0.53/0.53 WORST_CASE(?,O(n^1)) 0.53/0.53 0.53/0.53 Preprocessing Cost Relations 0.53/0.53 ===================================== 0.53/0.53 0.53/0.53 #### Computed strongly connected components 0.53/0.53 0. recursive : [eval_Loopus2015_original_bb3_in/8,eval_Loopus2015_original_bb4_in/8] 0.53/0.53 1. recursive : [eval_Loopus2015_original_1/6,eval_Loopus2015_original_2/7,eval_Loopus2015_original_3/8,eval_Loopus2015_original_4/9,eval_Loopus2015_original_bb1_in/5,eval_Loopus2015_original_bb2_in/5,eval_Loopus2015_original_bb3_in_loop_cont/6] 0.53/0.53 2. non_recursive : [eval_Loopus2015_original_stop/1] 0.53/0.53 3. non_recursive : [eval_Loopus2015_original_bb5_in/1] 0.53/0.53 4. non_recursive : [eval_Loopus2015_original_bb1_in_loop_cont/2] 0.53/0.53 5. non_recursive : [eval_Loopus2015_original_bb0_in/2] 0.53/0.53 6. non_recursive : [eval_Loopus2015_original_start/2] 0.53/0.53 0.53/0.53 #### Obtained direct recursion through partial evaluation 0.53/0.53 0. SCC is partially evaluated into eval_Loopus2015_original_bb3_in/8 0.53/0.53 1. SCC is partially evaluated into eval_Loopus2015_original_bb1_in/5 0.53/0.53 2. SCC is completely evaluated into other SCCs 0.53/0.53 3. SCC is completely evaluated into other SCCs 0.53/0.53 4. SCC is completely evaluated into other SCCs 0.53/0.53 5. SCC is partially evaluated into eval_Loopus2015_original_bb0_in/2 0.53/0.53 6. SCC is partially evaluated into eval_Loopus2015_original_start/2 0.53/0.53 0.53/0.53 Control-Flow Refinement of Cost Relations 0.53/0.53 ===================================== 0.53/0.53 0.53/0.53 ### Specialization of cost equations eval_Loopus2015_original_bb3_in/8 0.53/0.53 * CE 9 is refined into CE [10] 0.53/0.53 * CE 8 is refined into CE [11] 0.53/0.53 0.53/0.53 0.53/0.53 ### Cost equations --> "Loop" of eval_Loopus2015_original_bb3_in/8 0.53/0.53 * CEs [11] --> Loop 9 0.53/0.53 * CEs [10] --> Loop 10 0.53/0.53 0.53/0.53 ### Ranking functions of CR eval_Loopus2015_original_bb3_in(V_i_0,V_end_0,V_beg_0,V_2,V__end_0,V_4,V_k_0,B) 0.53/0.53 * RF of phase [9]: [V__end_0-V_k_0,V_i_0-V_k_0+1] 0.53/0.53 0.53/0.53 #### Partial ranking functions of CR eval_Loopus2015_original_bb3_in(V_i_0,V_end_0,V_beg_0,V_2,V__end_0,V_4,V_k_0,B) 0.53/0.53 * Partial RF of phase [9]: 0.53/0.53 - RF of loop [9:1]: 0.53/0.53 V__end_0-V_k_0 0.53/0.53 V_i_0-V_k_0+1 0.53/0.53 0.53/0.53 0.53/0.53 ### Specialization of cost equations eval_Loopus2015_original_bb1_in/5 0.53/0.53 * CE 7 is refined into CE [12] 0.53/0.53 * CE 6 is refined into CE [13] 0.53/0.53 * CE 3 is refined into CE [14] 0.53/0.53 * CE 4 is refined into CE [15,16] 0.53/0.53 * CE 5 is refined into CE [17] 0.53/0.53 0.53/0.53 0.53/0.53 ### Cost equations --> "Loop" of eval_Loopus2015_original_bb1_in/5 0.53/0.53 * CEs [13] --> Loop 11 0.53/0.53 * CEs [16] --> Loop 12 0.53/0.53 * CEs [15] --> Loop 13 0.53/0.53 * CEs [14] --> Loop 14 0.53/0.53 * CEs [17] --> Loop 15 0.53/0.53 * CEs [12] --> Loop 16 0.53/0.53 0.53/0.53 ### Ranking functions of CR eval_Loopus2015_original_bb1_in(V_len,V_i_0,V_end_0,V_beg_0,B) 0.53/0.53 * RF of phase [11,12,13,14,15]: [V_len-V_i_0] 0.53/0.53 0.53/0.53 #### Partial ranking functions of CR eval_Loopus2015_original_bb1_in(V_len,V_i_0,V_end_0,V_beg_0,B) 0.53/0.53 * Partial RF of phase [11,12,13,14,15]: 0.53/0.53 - RF of loop [11:1,12:1,13:1,14:1,15:1]: 0.53/0.53 V_len-V_i_0 0.53/0.53 - RF of loop [12:1]: 0.53/0.53 V_end_0-V_beg_0 depends on loops [15:1] 0.53/0.53 V_i_0-V_beg_0 depends on loops [11:1,15:1] 0.53/0.53 V_len/2-V_beg_0/2-1/2 0.53/0.53 - RF of loop [12:1,13:1,14:1,15:1]: 0.53/0.53 V_len-V_end_0 0.53/0.53 - RF of loop [13:1,14:1]: 0.53/0.53 V_len-V_beg_0 0.53/0.53 0.53/0.53 0.53/0.53 ### Specialization of cost equations eval_Loopus2015_original_bb0_in/2 0.53/0.53 * CE 2 is refined into CE [18,19] 0.53/0.53 0.53/0.53 0.53/0.53 ### Cost equations --> "Loop" of eval_Loopus2015_original_bb0_in/2 0.53/0.53 * CEs [19] --> Loop 17 0.53/0.53 * CEs [18] --> Loop 18 0.53/0.53 0.53/0.53 ### Ranking functions of CR eval_Loopus2015_original_bb0_in(V_len,B) 0.53/0.53 0.53/0.53 #### Partial ranking functions of CR eval_Loopus2015_original_bb0_in(V_len,B) 0.53/0.53 0.53/0.53 0.53/0.53 ### Specialization of cost equations eval_Loopus2015_original_start/2 0.53/0.53 * CE 1 is refined into CE [20,21] 0.53/0.53 0.53/0.53 0.53/0.53 ### Cost equations --> "Loop" of eval_Loopus2015_original_start/2 0.53/0.53 * CEs [21] --> Loop 19 0.53/0.53 * CEs [20] --> Loop 20 0.53/0.53 0.53/0.53 ### Ranking functions of CR eval_Loopus2015_original_start(V_len,B) 0.53/0.53 0.53/0.53 #### Partial ranking functions of CR eval_Loopus2015_original_start(V_len,B) 0.53/0.53 0.53/0.53 0.53/0.53 Computing Bounds 0.53/0.53 ===================================== 0.53/0.53 0.53/0.53 #### Cost of chains of eval_Loopus2015_original_bb3_in(V_i_0,V_end_0,V_beg_0,V_2,V__end_0,V_4,V_k_0,B): 0.53/0.53 * Chain [[9],10]: 1*it(9)+0 0.53/0.53 Such that:it(9) =< V__end_0-V_k_0 0.53/0.53 0.53/0.53 with precondition: [B=2,V_beg_0>=0,V_4>=1,V_i_0>=V_end_0,V__end_0>=V_end_0,V_end_0>=V_beg_0,V_k_0>=V_beg_0,V_i_0+1>=V__end_0,V__end_0>=V_k_0+1] 0.53/0.53 0.53/0.53 * Chain [10]: 0 0.53/0.53 with precondition: [B=2,V_k_0=V__end_0,V_beg_0>=0,V_4>=1,V_i_0>=V_end_0,V_k_0>=V_end_0,V_end_0>=V_beg_0,V_i_0+1>=V_k_0] 0.53/0.53 0.53/0.53 0.53/0.53 #### Cost of chains of eval_Loopus2015_original_bb1_in(V_len,V_i_0,V_end_0,V_beg_0,B): 0.53/0.53 * Chain [[11,12,13,14,15],16]: 1*it(11)+1*it(12)+2*it(13)+1*it(15)+1*s(5)+1*s(6)+0 0.53/0.53 Such that:aux(14) =< V_len 0.53/0.53 it(12) =< V_len/2-V_beg_0/2 0.53/0.53 aux(23) =< V_len-V_i_0 0.53/0.53 aux(24) =< V_len-V_end_0 0.53/0.53 aux(25) =< V_len-V_beg_0 0.53/0.53 aux(26) =< V_i_0-V_beg_0 0.53/0.53 aux(27) =< V_end_0-V_beg_0 0.53/0.53 aux(22) =< aux(25) 0.53/0.53 aux(6) =< aux(26) 0.53/0.53 aux(22) =< aux(26) 0.53/0.53 aux(6) =< aux(27) 0.53/0.53 aux(12) =< aux(14) 0.53/0.53 it(11) =< aux(23) 0.53/0.53 it(12) =< aux(23) 0.53/0.53 it(13) =< aux(23) 0.53/0.53 it(15) =< aux(23) 0.53/0.53 it(12) =< aux(24) 0.53/0.53 it(13) =< aux(24) 0.53/0.53 it(15) =< aux(24) 0.53/0.53 it(13) =< aux(25) 0.53/0.53 s(5) =< aux(25) 0.53/0.53 s(6) =< aux(25) 0.53/0.53 aux(12) =< aux(14) 0.53/0.53 aux(11) =< it(15)*aux(14) 0.53/0.53 aux(2) =< it(15)*aux(14) 0.53/0.53 s(5) =< it(15)+it(11)+aux(22) 0.53/0.53 s(5) =< it(15)+it(11)+aux(26) 0.53/0.53 it(12) =< it(15)+it(11)+aux(22) 0.53/0.53 it(12) =< it(15)+it(11)+aux(26) 0.53/0.53 aux(13) =< it(15)*aux(12) 0.53/0.53 aux(2) =< it(15)*aux(12) 0.53/0.53 aux(5) =< aux(11) 0.53/0.53 aux(5) =< aux(13) 0.53/0.53 it(12) =< aux(2)+aux(27) 0.53/0.53 it(12) =< aux(5)+aux(6) 0.53/0.53 s(5) =< it(12)*aux(25) 0.53/0.53 0.53/0.53 with precondition: [B=3,V_beg_0>=0,V_len>=V_i_0+1,V_i_0>=V_end_0,V_end_0>=V_beg_0] 0.53/0.53 0.53/0.53 * Chain [16]: 0 0.53/0.53 with precondition: [B=3,V_beg_0>=0,V_i_0>=V_len,V_i_0>=V_end_0,V_end_0>=V_beg_0] 0.53/0.53 0.53/0.53 0.53/0.53 #### Cost of chains of eval_Loopus2015_original_bb0_in(V_len,B): 0.53/0.53 * Chain [18]: 0 0.53/0.53 with precondition: [0>=V_len] 0.53/0.53 0.53/0.53 * Chain [17]: 1*s(8)+5*s(17)+1*s(20)+0 0.53/0.53 Such that:s(8) =< V_len/2 0.53/0.53 aux(29) =< V_len 0.53/0.53 s(16) =< aux(29) 0.53/0.53 s(17) =< aux(29) 0.53/0.53 s(8) =< aux(29) 0.53/0.53 s(20) =< aux(29) 0.53/0.53 s(16) =< aux(29) 0.53/0.53 s(22) =< s(17)*aux(29) 0.53/0.53 s(23) =< s(17)*aux(29) 0.53/0.53 s(20) =< s(17)+s(17) 0.53/0.53 s(20) =< s(17)+s(17) 0.53/0.53 s(8) =< s(17)+s(17) 0.53/0.53 s(8) =< s(17)+s(17) 0.53/0.53 s(24) =< s(17)*s(16) 0.53/0.53 s(23) =< s(17)*s(16) 0.53/0.53 s(25) =< s(22) 0.53/0.53 s(25) =< s(24) 0.53/0.53 s(8) =< s(23) 0.53/0.53 s(8) =< s(25) 0.53/0.53 s(20) =< s(8)*aux(29) 0.53/0.53 0.53/0.53 with precondition: [V_len>=1] 0.53/0.53 0.53/0.53 0.53/0.53 #### Cost of chains of eval_Loopus2015_original_start(V_len,B): 0.53/0.53 * Chain [20]: 0 0.53/0.53 with precondition: [0>=V_len] 0.53/0.53 0.53/0.53 * Chain [19]: 1*s(26)+5*s(29)+1*s(30)+0 0.53/0.53 Such that:s(27) =< V_len 0.53/0.53 s(26) =< V_len/2 0.53/0.53 s(28) =< s(27) 0.53/0.53 s(29) =< s(27) 0.53/0.53 s(26) =< s(27) 0.53/0.53 s(30) =< s(27) 0.53/0.53 s(28) =< s(27) 0.53/0.53 s(31) =< s(29)*s(27) 0.53/0.53 s(32) =< s(29)*s(27) 0.53/0.53 s(30) =< s(29)+s(29) 0.53/0.53 s(30) =< s(29)+s(29) 0.53/0.53 s(26) =< s(29)+s(29) 0.53/0.53 s(26) =< s(29)+s(29) 0.53/0.53 s(33) =< s(29)*s(28) 0.53/0.53 s(32) =< s(29)*s(28) 0.53/0.53 s(34) =< s(31) 0.53/0.53 s(34) =< s(33) 0.53/0.53 s(26) =< s(32) 0.53/0.53 s(26) =< s(34) 0.53/0.53 s(30) =< s(26)*s(27) 0.53/0.53 0.53/0.53 with precondition: [V_len>=1] 0.53/0.53 0.53/0.53 0.53/0.53 Closed-form bounds of eval_Loopus2015_original_start(V_len,B): 0.53/0.53 ------------------------------------- 0.53/0.53 * Chain [20] with precondition: [0>=V_len] 0.53/0.53 - Upper bound: 0 0.53/0.53 - Complexity: constant 0.53/0.53 * Chain [19] with precondition: [V_len>=1] 0.53/0.53 - Upper bound: 13/2*V_len 0.53/0.53 - Complexity: n 0.53/0.53 0.53/0.53 ### Maximum cost of eval_Loopus2015_original_start(V_len,B): nat(V_len)*6+nat(V_len/2) 0.53/0.53 Asymptotic class: n 0.53/0.53 * Total analysis performed in 419 ms. 0.53/0.53 0.54/0.64 EOF