s(11) =< s(9)*aux(9) 0.05/0.31 s(12) =< s(9)*s(10) 0.05/0.31 0.05/0.31 with precondition: [V_x>=2] 0.05/0.31 0.05/0.31 0.05/0.31 #### Cost of chains of eval_perfect2_start(V_x,B): 0.05/0.31 * Chain [27]: 0 0.05/0.31 with precondition: [V_x=1] 0.05/0.31 0.05/0.31 * Chain [26]: 0 0.05/0.31 with precondition: [0>=V_x] 0.05/0.31 0.05/0.31 * Chain [25]: 6*s(26)+3*s(28)+3*s(29)+0 0.05/0.31 Such that:s(25) =< V_x 0.05/0.31 s(26) =< s(25) 0.05/0.31 s(27) =< s(25) 0.05/0.31 s(28) =< s(26)*s(25) 0.05/0.31 s(29) =< s(26)*s(27) 0.05/0.31 0.05/0.31 with precondition: [V_x>=2] 0.05/0.31 0.05/0.31 0.05/0.31 Closed-form bounds of eval_perfect2_start(V_x,B): 0.05/0.31 ------------------------------------- 0.05/0.31 * Chain [27] with precondition: [V_x=1] 0.05/0.31 - Upper bound: 0 0.05/0.31 - Complexity: constant 0.05/0.31 * Chain [26] with precondition: [0>=V_x] 0.05/0.31 - Upper bound: 0 0.05/0.31 - Complexity: constant 0.05/0.31 * Chain [25] with precondition: [V_x>=2] 0.05/0.31 - Upper bound: 6*V_x*V_x+6*V_x 0.05/0.31 - Complexity: n^2 0.05/0.31 0.05/0.31 ### Maximum cost of eval_perfect2_start(V_x,B): nat(V_x)*6*nat(V_x)+nat(V_x)*6 0.05/0.31 Asymptotic class: n^2 0.05/0.31 * Total analysis performed in 228 ms. 0.05/0.31 0.05/0.42 EOF