0.05/0.18 WORST_CASE(?,O(n^2)) 0.05/0.18 0.05/0.18 Preprocessing Cost Relations 0.05/0.18 ===================================== 0.05/0.18 0.05/0.18 #### Computed strongly connected components 0.05/0.18 0. recursive : [eval_realselect_4/6,eval_realselect_5/6,eval_realselect_6/6,eval_realselect_bb2_in/5,eval_realselect_bb3_in/6] 0.05/0.18 1. recursive : [eval_realselect_bb1_in/3,eval_realselect_bb2_in_loop_cont/6,eval_realselect_bb4_in/5] 0.05/0.18 2. non_recursive : [eval_realselect_stop/1] 0.05/0.18 3. non_recursive : [eval_realselect_bb5_in/1] 0.05/0.18 4. non_recursive : [eval_realselect_bb1_in_loop_cont/2] 0.05/0.18 5. non_recursive : [eval_realselect_bb0_in/2] 0.05/0.18 6. non_recursive : [eval_realselect_start/2] 0.05/0.18 0.05/0.18 #### Obtained direct recursion through partial evaluation 0.05/0.18 0. SCC is partially evaluated into eval_realselect_bb2_in/5 0.05/0.18 1. SCC is partially evaluated into eval_realselect_bb1_in/3 0.05/0.18 2. SCC is completely evaluated into other SCCs 0.05/0.18 3. SCC is completely evaluated into other SCCs 0.05/0.18 4. SCC is completely evaluated into other SCCs 0.05/0.18 5. SCC is partially evaluated into eval_realselect_bb0_in/2 0.05/0.18 6. SCC is partially evaluated into eval_realselect_start/2 0.05/0.18 0.05/0.18 Control-Flow Refinement of Cost Relations 0.05/0.18 ===================================== 0.05/0.18 0.05/0.18 ### Specialization of cost equations eval_realselect_bb2_in/5 0.05/0.18 * CE 6 is refined into CE [7] 0.05/0.18 * CE 5 is refined into CE [8] 0.05/0.18 0.05/0.18 0.05/0.18 ### Cost equations --> "Loop" of eval_realselect_bb2_in/5 0.05/0.18 * CEs [8] --> Loop 7 0.05/0.18 * CEs [7] --> Loop 8 0.05/0.18 0.05/0.18 ### Ranking functions of CR eval_realselect_bb2_in(V_array_size,V_i_0_sink,B,C,D) 0.05/0.18 * RF of phase [7]: [V_array_size-V_i_0_sink-1] 0.05/0.18 0.05/0.18 #### Partial ranking functions of CR eval_realselect_bb2_in(V_array_size,V_i_0_sink,B,C,D) 0.05/0.18 * Partial RF of phase [7]: 0.05/0.18 - RF of loop [7:1]: 0.05/0.18 V_array_size-V_i_0_sink-1 0.05/0.18 0.05/0.18 0.05/0.18 ### Specialization of cost equations eval_realselect_bb1_in/3 0.05/0.18 * CE 4 is refined into CE [9] 0.05/0.18 * CE 3 is refined into CE [10] 0.05/0.18 0.05/0.18 0.05/0.18 ### Cost equations --> "Loop" of eval_realselect_bb1_in/3 0.05/0.18 * CEs [10] --> Loop 9 0.05/0.18 * CEs [9] --> Loop 10 0.05/0.18 0.05/0.18 ### Ranking functions of CR eval_realselect_bb1_in(V_array_size,V_i_0,B) 0.05/0.18 * RF of phase [9]: [V_array_size-V_i_0-1] 0.05/0.18 0.05/0.18 #### Partial ranking functions of CR eval_realselect_bb1_in(V_array_size,V_i_0,B) 0.05/0.18 * Partial RF of phase [9]: 0.05/0.18 - RF of loop [9:1]: 0.05/0.18 V_array_size-V_i_0-1 0.05/0.18 0.05/0.18 0.05/0.18 ### Specialization of cost equations eval_realselect_bb0_in/2 0.05/0.18 * CE 2 is refined into CE [11,12] 0.05/0.18 0.05/0.18 0.05/0.18 ### Cost equations --> "Loop" of eval_realselect_bb0_in/2 0.05/0.18 * CEs [12] --> Loop 11 0.05/0.18 * CEs [11] --> Loop 12 0.05/0.18 0.05/0.18 ### Ranking functions of CR eval_realselect_bb0_in(V_array_size,B) 0.05/0.18 0.05/0.18 #### Partial ranking functions of CR eval_realselect_bb0_in(V_array_size,B) 0.05/0.18 0.05/0.18 0.05/0.18 ### Specialization of cost equations eval_realselect_start/2 0.05/0.18 * CE 1 is refined into CE [13,14] 0.05/0.18 0.05/0.18 0.05/0.18 ### Cost equations --> "Loop" of eval_realselect_start/2 0.05/0.18 * CEs [14] --> Loop 13 0.05/0.18 * CEs [13] --> Loop 14 0.05/0.18 0.05/0.18 ### Ranking functions of CR eval_realselect_start(V_array_size,B) 0.05/0.18 0.05/0.18 #### Partial ranking functions of CR eval_realselect_start(V_array_size,B) 0.05/0.18 0.05/0.18 0.05/0.18 Computing Bounds 0.05/0.18 ===================================== 0.05/0.18 0.05/0.18 #### Cost of chains of eval_realselect_bb2_in(V_array_size,V_i_0_sink,B,C,D): 0.05/0.18 * Chain [[7],8]: 1*it(7)+0 0.05/0.18 Such that:it(7) =< -V_i_0_sink+D 0.05/0.18 0.05/0.18 with precondition: [B=2,V_array_size=C+1,V_array_size=D,V_i_0_sink>=0,V_array_size>=V_i_0_sink+2] 0.05/0.18 0.05/0.18 0.05/0.18 #### Cost of chains of eval_realselect_bb1_in(V_array_size,V_i_0,B): 0.05/0.18 * Chain [[9],10]: 1*it(9)+1*s(3)+0 0.05/0.18 Such that:aux(3) =< V_array_size-V_i_0 0.05/0.18 it(9) =< aux(3) 0.05/0.18 s(3) =< it(9)*aux(3) 0.05/0.18 0.05/0.18 with precondition: [B=3,V_i_0>=0,V_array_size>=V_i_0+2] 0.05/0.18 0.05/0.18 * Chain [10]: 0 0.05/0.18 with precondition: [B=3,V_i_0>=0,V_i_0+1>=V_array_size] 0.05/0.18 0.05/0.18 0.05/0.18 #### Cost of chains of eval_realselect_bb0_in(V_array_size,B): 0.05/0.18 * Chain [12]: 0 0.05/0.18 with precondition: [1>=V_array_size] 0.05/0.18 0.05/0.18 * Chain [11]: 1*s(5)+1*s(6)+0 0.05/0.18 Such that:s(4) =< V_array_size 0.05/0.18 s(5) =< s(4) 0.05/0.18 s(6) =< s(5)*s(4) 0.05/0.18 0.05/0.18 with precondition: [V_array_size>=2] 0.05/0.18 0.05/0.18 0.05/0.18 #### Cost of chains of eval_realselect_start(V_array_size,B): 0.05/0.18 * Chain [14]: 0 0.05/0.18 with precondition: [1>=V_array_size] 0.05/0.18 0.05/0.18 * Chain [13]: 1*s(8)+1*s(9)+0 0.05/0.18 Such that:s(7) =< V_array_size 0.05/0.18 s(8) =< s(7) 0.05/0.18 s(9) =< s(8)*s(7) 0.05/0.18 0.05/0.18 with precondition: [V_array_size>=2] 0.05/0.18 0.05/0.18 0.05/0.18 Closed-form bounds of eval_realselect_start(V_array_size,B): 0.05/0.18 ------------------------------------- 0.05/0.18 * Chain [14] with precondition: [1>=V_array_size] 0.05/0.18 - Upper bound: 0 0.05/0.18 - Complexity: constant 0.05/0.18 * Chain [13] with precondition: [V_array_size>=2] 0.05/0.18 - Upper bound: V_array_size*V_array_size+V_array_size 0.05/0.18 - Complexity: n^2 0.05/0.18 0.05/0.18 ### Maximum cost of eval_realselect_start(V_array_size,B): nat(V_array_size)*nat(V_array_size)+nat(V_array_size) 0.05/0.18 Asymptotic class: n^2 0.05/0.18 * Total analysis performed in 103 ms. 0.05/0.18 0.05/0.28 EOF