0.04/0.51 WORST_CASE(?,O(n^1)) 0.04/0.51 0.04/0.51 Preprocessing Cost Relations 0.04/0.51 ===================================== 0.04/0.51 0.04/0.51 #### Computed strongly connected components 0.04/0.51 0. recursive : [eval_start_5/9,eval_start_6/9,eval_start_bb2_in/9,eval_start_bb3_in/9] 0.04/0.51 1. recursive : [eval_start_bb1_in/9,eval_start_bb2_in_loop_cont/10] 0.04/0.51 2. non_recursive : [eval_start_stop/6] 0.04/0.51 3. non_recursive : [eval_start_bb4_in/6] 0.04/0.51 4. non_recursive : [exit_location/1] 0.04/0.51 5. non_recursive : [eval_start_bb1_in_loop_cont/7] 0.04/0.51 6. non_recursive : [eval_start_2/6] 0.04/0.51 7. non_recursive : [eval_start_1/6] 0.04/0.51 8. non_recursive : [eval_start_0/6] 0.04/0.51 9. non_recursive : [eval_start_bb0_in/6] 0.04/0.51 10. non_recursive : [eval_start_start/6] 0.04/0.51 0.04/0.51 #### Obtained direct recursion through partial evaluation 0.04/0.51 0. SCC is partially evaluated into eval_start_bb2_in/9 0.04/0.51 1. SCC is partially evaluated into eval_start_bb1_in/9 0.04/0.51 2. SCC is completely evaluated into other SCCs 0.04/0.51 3. SCC is completely evaluated into other SCCs 0.04/0.51 4. SCC is completely evaluated into other SCCs 0.04/0.51 5. SCC is partially evaluated into eval_start_bb1_in_loop_cont/7 0.04/0.51 6. SCC is partially evaluated into eval_start_2/6 0.04/0.51 7. SCC is completely evaluated into other SCCs 0.04/0.51 8. SCC is completely evaluated into other SCCs 0.04/0.51 9. SCC is completely evaluated into other SCCs 0.04/0.51 10. SCC is partially evaluated into eval_start_start/6 0.04/0.51 0.04/0.51 Control-Flow Refinement of Cost Relations 0.04/0.51 ===================================== 0.04/0.51 0.04/0.51 ### Specialization of cost equations eval_start_bb2_in/9 0.04/0.51 * CE 12 is refined into CE [13] 0.04/0.51 * CE 11 is refined into CE [14] 0.04/0.51 * CE 10 is refined into CE [15] 0.04/0.51 * CE 9 is refined into CE [16] 0.04/0.51 0.04/0.51 0.04/0.51 ### Cost equations --> "Loop" of eval_start_bb2_in/9 0.04/0.51 * CEs [16] --> Loop 13 0.04/0.51 * CEs [13] --> Loop 14 0.04/0.51 * CEs [15] --> Loop 15 0.04/0.51 * CEs [14] --> Loop 16 0.04/0.51 0.04/0.51 ### Ranking functions of CR eval_start_bb2_in(V__0,V__0_sink,V_1,V_3,B,C,D,E,F) 0.04/0.51 * RF of phase [13]: [V__0_sink-1] 0.04/0.51 0.04/0.51 #### Partial ranking functions of CR eval_start_bb2_in(V__0,V__0_sink,V_1,V_3,B,C,D,E,F) 0.04/0.51 * Partial RF of phase [13]: 0.04/0.51 - RF of loop [13:1]: 0.04/0.51 V__0_sink-1 0.04/0.51 0.04/0.51 0.04/0.51 ### Specialization of cost equations eval_start_bb1_in/9 0.04/0.51 * CE 5 is refined into CE [17] 0.04/0.51 * CE 3 is refined into CE [18,19] 0.04/0.51 * CE 6 is refined into CE [20] 0.04/0.51 * CE 4 is refined into CE [21,22,23,24] 0.04/0.51 0.04/0.51 0.04/0.51 ### Cost equations --> "Loop" of eval_start_bb1_in/9 0.04/0.51 * CEs [24] --> Loop 17 0.04/0.51 * CEs [23] --> Loop 18 0.04/0.51 * CEs [22] --> Loop 19 0.04/0.51 * CEs [21] --> Loop 20 0.04/0.51 * CEs [17] --> Loop 21 0.04/0.51 * CEs [19] --> Loop 22 0.04/0.51 * CEs [18] --> Loop 23 0.04/0.51 * CEs [20] --> Loop 24 0.04/0.51 0.04/0.51 ### Ranking functions of CR eval_start_bb1_in(V__0,V__0_sink,V_1,V_3,B,C,D,E,F) 0.04/0.51 * RF of phase [17,18]: [V__0-1] 0.04/0.51 0.04/0.51 #### Partial ranking functions of CR eval_start_bb1_in(V__0,V__0_sink,V_1,V_3,B,C,D,E,F) 0.04/0.51 * Partial RF of phase [17,18]: 0.04/0.51 - RF of loop [17:1]: 0.04/0.51 V__0/2-1 0.04/0.51 - RF of loop [18:1]: 0.04/0.51 V__0-1 0.04/0.51 0.04/0.51 0.04/0.51 ### Specialization of cost equations eval_start_bb1_in_loop_cont/7 0.04/0.51 * CE 7 is refined into CE [25] 0.04/0.51 * CE 8 is refined into CE [26] 0.04/0.51 0.04/0.51 0.04/0.51 ### Cost equations --> "Loop" of eval_start_bb1_in_loop_cont/7 0.04/0.51 * CEs [25] --> Loop 25 0.04/0.51 * CEs [26] --> Loop 26 0.04/0.51 0.04/0.51 ### Ranking functions of CR eval_start_bb1_in_loop_cont(A,B,C,D,E,F,G) 0.04/0.51 0.04/0.51 #### Partial ranking functions of CR eval_start_bb1_in_loop_cont(A,B,C,D,E,F,G) 0.04/0.51 0.04/0.51 0.04/0.51 ### Specialization of cost equations eval_start_2/6 0.04/0.51 * CE 2 is refined into CE [27,28,29,30,31,32,33,34,35,36] 0.04/0.51 0.04/0.51 0.04/0.51 ### Cost equations --> "Loop" of eval_start_2/6 0.04/0.51 * CEs [32,34] --> Loop 27 0.04/0.51 * CEs [31,33,35] --> Loop 28 0.04/0.51 * CEs [30] --> Loop 29 0.04/0.51 * CEs [36] --> Loop 30 0.04/0.51 * CEs [27,28] --> Loop 31 0.04/0.51 * CEs [29] --> Loop 32 0.04/0.51 0.04/0.51 ### Ranking functions of CR eval_start_2(V__0,V__0_sink,V_1,V_3,V_n,B) 0.04/0.51 0.04/0.51 #### Partial ranking functions of CR eval_start_2(V__0,V__0_sink,V_1,V_3,V_n,B) 0.04/0.51 0.04/0.51 0.04/0.51 ### Specialization of cost equations eval_start_start/6 0.04/0.51 * CE 1 is refined into CE [37,38,39,40,41,42] 0.04/0.51 0.04/0.51 0.04/0.51 ### Cost equations --> "Loop" of eval_start_start/6 0.04/0.51 * CEs [42] --> Loop 33 0.04/0.51 * CEs [41] --> Loop 34 0.04/0.51 * CEs [40] --> Loop 35 0.04/0.51 * CEs [39] --> Loop 36 0.04/0.51 * CEs [38] --> Loop 37 0.04/0.51 * CEs [37] --> Loop 38 0.04/0.51 0.04/0.51 ### Ranking functions of CR eval_start_start(V__0,V__0_sink,V_1,V_3,V_n,B) 0.04/0.51 0.04/0.51 #### Partial ranking functions of CR eval_start_start(V__0,V__0_sink,V_1,V_3,V_n,B) 0.04/0.51 0.04/0.51 0.04/0.51 Computing Bounds 0.04/0.51 ===================================== 0.04/0.51 0.04/0.51 #### Cost of chains of eval_start_bb2_in(V__0,V__0_sink,V_1,V_3,B,C,D,E,F): 0.04/0.51 * Chain [[13],16]: 1*it(13)+0 0.04/0.51 Such that:it(13) =< V__0_sink 0.04/0.51 0.04/0.51 with precondition: [B=2,C=0,D=1,E=1,0>=F,V__0_sink>=2,V__0>=V__0_sink] 0.04/0.51 0.04/0.51 * Chain [[13],15]: 1*it(13)+0 0.04/0.51 Such that:it(13) =< V__0_sink-D 0.04/0.51 0.04/0.51 with precondition: [B=2,C+1=D,C=E,C>=1,F>=1,V__0>=V__0_sink,V__0_sink>=C+2] 0.04/0.51 0.04/0.51 * Chain [[13],14]: 1*it(13)+0 0.04/0.51 Such that:it(13) =< V__0_sink 0.04/0.51 0.04/0.51 with precondition: [B=3,V__0_sink>=2,V__0>=V__0_sink] 0.04/0.51 0.04/0.51 * Chain [16]: 0 0.04/0.51 with precondition: [V__0_sink=1,B=2,C=0,D=1,E=V_1,F=V_3,V__0>=1] 0.04/0.51 0.04/0.51 * Chain [15]: 0 0.04/0.51 with precondition: [B=2,V__0_sink=C+1,V__0_sink=D,V__0_sink=E+1,V__0_sink>=2,F>=1,V__0>=V__0_sink] 0.04/0.51 0.04/0.51 * Chain [14]: 0 0.04/0.51 with precondition: [B=3,V__0_sink>=1,V__0>=V__0_sink] 0.04/0.51 0.04/0.51 0.04/0.51 #### Cost of chains of eval_start_bb1_in(V__0,V__0_sink,V_1,V_3,B,C,D,E,F): 0.04/0.51 * Chain [[17,18],24]: 1*it(17)+2*it(18)+0 0.04/0.51 Such that:it(17) =< V__0/2 0.04/0.51 aux(3) =< V__0 0.04/0.51 it(17) =< aux(3) 0.04/0.51 it(18) =< aux(3) 0.04/0.51 0.04/0.51 with precondition: [B=3,V__0>=2] 0.04/0.51 0.04/0.51 * Chain [[17,18],23]: 1*it(17)+2*it(18)+0 0.04/0.51 Such that:it(17) =< V__0/2 0.04/0.51 aux(4) =< V__0 0.04/0.51 it(17) =< aux(4) 0.04/0.51 it(18) =< aux(4) 0.04/0.51 0.04/0.51 with precondition: [B=3,V__0>=2] 0.04/0.51 0.04/0.51 * Chain [[17,18],22]: 1*it(17)+3*it(18)+0 0.04/0.51 Such that:it(17) =< V__0/2 0.04/0.51 aux(5) =< V__0 0.04/0.51 it(17) =< aux(5) 0.04/0.51 it(18) =< aux(5) 0.04/0.51 0.04/0.51 with precondition: [B=3,V__0>=3] 0.04/0.51 0.04/0.51 * Chain [[17,18],20,24]: 1*it(17)+2*it(18)+1 0.04/0.51 Such that:it(17) =< V__0/2 0.04/0.51 aux(6) =< V__0 0.04/0.51 it(17) =< aux(6) 0.04/0.51 it(18) =< aux(6) 0.04/0.51 0.04/0.51 with precondition: [B=3,V__0>=2] 0.04/0.51 0.04/0.51 * Chain [[17,18],20,21]: 1*it(17)+2*it(18)+1 0.04/0.51 Such that:it(17) =< V__0/2 0.04/0.51 aux(7) =< V__0 0.04/0.51 it(17) =< aux(7) 0.04/0.51 it(18) =< aux(7) 0.04/0.51 0.04/0.51 with precondition: [B=4,C=0,D=1,E=1,V__0>=2,F>=1] 0.04/0.51 0.04/0.51 * Chain [[17,18],19,24]: 1*it(17)+3*it(18)+1 0.04/0.51 Such that:it(17) =< V__0/2 0.04/0.51 aux(8) =< V__0 0.04/0.51 it(17) =< aux(8) 0.04/0.51 it(18) =< aux(8) 0.04/0.51 0.04/0.51 with precondition: [B=3,V__0>=3] 0.04/0.51 0.04/0.51 * Chain [[17,18],19,21]: 1*it(17)+3*it(18)+1 0.04/0.51 Such that:it(17) =< V__0/2 0.04/0.51 aux(9) =< V__0 0.04/0.51 it(17) =< aux(9) 0.04/0.51 it(18) =< aux(9) 0.04/0.51 0.04/0.51 with precondition: [B=4,C=0,D=1,E=1,0>=F,V__0>=3] 0.04/0.51 0.04/0.51 * Chain [24]: 0 0.04/0.51 with precondition: [B=3] 0.04/0.51 0.04/0.51 * Chain [23]: 0 0.04/0.51 with precondition: [B=3,V__0>=1] 0.04/0.51 0.04/0.51 * Chain [22]: 1*s(4)+0 0.04/0.51 Such that:s(4) =< V__0 0.04/0.51 0.04/0.51 with precondition: [B=3,V__0>=2] 0.04/0.51 0.04/0.51 * Chain [21]: 0 0.04/0.51 with precondition: [B=4,D=V__0_sink,E=V_1,F=V_3,V__0=C,0>=V__0] 0.04/0.51 0.04/0.51 * Chain [20,24]: 1 0.04/0.51 with precondition: [V__0=1,B=3] 0.04/0.51 0.04/0.51 * Chain [20,21]: 1 0.04/0.51 with precondition: [V__0=1,B=4,C=0,D=1,V_1=E,V_3=F] 0.04/0.51 0.04/0.51 * Chain [19,24]: 1*s(5)+1 0.04/0.51 Such that:s(5) =< V__0 0.04/0.51 0.04/0.51 with precondition: [B=3,V__0>=2] 0.04/0.51 0.04/0.51 * Chain [19,21]: 1*s(5)+1 0.04/0.51 Such that:s(5) =< V__0 0.04/0.51 0.04/0.51 with precondition: [B=4,C=0,D=1,E=1,0>=F,V__0>=2] 0.04/0.51 0.04/0.51 0.04/0.51 #### Cost of chains of eval_start_bb1_in_loop_cont(A,B,C,D,E,F,G): 0.04/0.51 * Chain [26]: 0 0.04/0.51 with precondition: [A=3] 0.04/0.51 0.04/0.51 * Chain [25]: 0 0.04/0.51 with precondition: [A=4] 0.04/0.51 0.04/0.51 0.04/0.51 #### Cost of chains of eval_start_2(V__0,V__0_sink,V_1,V_3,V_n,B): 0.04/0.51 * Chain [32]: 0 0.04/0.51 with precondition: [] 0.04/0.51 0.04/0.51 * Chain [31]: 1 0.04/0.51 with precondition: [V_n=1] 0.04/0.51 0.04/0.51 * Chain [30]: 0 0.04/0.51 with precondition: [0>=V_n] 0.04/0.51 0.04/0.51 * Chain [29]: 0 0.04/0.51 with precondition: [V_n>=1] 0.04/0.51 0.04/0.51 * Chain [28]: 11*s(25)+4*s(26)+1 0.04/0.51 Such that:aux(14) =< V_n 0.04/0.51 aux(15) =< V_n/2 0.04/0.51 s(25) =< aux(14) 0.04/0.51 s(26) =< aux(15) 0.04/0.51 s(26) =< aux(14) 0.04/0.51 0.04/0.51 with precondition: [V_n>=2] 0.04/0.51 0.04/0.51 * Chain [27]: 3*s(33)+9*s(34)+1 0.04/0.51 Such that:aux(16) =< V_n 0.04/0.51 aux(17) =< V_n/2 0.04/0.51 s(33) =< aux(17) 0.04/0.51 s(33) =< aux(16) 0.04/0.51 s(34) =< aux(16) 0.04/0.51 0.04/0.51 with precondition: [V_n>=3] 0.04/0.51 0.04/0.51 0.04/0.51 #### Cost of chains of eval_start_start(V__0,V__0_sink,V_1,V_3,V_n,B): 0.04/0.51 * Chain [38]: 0 0.04/0.51 with precondition: [] 0.04/0.51 0.04/0.51 * Chain [37]: 1 0.04/0.51 with precondition: [V_n=1] 0.04/0.51 0.04/0.51 * Chain [36]: 0 0.04/0.51 with precondition: [0>=V_n] 0.04/0.51 0.04/0.51 * Chain [35]: 0 0.04/0.51 with precondition: [V_n>=1] 0.04/0.51 0.04/0.51 * Chain [34]: 11*s(40)+4*s(41)+1 0.04/0.51 Such that:s(38) =< V_n 0.04/0.51 s(39) =< V_n/2 0.04/0.51 s(40) =< s(38) 0.04/0.51 s(41) =< s(39) 0.04/0.51 s(41) =< s(38) 0.04/0.51 0.04/0.51 with precondition: [V_n>=2] 0.04/0.51 0.04/0.51 * Chain [33]: 3*s(44)+9*s(45)+1 0.04/0.51 Such that:s(42) =< V_n 0.04/0.51 s(43) =< V_n/2 0.04/0.51 s(44) =< s(43) 0.04/0.51 s(44) =< s(42) 0.04/0.51 s(45) =< s(42) 0.04/0.51 0.04/0.51 with precondition: [V_n>=3] 0.04/0.51 0.04/0.51 0.04/0.51 Closed-form bounds of eval_start_start(V__0,V__0_sink,V_1,V_3,V_n,B): 0.04/0.51 ------------------------------------- 0.04/0.51 * Chain [38] with precondition: [] 0.04/0.51 - Upper bound: 0 0.04/0.51 - Complexity: constant 0.04/0.51 * Chain [37] with precondition: [V_n=1] 0.04/0.51 - Upper bound: 1 0.04/0.51 - Complexity: constant 0.04/0.51 * Chain [36] with precondition: [0>=V_n] 0.04/0.51 - Upper bound: 0 0.04/0.51 - Complexity: constant 0.04/0.51 * Chain [35] with precondition: [V_n>=1] 0.04/0.51 - Upper bound: 0 0.04/0.51 - Complexity: constant 0.04/0.51 * Chain [34] with precondition: [V_n>=2] 0.04/0.51 - Upper bound: 13*V_n+1 0.04/0.51 - Complexity: n 0.04/0.51 * Chain [33] with precondition: [V_n>=3] 0.04/0.51 - Upper bound: 21/2*V_n+1 0.04/0.51 - Complexity: n 0.04/0.51 0.04/0.51 ### Maximum cost of eval_start_start(V__0,V__0_sink,V_1,V_3,V_n,B): nat(V_n/2)*3+nat(V_n)*9+(nat(V_n)*2+nat(V_n/2))+1 0.04/0.51 Asymptotic class: n 0.04/0.51 * Total analysis performed in 422 ms. 0.04/0.51 0.51/0.61 EOF