0.79/0.80 WORST_CASE(?,O(n^1)) 0.79/0.80 0.79/0.80 Preprocessing Cost Relations 0.79/0.80 ===================================== 0.79/0.80 0.79/0.80 #### Computed strongly connected components 0.79/0.80 0. recursive : [eval_send_tree_bb5_in/5] 0.79/0.80 1. recursive : [eval_send_tree_2/7,eval_send_tree_3/8,eval_send_tree_6/7,eval_send_tree_7/8,eval_send_tree_8/8,eval_send_tree_9/8,eval_send_tree_bb1_in/6,eval_send_tree_bb2_in/6,eval_send_tree_bb3_in/7,eval_send_tree_bb4_in/7,eval_send_tree_bb5_in_loop_cont/11,eval_send_tree_bb6_in/7,eval_send_tree_bb7_in/8,eval_send_tree_bb8_in/10] 0.79/0.80 2. non_recursive : [eval_send_tree_stop/1] 0.79/0.80 3. non_recursive : [eval_send_tree_bb9_in/1] 0.79/0.80 4. non_recursive : [eval_send_tree_bb1_in_loop_cont/2] 0.79/0.80 5. non_recursive : [eval_send_tree_bb0_in/4] 0.79/0.80 6. non_recursive : [eval_send_tree_start/4] 0.79/0.80 0.79/0.80 #### Obtained direct recursion through partial evaluation 0.79/0.80 0. SCC is partially evaluated into eval_send_tree_bb5_in/5 0.79/0.80 1. SCC is partially evaluated into eval_send_tree_bb1_in/6 0.79/0.80 2. SCC is completely evaluated into other SCCs 0.79/0.80 3. SCC is completely evaluated into other SCCs 0.79/0.80 4. SCC is completely evaluated into other SCCs 0.79/0.80 5. SCC is partially evaluated into eval_send_tree_bb0_in/4 0.79/0.80 6. SCC is partially evaluated into eval_send_tree_start/4 0.79/0.80 0.79/0.80 Control-Flow Refinement of Cost Relations 0.79/0.80 ===================================== 0.79/0.80 0.79/0.80 ### Specialization of cost equations eval_send_tree_bb5_in/5 0.79/0.80 * CE 10 is refined into CE [11] 0.79/0.80 * CE 9 is refined into CE [12] 0.79/0.80 0.79/0.80 0.79/0.80 ### Cost equations --> "Loop" of eval_send_tree_bb5_in/5 0.79/0.80 * CEs [12] --> Loop 11 0.79/0.80 * CEs [11] --> Loop 12 0.79/0.80 0.79/0.80 ### Ranking functions of CR eval_send_tree_bb5_in(V_count_1,B,C,D,E) 0.79/0.80 * RF of phase [11]: [V_count_1-1] 0.79/0.80 0.79/0.80 #### Partial ranking functions of CR eval_send_tree_bb5_in(V_count_1,B,C,D,E) 0.79/0.80 * Partial RF of phase [11]: 0.79/0.80 - RF of loop [11:1]: 0.79/0.80 V_count_1-1 0.79/0.80 0.79/0.80 0.79/0.80 ### Specialization of cost equations eval_send_tree_bb1_in/6 0.79/0.80 * CE 8 is refined into CE [13] 0.79/0.80 * CE 4 is refined into CE [14,15] 0.79/0.80 * CE 6 is refined into CE [16,17] 0.79/0.80 * CE 3 is refined into CE [18] 0.79/0.80 * CE 5 is refined into CE [19] 0.79/0.80 * CE 7 is refined into CE [20] 0.79/0.80 0.79/0.80 0.79/0.80 ### Cost equations --> "Loop" of eval_send_tree_bb1_in/6 0.79/0.80 * CEs [18] --> Loop 13 0.79/0.80 * CEs [19] --> Loop 14 0.79/0.80 * CEs [20] --> Loop 15 0.79/0.80 * CEs [14] --> Loop 16 0.79/0.80 * CEs [16] --> Loop 17 0.79/0.80 * CEs [15] --> Loop 18 0.79/0.80 * CEs [17] --> Loop 19 0.79/0.80 * CEs [13] --> Loop 20 0.79/0.80 0.79/0.80 ### Ranking functions of CR eval_send_tree_bb1_in(V_max_code,V_max_count,V_min_count,V_count_0,V_n_0,B) 0.79/0.80 * RF of phase [13,14,15,16,17,18,19]: [V_max_code-V_n_0+1] 0.79/0.80 0.79/0.80 #### Partial ranking functions of CR eval_send_tree_bb1_in(V_max_code,V_max_count,V_min_count,V_count_0,V_n_0,B) 0.79/0.80 * Partial RF of phase [13,14,15,16,17,18,19]: 0.79/0.80 - RF of loop [13:1]: 0.79/0.80 V_max_code-V_count_0+1 depends on loops [14:1,15:1,16:1,17:1] 0.79/0.80 V_max_count-V_count_0-1 depends on loops [14:1,15:1,16:1,17:1] 0.79/0.80 - RF of loop [13:1,14:1,15:1,16:1,17:1,18:1,19:1]: 0.79/0.80 V_max_code-V_n_0+1 0.79/0.80 - RF of loop [16:1,17:1]: 0.79/0.80 V_count_0 depends on loops [13:1] 0.79/0.80 - RF of loop [17:1]: 0.79/0.80 -V_max_count+V_count_0+2 depends on loops [13:1] 0.79/0.80 0.79/0.80 0.79/0.80 ### Specialization of cost equations eval_send_tree_bb0_in/4 0.79/0.80 * CE 2 is refined into CE [21,22] 0.79/0.80 0.79/0.80 0.79/0.80 ### Cost equations --> "Loop" of eval_send_tree_bb0_in/4 0.79/0.80 * CEs [22] --> Loop 21 0.79/0.80 * CEs [21] --> Loop 22 0.79/0.80 0.79/0.80 ### Ranking functions of CR eval_send_tree_bb0_in(V_max_code,V_max_count,V_min_count,B) 0.79/0.80 0.79/0.80 #### Partial ranking functions of CR eval_send_tree_bb0_in(V_max_code,V_max_count,V_min_count,B) 0.79/0.80 0.79/0.80 0.79/0.80 ### Specialization of cost equations eval_send_tree_start/4 0.79/0.80 * CE 1 is refined into CE [23,24] 0.79/0.80 0.79/0.80 0.79/0.80 ### Cost equations --> "Loop" of eval_send_tree_start/4 0.79/0.80 * CEs [24] --> Loop 23 0.79/0.80 * CEs [23] --> Loop 24 0.79/0.80 0.79/0.80 ### Ranking functions of CR eval_send_tree_start(V_max_code,V_max_count,V_min_count,B) 0.79/0.80 0.79/0.80 #### Partial ranking functions of CR eval_send_tree_start(V_max_code,V_max_count,V_min_count,B) 0.79/0.80 0.79/0.80 0.79/0.80 Computing Bounds 0.79/0.80 ===================================== 0.79/0.80 0.79/0.80 #### Cost of chains of eval_send_tree_bb5_in(V_count_1,B,C,D,E): 0.79/0.80 * Chain [[11],12]: 1*it(11)+0 0.79/0.80 Such that:it(11) =< V_count_1 0.79/0.80 0.79/0.80 with precondition: [B=2,D=1,E=0,V_count_1>=2] 0.79/0.80 0.79/0.80 * Chain [12]: 0 0.79/0.80 with precondition: [B=2,E=0,V_count_1=D,1>=V_count_1] 0.79/0.80 0.79/0.80 0.79/0.80 #### Cost of chains of eval_send_tree_bb1_in(V_max_code,V_max_count,V_min_count,V_count_0,V_n_0,B): 0.79/0.80 * Chain [[13,14,15,16,17,18,19],20]: 4*it(13)+3*it(17)+2*s(5)+0 0.79/0.80 Such that:aux(75) =< V_max_code+V_count_0-V_n_0+1 0.79/0.80 aux(76) =< V_max_code-V_n_0+1 0.79/0.80 it(17) =< aux(75) 0.79/0.80 s(5) =< aux(75) 0.79/0.80 it(13) =< aux(76) 0.79/0.80 it(17) =< aux(76) 0.79/0.80 0.79/0.80 with precondition: [B=3,V_count_0>=0,V_n_0>=V_count_0,V_max_code>=V_n_0] 0.79/0.80 0.79/0.80 * Chain [20]: 0 0.79/0.80 with precondition: [B=3,V_count_0>=0,V_n_0>=V_max_code+1,V_n_0>=V_count_0] 0.79/0.80 0.79/0.80 0.79/0.80 #### Cost of chains of eval_send_tree_bb0_in(V_max_code,V_max_count,V_min_count,B): 0.79/0.80 * Chain [22]: 0 0.79/0.80 with precondition: [0>=V_max_code+1] 0.79/0.80 0.79/0.80 * Chain [21]: 9*s(9)+0 0.79/0.80 Such that:aux(77) =< V_max_code+1 0.79/0.80 s(9) =< aux(77) 0.79/0.80 0.79/0.80 with precondition: [V_max_code>=0] 0.79/0.80 0.79/0.80 0.79/0.80 #### Cost of chains of eval_send_tree_start(V_max_code,V_max_count,V_min_count,B): 0.79/0.80 * Chain [24]: 0 0.79/0.80 with precondition: [0>=V_max_code+1] 0.79/0.80 0.79/0.80 * Chain [23]: 9*s(13)+0 0.79/0.80 Such that:s(12) =< V_max_code+1 0.79/0.80 s(13) =< s(12) 0.79/0.80 0.79/0.80 with precondition: [V_max_code>=0] 0.79/0.80 0.79/0.80 0.79/0.80 Closed-form bounds of eval_send_tree_start(V_max_code,V_max_count,V_min_count,B): 0.79/0.80 ------------------------------------- 0.79/0.80 * Chain [24] with precondition: [0>=V_max_code+1] 0.79/0.80 - Upper bound: 0 0.79/0.80 - Complexity: constant 0.79/0.80 * Chain [23] with precondition: [V_max_code>=0] 0.79/0.80 - Upper bound: 9*V_max_code+9 0.79/0.80 - Complexity: n 0.79/0.80 0.79/0.80 ### Maximum cost of eval_send_tree_start(V_max_code,V_max_count,V_min_count,B): nat(V_max_code+1)*9 0.79/0.80 Asymptotic class: n 0.79/0.80 * Total analysis performed in 629 ms. 0.79/0.80 0.81/0.90 EOF