0.06/0.28 WORST_CASE(?,O(n^2)) 0.06/0.28 0.06/0.28 Preprocessing Cost Relations 0.06/0.28 ===================================== 0.06/0.28 0.06/0.28 #### Computed strongly connected components 0.06/0.28 0. recursive : [eval_perfect1_bb3_in/4,eval_perfect1_bb4_in/4] 0.06/0.28 1. recursive : [eval_perfect1_bb2_in/5,eval_perfect1_bb3_in_loop_cont/7,eval_perfect1_bb5_in/6] 0.06/0.28 2. non_recursive : [eval_perfect1_stop/1] 0.06/0.28 3. non_recursive : [eval_perfect1_bb7_in/1] 0.06/0.28 4. non_recursive : [eval_perfect1_bb6_in/2] 0.06/0.28 5. non_recursive : [eval_perfect1_bb2_in_loop_cont/3] 0.06/0.28 6. non_recursive : [eval_perfect1_bb1_in/2] 0.06/0.28 7. non_recursive : [eval_perfect1_bb0_in/2] 0.06/0.28 8. non_recursive : [eval_perfect1_start/2] 0.06/0.28 0.06/0.28 #### Obtained direct recursion through partial evaluation 0.06/0.28 0. SCC is partially evaluated into eval_perfect1_bb3_in/4 0.06/0.28 1. SCC is partially evaluated into eval_perfect1_bb2_in/5 0.06/0.28 2. SCC is completely evaluated into other SCCs 0.06/0.28 3. SCC is completely evaluated into other SCCs 0.06/0.28 4. SCC is partially evaluated into eval_perfect1_bb6_in/2 0.06/0.28 5. SCC is completely evaluated into other SCCs 0.06/0.28 6. SCC is partially evaluated into eval_perfect1_bb1_in/2 0.06/0.28 7. SCC is partially evaluated into eval_perfect1_bb0_in/2 0.06/0.28 8. SCC is partially evaluated into eval_perfect1_start/2 0.06/0.28 0.06/0.28 Control-Flow Refinement of Cost Relations 0.06/0.28 ===================================== 0.06/0.28 0.06/0.28 ### Specialization of cost equations eval_perfect1_bb3_in/4 0.06/0.28 * CE 13 is refined into CE [14] 0.06/0.28 * CE 12 is refined into CE [15] 0.06/0.28 0.06/0.28 0.06/0.28 ### Cost equations --> "Loop" of eval_perfect1_bb3_in/4 0.06/0.28 * CEs [15] --> Loop 13 0.06/0.28 * CEs [14] --> Loop 14 0.06/0.28 0.06/0.28 ### Ranking functions of CR eval_perfect1_bb3_in(V_y1_0,V_y2_1,B,C) 0.06/0.28 * RF of phase [13]: [-V_y1_0+V_y2_1+1,V_y2_1] 0.06/0.28 0.06/0.28 #### Partial ranking functions of CR eval_perfect1_bb3_in(V_y1_0,V_y2_1,B,C) 0.06/0.28 * Partial RF of phase [13]: 0.06/0.28 - RF of loop [13:1]: 0.06/0.28 -V_y1_0+V_y2_1+1 0.06/0.28 V_y2_1 0.06/0.28 0.06/0.28 0.06/0.28 ### Specialization of cost equations eval_perfect1_bb2_in/5 0.06/0.28 * CE 8 is refined into CE [16] 0.06/0.28 * CE 7 is refined into CE [17] 0.06/0.28 * CE 5 is refined into CE [18] 0.06/0.28 * CE 6 is discarded (unfeasible) 0.06/0.28 0.06/0.28 0.06/0.28 ### Cost equations --> "Loop" of eval_perfect1_bb2_in/5 0.06/0.28 * CEs [17] --> Loop 15 0.06/0.28 * CEs [18] --> Loop 16 0.06/0.28 * CEs [16] --> Loop 17 0.06/0.28 0.06/0.28 ### Ranking functions of CR eval_perfect1_bb2_in(V_x,V_y3_0,V_y1_0,B,C) 0.06/0.28 * RF of phase [15,16]: [V_y1_0] 0.06/0.28 0.06/0.28 #### Partial ranking functions of CR eval_perfect1_bb2_in(V_x,V_y3_0,V_y1_0,B,C) 0.06/0.28 * Partial RF of phase [15,16]: 0.06/0.28 - RF of loop [15:1]: 0.06/0.28 V_y1_0 0.06/0.28 - RF of loop [16:1]: 0.06/0.28 V_y1_0-1 0.06/0.28 0.06/0.28 0.06/0.28 ### Specialization of cost equations eval_perfect1_bb6_in/2 0.06/0.28 * CE 10 is refined into CE [19] 0.06/0.28 * CE 9 is refined into CE [20] 0.06/0.28 * CE 11 is refined into CE [21] 0.06/0.28 0.06/0.28 0.06/0.28 ### Cost equations --> "Loop" of eval_perfect1_bb6_in/2 0.06/0.28 * CEs [19] --> Loop 18 0.06/0.28 * CEs [20] --> Loop 19 0.06/0.28 * CEs [21] --> Loop 20 0.06/0.28 0.06/0.28 ### Ranking functions of CR eval_perfect1_bb6_in(V_y3_0,B) 0.06/0.28 0.06/0.28 #### Partial ranking functions of CR eval_perfect1_bb6_in(V_y3_0,B) 0.06/0.28 0.06/0.28 0.06/0.28 ### Specialization of cost equations eval_perfect1_bb1_in/2 0.06/0.28 * CE 4 is refined into CE [22,23,24] 0.06/0.28 0.06/0.28 0.06/0.28 ### Cost equations --> "Loop" of eval_perfect1_bb1_in/2 0.06/0.28 * CEs [22,23,24] --> Loop 21 0.06/0.28 0.06/0.28 ### Ranking functions of CR eval_perfect1_bb1_in(V_x,B) 0.06/0.28 0.06/0.28 #### Partial ranking functions of CR eval_perfect1_bb1_in(V_x,B) 0.06/0.28 0.06/0.28 0.06/0.28 ### Specialization of cost equations eval_perfect1_bb0_in/2 0.06/0.28 * CE 3 is refined into CE [25] 0.06/0.28 * CE 2 is refined into CE [26] 0.06/0.28 0.06/0.28 0.06/0.28 ### Cost equations --> "Loop" of eval_perfect1_bb0_in/2 0.06/0.28 * CEs [25] --> Loop 22 0.06/0.28 * CEs [26] --> Loop 23 0.06/0.28 0.06/0.28 ### Ranking functions of CR eval_perfect1_bb0_in(V_x,B) 0.06/0.28 0.06/0.28 #### Partial ranking functions of CR eval_perfect1_bb0_in(V_x,B) 0.06/0.28 0.06/0.28 0.06/0.28 ### Specialization of cost equations eval_perfect1_start/2 0.06/0.28 * CE 1 is refined into CE [27,28] 0.06/0.28 0.06/0.28 0.06/0.28 ### Cost equations --> "Loop" of eval_perfect1_start/2 0.06/0.28 * CEs [28] --> Loop 24 0.06/0.28 * CEs [27] --> Loop 25 0.06/0.28 0.06/0.28 ### Ranking functions of CR eval_perfect1_start(V_x,B) 0.06/0.28 0.06/0.28 #### Partial ranking functions of CR eval_perfect1_start(V_x,B) 0.06/0.28 0.06/0.28 0.06/0.28 Computing Bounds 0.06/0.28 ===================================== 0.06/0.28 0.06/0.28 #### Cost of chains of eval_perfect1_bb3_in(V_y1_0,V_y2_1,B,C): 0.06/0.28 * Chain [[13],14]: 1*it(13)+0 0.06/0.28 Such that:it(13) =< -V_y1_0+V_y2_1+1 0.06/0.28 0.06/0.28 with precondition: [B=2,C>=0,V_y1_0>=C+1,V_y2_1>=V_y1_0+C] 0.06/0.28 0.06/0.28 0.06/0.28 #### Cost of chains of eval_perfect1_bb2_in(V_x,V_y3_0,V_y1_0,B,C): 0.06/0.28 * Chain [[15,16],17]: 2*it(15)+1*s(5)+1*s(6)+0 0.06/0.28 Such that:aux(1) =< V_x 0.06/0.28 aux(5) =< V_y1_0 0.06/0.28 it(15) =< aux(5) 0.06/0.28 aux(2) =< aux(1) 0.06/0.28 s(5) =< it(15)*aux(1) 0.06/0.28 s(6) =< it(15)*aux(2) 0.06/0.28 0.06/0.28 with precondition: [B=3,V_y1_0>=1,V_x>=V_y3_0,V_x>=V_y1_0+1,V_y3_0>=C+1] 0.06/0.28 0.06/0.28 0.06/0.28 #### Cost of chains of eval_perfect1_bb6_in(V_y3_0,B): 0.06/0.28 * Chain [20]: 0 0.06/0.28 with precondition: [V_y3_0=0] 0.06/0.28 0.06/0.28 * Chain [19]: 0 0.06/0.28 with precondition: [0>=V_y3_0+1] 0.06/0.28 0.06/0.28 * Chain [18]: 0 0.06/0.28 with precondition: [V_y3_0>=1] 0.06/0.28 0.06/0.28 0.06/0.28 #### Cost of chains of eval_perfect1_bb1_in(V_x,B): 0.06/0.28 * Chain [21]: 6*s(9)+3*s(11)+3*s(12)+0 0.06/0.28 Such that:aux(9) =< V_x 0.06/0.28 s(9) =< aux(9) 0.06/0.28 s(10) =< aux(9) 0.06/0.28 s(11) =< s(9)*aux(9) 0.06/0.28 s(12) =< s(9)*s(10) 0.06/0.28 0.06/0.28 with precondition: [V_x>=2] 0.06/0.28 0.06/0.28 0.06/0.28 #### Cost of chains of eval_perfect1_bb0_in(V_x,B): 0.06/0.28 * Chain [23]: 0 0.06/0.28 with precondition: [1>=V_x] 0.06/0.28 0.06/0.28 * Chain [22]: 6*s(26)+3*s(28)+3*s(29)+0 0.06/0.28 Such that:s(25) =< V_x 0.06/0.28 s(26) =< s(25) 0.06/0.28 s(27) =< s(25) 0.06/0.28 s(28) =< s(26)*s(25) 0.06/0.28 s(29) =< s(26)*s(27) 0.06/0.28 0.06/0.28 with precondition: [V_x>=2] 0.06/0.28 0.06/0.28 0.06/0.28 #### Cost of chains of eval_perfect1_start(V_x,B): 0.06/0.28 * Chain [25]: 0 0.06/0.28 with precondition: [1>=V_x] 0.06/0.28 0.06/0.28 * Chain [24]: 6*s(31)+3*s(33)+3*s(34)+0 0.06/0.28 Such that:s(30) =< V_x 0.06/0.28 s(31) =< s(30) 0.06/0.28 s(32) =< s(30) 0.06/0.28 s(33) =< s(31)*s(30) 0.06/0.28 s(34) =< s(31)*s(32) 0.06/0.28 0.06/0.28 with precondition: [V_x>=2] 0.06/0.28 0.06/0.28 0.06/0.28 Closed-form bounds of eval_perfect1_start(V_x,B): 0.06/0.28 ------------------------------------- 0.06/0.28 * Chain [25] with precondition: [1>=V_x] 0.06/0.28 - Upper bound: 0 0.06/0.28 - Complexity: constant 0.06/0.28 * Chain [24] with precondition: [V_x>=2] 0.06/0.28 - Upper bound: 6*V_x*V_x+6*V_x 0.06/0.28 - Complexity: n^2 0.06/0.28 0.06/0.28 ### Maximum cost of eval_perfect1_start(V_x,B): nat(V_x)*6*nat(V_x)+nat(V_x)*6 0.06/0.28 Asymptotic class: n^2 0.06/0.28 * Total analysis performed in 193 ms. 0.06/0.28 0.06/0.38 EOF