0.06/0.41 WORST_CASE(?,O(n^2)) 0.06/0.41 0.06/0.41 Preprocessing Cost Relations 0.06/0.41 ===================================== 0.06/0.41 0.06/0.41 #### Computed strongly connected components 0.06/0.41 0. recursive : [eval_asctoeg_0/5,eval_asctoeg_1/6,eval_asctoeg_bb2_in/5,eval_asctoeg_bb3_in/5,eval_asctoeg_bb4_in/6] 0.06/0.41 1. recursive : [eval_asctoeg_6/5,eval_asctoeg_7/6,eval_asctoeg__critedge_in/4,eval_asctoeg_bb5_in/5] 0.06/0.41 2. recursive : [eval_asctoeg__critedge1_in/6,eval_asctoeg__critedge_in_loop_cont/7,eval_asctoeg_bb1_in/3,eval_asctoeg_bb2_in_loop_cont/6] 0.06/0.41 3. non_recursive : [eval_asctoeg_stop/1] 0.06/0.41 4. non_recursive : [eval_asctoeg_bb6_in/1] 0.06/0.41 5. non_recursive : [eval_asctoeg_bb1_in_loop_cont/2] 0.06/0.41 6. non_recursive : [eval_asctoeg_bb0_in/2] 0.06/0.41 7. non_recursive : [eval_asctoeg_start/2] 0.06/0.41 0.06/0.41 #### Obtained direct recursion through partial evaluation 0.06/0.41 0. SCC is partially evaluated into eval_asctoeg_bb2_in/5 0.06/0.41 1. SCC is partially evaluated into eval_asctoeg__critedge_in/4 0.06/0.41 2. SCC is partially evaluated into eval_asctoeg_bb1_in/3 0.06/0.41 3. SCC is completely evaluated into other SCCs 0.06/0.41 4. SCC is completely evaluated into other SCCs 0.06/0.41 5. SCC is completely evaluated into other SCCs 0.06/0.41 6. SCC is partially evaluated into eval_asctoeg_bb0_in/2 0.06/0.41 7. SCC is partially evaluated into eval_asctoeg_start/2 0.06/0.41 0.06/0.41 Control-Flow Refinement of Cost Relations 0.06/0.41 ===================================== 0.06/0.41 0.06/0.41 ### Specialization of cost equations eval_asctoeg_bb2_in/5 0.06/0.41 * CE 5 is refined into CE [11] 0.06/0.41 * CE 7 is refined into CE [12] 0.06/0.41 * CE 6 is refined into CE [13] 0.06/0.41 0.06/0.41 0.06/0.41 ### Cost equations --> "Loop" of eval_asctoeg_bb2_in/5 0.06/0.41 * CEs [13] --> Loop 11 0.06/0.41 * CEs [11] --> Loop 12 0.06/0.41 * CEs [12] --> Loop 13 0.06/0.41 0.06/0.41 ### Ranking functions of CR eval_asctoeg_bb2_in(V_s,V_sp_0,B,C,D) 0.06/0.41 * RF of phase [11]: [V_s-V_sp_0] 0.06/0.41 0.06/0.41 #### Partial ranking functions of CR eval_asctoeg_bb2_in(V_s,V_sp_0,B,C,D) 0.06/0.41 * Partial RF of phase [11]: 0.06/0.41 - RF of loop [11:1]: 0.06/0.41 V_s-V_sp_0 0.06/0.41 0.06/0.41 0.06/0.41 ### Specialization of cost equations eval_asctoeg__critedge_in/4 0.06/0.41 * CE 8 is refined into CE [14] 0.06/0.41 * CE 10 is refined into CE [15] 0.06/0.41 * CE 9 is refined into CE [16] 0.06/0.41 0.06/0.41 0.06/0.41 ### Cost equations --> "Loop" of eval_asctoeg__critedge_in/4 0.06/0.41 * CEs [16] --> Loop 14 0.06/0.41 * CEs [14] --> Loop 15 0.06/0.41 * CEs [15] --> Loop 16 0.06/0.41 0.06/0.41 ### Ranking functions of CR eval_asctoeg__critedge_in(V_sp_0_sink,B,C,D) 0.06/0.41 * RF of phase [14]: [V_sp_0_sink-1] 0.06/0.41 0.06/0.41 #### Partial ranking functions of CR eval_asctoeg__critedge_in(V_sp_0_sink,B,C,D) 0.06/0.41 * Partial RF of phase [14]: 0.06/0.41 - RF of loop [14:1]: 0.06/0.41 V_sp_0_sink-1 0.06/0.41 0.06/0.41 0.06/0.41 ### Specialization of cost equations eval_asctoeg_bb1_in/3 0.06/0.41 * CE 4 is refined into CE [17] 0.06/0.41 * CE 3 is refined into CE [18,19,20,21,22,23,24,25,26] 0.06/0.41 0.06/0.41 0.06/0.41 ### Cost equations --> "Loop" of eval_asctoeg_bb1_in/3 0.06/0.41 * CEs [22] --> Loop 17 0.06/0.41 * CEs [18,24] --> Loop 18 0.06/0.41 * CEs [26] --> Loop 19 0.06/0.41 * CEs [21,23,25] --> Loop 20 0.06/0.41 * CEs [20] --> Loop 21 0.06/0.41 * CEs [19] --> Loop 22 0.06/0.41 * CEs [17] --> Loop 23 0.06/0.41 0.06/0.41 ### Ranking functions of CR eval_asctoeg_bb1_in(V_s,V_k_0,B) 0.06/0.41 * RF of phase [17,18,19,20,21]: [V_k_0] 0.06/0.41 0.06/0.41 #### Partial ranking functions of CR eval_asctoeg_bb1_in(V_s,V_k_0,B) 0.06/0.41 * Partial RF of phase [17,18,19,20,21]: 0.06/0.41 - RF of loop [17:1,18:1,19:1,20:1,21:1]: 0.06/0.41 V_k_0 0.06/0.41 0.06/0.41 0.06/0.41 ### Specialization of cost equations eval_asctoeg_bb0_in/2 0.06/0.41 * CE 2 is refined into CE [27,28,29] 0.06/0.41 0.06/0.41 0.06/0.41 ### Cost equations --> "Loop" of eval_asctoeg_bb0_in/2 0.06/0.41 * CEs [29] --> Loop 24 0.06/0.41 * CEs [28] --> Loop 25 0.06/0.41 * CEs [27] --> Loop 26 0.06/0.41 0.06/0.41 ### Ranking functions of CR eval_asctoeg_bb0_in(V_s,B) 0.06/0.41 0.06/0.41 #### Partial ranking functions of CR eval_asctoeg_bb0_in(V_s,B) 0.06/0.41 0.06/0.41 0.06/0.41 ### Specialization of cost equations eval_asctoeg_start/2 0.06/0.41 * CE 1 is refined into CE [30,31,32] 0.06/0.41 0.06/0.41 0.06/0.41 ### Cost equations --> "Loop" of eval_asctoeg_start/2 0.06/0.41 * CEs [32] --> Loop 27 0.06/0.41 * CEs [31] --> Loop 28 0.06/0.41 * CEs [30] --> Loop 29 0.06/0.41 0.06/0.41 ### Ranking functions of CR eval_asctoeg_start(V_s,B) 0.06/0.41 0.06/0.41 #### Partial ranking functions of CR eval_asctoeg_start(V_s,B) 0.06/0.41 0.06/0.41 0.06/0.41 Computing Bounds 0.06/0.41 ===================================== 0.06/0.41 0.06/0.41 #### Cost of chains of eval_asctoeg_bb2_in(V_s,V_sp_0,B,C,D): 0.06/0.41 * Chain [[11],13]: 1*it(11)+0 0.06/0.41 Such that:it(11) =< -V_sp_0+D 0.06/0.41 0.06/0.41 with precondition: [B=3,V_s=C,V_s=D,V_sp_0>=0,V_s>=V_sp_0+1] 0.06/0.41 0.06/0.41 * Chain [[11],12]: 1*it(11)+0 0.06/0.41 Such that:it(11) =< -V_sp_0+D 0.06/0.41 0.06/0.41 with precondition: [B=3,C=D,V_sp_0>=0,C>=V_sp_0+1,V_s>=C+1] 0.06/0.41 0.06/0.41 * Chain [12]: 0 0.06/0.41 with precondition: [B=3,V_sp_0=C,V_sp_0=D,V_sp_0>=0,V_s>=V_sp_0+1] 0.06/0.41 0.06/0.41 0.06/0.41 #### Cost of chains of eval_asctoeg__critedge_in(V_sp_0_sink,B,C,D): 0.06/0.41 * Chain [[14],16]: 1*it(14)+0 0.06/0.41 Such that:it(14) =< V_sp_0_sink 0.06/0.41 0.06/0.41 with precondition: [B=2,C=1,D=0,V_sp_0_sink>=2] 0.06/0.41 0.06/0.41 * Chain [[14],15]: 1*it(14)+0 0.06/0.41 Such that:it(14) =< V_sp_0_sink-D 0.06/0.41 0.06/0.41 with precondition: [B=2,C=D+1,C>=2,V_sp_0_sink>=C+1] 0.06/0.41 0.06/0.41 * Chain [16]: 0 0.06/0.41 with precondition: [B=2,V_sp_0_sink=C,V_sp_0_sink=D+1,1>=V_sp_0_sink] 0.06/0.41 0.06/0.41 * Chain [15]: 0 0.06/0.41 with precondition: [B=2,V_sp_0_sink=C,V_sp_0_sink=D+1,V_sp_0_sink>=2] 0.06/0.41 0.06/0.41 0.06/0.41 #### Cost of chains of eval_asctoeg_bb1_in(V_s,V_k_0,B): 0.06/0.41 * Chain [[17,18,19,20,21],23]: 6*it(17)+2*s(21)+6*s(24)+2*s(27)+0 0.06/0.41 Such that:aux(7) =< V_s 0.06/0.41 aux(14) =< V_k_0 0.06/0.41 it(17) =< aux(14) 0.06/0.41 aux(8) =< aux(7) 0.06/0.41 s(23) =< it(17)*aux(7) 0.06/0.41 s(27) =< it(17)*aux(8) 0.06/0.41 s(25) =< it(17)*aux(8) 0.06/0.41 s(24) =< s(25) 0.06/0.41 s(21) =< s(23) 0.06/0.41 0.06/0.41 with precondition: [B=4,V_k_0>=1,V_s>=V_k_0] 0.06/0.41 0.06/0.41 * Chain [23]: 0 0.06/0.41 with precondition: [B=4,0>=V_k_0,V_s>=V_k_0] 0.06/0.41 0.06/0.41 * Chain [22,23]: 1*s(30)+1 0.06/0.41 Such that:s(30) =< 1 0.06/0.41 0.06/0.41 with precondition: [V_s=1,V_k_0=1,B=4] 0.06/0.41 0.06/0.41 0.06/0.41 #### Cost of chains of eval_asctoeg_bb0_in(V_s,B): 0.06/0.41 * Chain [26]: 1*s(31)+1 0.06/0.41 Such that:s(31) =< 1 0.06/0.41 0.06/0.41 with precondition: [V_s=1] 0.06/0.41 0.06/0.41 * Chain [25]: 0 0.06/0.41 with precondition: [0>=V_s] 0.06/0.41 0.06/0.41 * Chain [24]: 6*s(34)+2*s(37)+6*s(39)+2*s(40)+0 0.06/0.41 Such that:aux(15) =< V_s 0.06/0.41 s(34) =< aux(15) 0.06/0.41 s(35) =< aux(15) 0.06/0.41 s(36) =< s(34)*aux(15) 0.06/0.41 s(37) =< s(34)*s(35) 0.06/0.41 s(38) =< s(34)*s(35) 0.06/0.41 s(39) =< s(38) 0.06/0.41 s(40) =< s(36) 0.06/0.41 0.06/0.41 with precondition: [V_s>=1] 0.06/0.41 0.06/0.41 0.06/0.41 #### Cost of chains of eval_asctoeg_start(V_s,B): 0.06/0.41 * Chain [29]: 1*s(41)+1 0.06/0.41 Such that:s(41) =< 1 0.06/0.41 0.06/0.41 with precondition: [V_s=1] 0.06/0.41 0.06/0.41 * Chain [28]: 0 0.06/0.41 with precondition: [0>=V_s] 0.06/0.41 0.06/0.41 * Chain [27]: 6*s(43)+2*s(46)+6*s(48)+2*s(49)+0 0.06/0.41 Such that:s(42) =< V_s 0.06/0.41 s(43) =< s(42) 0.06/0.41 s(44) =< s(42) 0.06/0.41 s(45) =< s(43)*s(42) 0.06/0.41 s(46) =< s(43)*s(44) 0.06/0.41 s(47) =< s(43)*s(44) 0.06/0.41 s(48) =< s(47) 0.06/0.41 s(49) =< s(45) 0.06/0.41 0.06/0.41 with precondition: [V_s>=1] 0.06/0.41 0.06/0.41 0.06/0.41 Closed-form bounds of eval_asctoeg_start(V_s,B): 0.06/0.41 ------------------------------------- 0.06/0.41 * Chain [29] with precondition: [V_s=1] 0.06/0.41 - Upper bound: 2 0.06/0.41 - Complexity: constant 0.06/0.41 * Chain [28] with precondition: [0>=V_s] 0.06/0.41 - Upper bound: 0 0.06/0.41 - Complexity: constant 0.06/0.41 * Chain [27] with precondition: [V_s>=1] 0.06/0.41 - Upper bound: 10*V_s*V_s+6*V_s 0.06/0.41 - Complexity: n^2 0.06/0.41 0.06/0.41 ### Maximum cost of eval_asctoeg_start(V_s,B): max([2,nat(V_s)*10*nat(V_s)+nat(V_s)*6]) 0.06/0.41 Asymptotic class: n^2 0.06/0.41 * Total analysis performed in 307 ms. 0.06/0.41 0.06/0.51 EOF