0.06/0.36 WORST_CASE(?,O(n^1)) 0.06/0.36 0.06/0.36 Preprocessing Cost Relations 0.06/0.36 ===================================== 0.06/0.36 0.06/0.36 #### Computed strongly connected components 0.06/0.36 0. recursive : [eval_s_SFD_process_8/5,eval_s_SFD_process_9/6,eval_s_SFD_process_bb5_in/4,eval_s_SFD_process_bb6_in/4] 0.06/0.36 1. recursive : [eval_s_SFD_process_1/5,eval_s_SFD_process_2/6,eval_s_SFD_process_4/7,eval_s_SFD_process_5/8,eval_s_SFD_process_bb1_in/4,eval_s_SFD_process_bb2_in/4,eval_s_SFD_process_bb3_in/6,eval_s_SFD_process_bb4_in/6,eval_s_SFD_process_bb5_in_loop_cont/9,eval_s_SFD_process_bb7_in/8] 0.06/0.36 2. non_recursive : [eval_s_SFD_process_stop/1] 0.06/0.36 3. non_recursive : [eval_s_SFD_process_bb8_in/1] 0.06/0.36 4. non_recursive : [eval_s_SFD_process_bb1_in_loop_cont/2] 0.06/0.36 5. non_recursive : [eval_s_SFD_process_bb0_in/4] 0.06/0.36 6. non_recursive : [eval_s_SFD_process_start/4] 0.06/0.36 0.06/0.36 #### Obtained direct recursion through partial evaluation 0.06/0.36 0. SCC is partially evaluated into eval_s_SFD_process_bb5_in/4 0.06/0.36 1. SCC is partially evaluated into eval_s_SFD_process_bb1_in/4 0.06/0.36 2. SCC is completely evaluated into other SCCs 0.06/0.36 3. SCC is completely evaluated into other SCCs 0.06/0.36 4. SCC is completely evaluated into other SCCs 0.06/0.36 5. SCC is partially evaluated into eval_s_SFD_process_bb0_in/4 0.06/0.36 6. SCC is partially evaluated into eval_s_SFD_process_start/4 0.06/0.36 0.06/0.36 Control-Flow Refinement of Cost Relations 0.06/0.36 ===================================== 0.06/0.36 0.06/0.36 ### Specialization of cost equations eval_s_SFD_process_bb5_in/4 0.06/0.36 * CE 9 is refined into CE [11] 0.06/0.36 * CE 10 is refined into CE [12] 0.06/0.36 * CE 8 is refined into CE [13] 0.06/0.36 0.06/0.36 0.06/0.36 ### Cost equations --> "Loop" of eval_s_SFD_process_bb5_in/4 0.06/0.36 * CEs [13] --> Loop 11 0.06/0.36 * CEs [11] --> Loop 12 0.06/0.36 * CEs [12] --> Loop 13 0.06/0.36 0.06/0.36 ### Ranking functions of CR eval_s_SFD_process_bb5_in(V__2,B,C,D) 0.06/0.36 * RF of phase [11]: [V__2] 0.06/0.36 0.06/0.36 #### Partial ranking functions of CR eval_s_SFD_process_bb5_in(V__2,B,C,D) 0.06/0.36 * Partial RF of phase [11]: 0.06/0.36 - RF of loop [11:1]: 0.06/0.36 V__2 0.06/0.36 0.06/0.36 0.06/0.36 ### Specialization of cost equations eval_s_SFD_process_bb1_in/4 0.06/0.36 * CE 7 is refined into CE [14] 0.06/0.36 * CE 3 is refined into CE [15,16,17] 0.06/0.36 * CE 4 is refined into CE [18] 0.06/0.36 * CE 6 is refined into CE [19] 0.06/0.36 * CE 5 is refined into CE [20] 0.06/0.36 0.06/0.36 0.06/0.36 ### Cost equations --> "Loop" of eval_s_SFD_process_bb1_in/4 0.06/0.36 * CEs [17] --> Loop 14 0.06/0.36 * CEs [18] --> Loop 15 0.06/0.36 * CEs [19] --> Loop 16 0.06/0.36 * CEs [16] --> Loop 17 0.06/0.36 * CEs [15] --> Loop 18 0.06/0.36 * CEs [20] --> Loop 19 0.06/0.36 * CEs [14] --> Loop 20 0.06/0.36 0.06/0.36 ### Ranking functions of CR eval_s_SFD_process_bb1_in(V_rlimit,V__01,V__0,B) 0.06/0.36 0.06/0.36 #### Partial ranking functions of CR eval_s_SFD_process_bb1_in(V_rlimit,V__01,V__0,B) 0.06/0.36 * Partial RF of phase [14,15,16,17,18,19]: 0.06/0.36 - RF of loop [14:1]: 0.06/0.36 V__01/2-1/2 depends on loops [16:1,19:1] 0.06/0.36 - RF of loop [15:1,16:1,19:1]: 0.06/0.36 V_rlimit-V__0 0.06/0.36 - RF of loop [17:1,18:1]: 0.06/0.36 V__01 depends on loops [16:1,19:1] 0.06/0.36 0.06/0.36 0.06/0.36 ### Specialization of cost equations eval_s_SFD_process_bb0_in/4 0.06/0.36 * CE 2 is refined into CE [21,22] 0.06/0.36 0.06/0.36 0.06/0.36 ### Cost equations --> "Loop" of eval_s_SFD_process_bb0_in/4 0.06/0.36 * CEs [21] --> Loop 21 0.06/0.36 * CEs [22] --> Loop 22 0.06/0.36 0.06/0.36 ### Ranking functions of CR eval_s_SFD_process_bb0_in(V_p,V_rlimit,V_match,B) 0.06/0.36 0.06/0.36 #### Partial ranking functions of CR eval_s_SFD_process_bb0_in(V_p,V_rlimit,V_match,B) 0.06/0.36 0.06/0.36 0.06/0.36 ### Specialization of cost equations eval_s_SFD_process_start/4 0.06/0.36 * CE 1 is refined into CE [23,24] 0.06/0.36 0.06/0.36 0.06/0.36 ### Cost equations --> "Loop" of eval_s_SFD_process_start/4 0.06/0.36 * CEs [24] --> Loop 23 0.06/0.36 * CEs [23] --> Loop 24 0.06/0.36 0.06/0.36 ### Ranking functions of CR eval_s_SFD_process_start(V_p,V_rlimit,V_match,B) 0.06/0.36 0.06/0.36 #### Partial ranking functions of CR eval_s_SFD_process_start(V_p,V_rlimit,V_match,B) 0.06/0.36 0.06/0.36 0.06/0.36 Computing Bounds 0.06/0.36 ===================================== 0.06/0.36 0.06/0.36 #### Cost of chains of eval_s_SFD_process_bb5_in(V__2,B,C,D): 0.06/0.36 * Chain [[11],13]: 1*it(11)+0 0.06/0.36 Such that:it(11) =< V__2 0.06/0.36 0.06/0.36 with precondition: [B=2,C=0,D=0,V__2>=1] 0.06/0.36 0.06/0.36 * Chain [[11],12]: 1*it(11)+0 0.06/0.36 Such that:it(11) =< V__2-D 0.06/0.36 0.06/0.36 with precondition: [B=2,C=D+1,C>=1,V__2>=C+1] 0.06/0.36 0.06/0.36 * Chain [12]: 0 0.06/0.36 with precondition: [B=2,V__2=C,V__2=D+1,V__2>=1] 0.06/0.36 0.06/0.36 0.06/0.36 #### Cost of chains of eval_s_SFD_process_bb1_in(V_rlimit,V__01,V__0,B): 0.06/0.36 * Chain [[14,15,16,17,18,19],20]: 1*it(14)+3*it(15)+2*it(17)+1*s(5)+1*s(6)+0 0.06/0.36 Such that:aux(13) =< V__01 0.06/0.36 aux(2) =< V__01/2 0.06/0.36 aux(14) =< V_rlimit-V__0 0.06/0.36 it(15) =< aux(14) 0.06/0.36 aux(5) =< max([aux(13),0])+it(15) 0.06/0.36 it(17) =< it(15)+aux(13) 0.06/0.36 s(5) =< it(15)+aux(13) 0.06/0.36 s(6) =< it(15)+aux(13) 0.06/0.36 it(14) =< aux(14)+it(15)*(1/2)+aux(2) 0.06/0.36 aux(9) =< aux(5) 0.06/0.36 s(5) =< it(14)*aux(5) 0.06/0.36 s(6) =< it(17)*aux(9) 0.06/0.36 0.06/0.36 with precondition: [B=3,V_rlimit>=V__0+1] 0.06/0.36 0.06/0.36 * Chain [20]: 0 0.06/0.36 with precondition: [B=3,V__0>=V_rlimit] 0.06/0.36 0.06/0.36 0.06/0.36 #### Cost of chains of eval_s_SFD_process_bb0_in(V_p,V_rlimit,V_match,B): 0.06/0.36 * Chain [22]: 3*s(10)+2*s(12)+1*s(13)+1*s(14)+1*s(15)+0 0.06/0.36 Such that:s(9) =< -V_p+V_rlimit 0.06/0.36 s(7) =< V_match 0.06/0.36 s(8) =< V_match/2 0.06/0.36 s(10) =< s(9) 0.06/0.36 s(11) =< max([s(7),0])+s(10) 0.06/0.36 s(12) =< s(10)+s(7) 0.06/0.36 s(13) =< s(10)+s(7) 0.06/0.36 s(14) =< s(10)+s(7) 0.06/0.36 s(15) =< s(9)+s(10)*(1/2)+s(8) 0.06/0.36 s(16) =< s(11) 0.06/0.36 s(13) =< s(15)*s(11) 0.06/0.36 s(14) =< s(12)*s(16) 0.06/0.36 0.06/0.36 with precondition: [V_rlimit>=V_p+1] 0.06/0.36 0.06/0.36 * Chain [21]: 0 0.06/0.36 with precondition: [V_p>=V_rlimit] 0.06/0.36 0.06/0.36 0.06/0.36 #### Cost of chains of eval_s_SFD_process_start(V_p,V_rlimit,V_match,B): 0.06/0.36 * Chain [24]: 3*s(20)+2*s(22)+1*s(23)+1*s(24)+1*s(25)+0 0.06/0.36 Such that:s(17) =< -V_p+V_rlimit 0.06/0.36 s(18) =< V_match 0.06/0.36 s(19) =< V_match/2 0.06/0.36 s(20) =< s(17) 0.06/0.36 s(21) =< max([s(18),0])+s(20) 0.06/0.36 s(22) =< s(20)+s(18) 0.06/0.36 s(23) =< s(20)+s(18) 0.06/0.36 s(24) =< s(20)+s(18) 0.06/0.36 s(25) =< s(17)+s(20)*(1/2)+s(19) 0.06/0.36 s(26) =< s(21) 0.06/0.36 s(23) =< s(25)*s(21) 0.06/0.36 s(24) =< s(22)*s(26) 0.06/0.36 0.06/0.36 with precondition: [V_rlimit>=V_p+1] 0.06/0.36 0.06/0.36 * Chain [23]: 0 0.06/0.36 with precondition: [V_p>=V_rlimit] 0.06/0.36 0.06/0.36 0.06/0.36 Closed-form bounds of eval_s_SFD_process_start(V_p,V_rlimit,V_match,B): 0.06/0.36 ------------------------------------- 0.06/0.36 * Chain [24] with precondition: [V_rlimit>=V_p+1] 0.06/0.36 - Upper bound: -17/2*V_p+17/2*V_rlimit+nat(V_match)*4+nat(V_match/2) 0.06/0.36 - Complexity: n 0.06/0.36 * Chain [23] with precondition: [V_p>=V_rlimit] 0.06/0.36 - Upper bound: 0 0.06/0.36 - Complexity: constant 0.06/0.36 0.06/0.36 ### Maximum cost of eval_s_SFD_process_start(V_p,V_rlimit,V_match,B): 17/2*nat(-V_p+V_rlimit)+nat(V_match)*4+nat(V_match/2) 0.06/0.36 Asymptotic class: n 0.06/0.36 * Total analysis performed in 253 ms. 0.06/0.36 0.06/0.46 EOF