0.59/0.60 WORST_CASE(?,O(n^1)) 0.59/0.60 0.59/0.60 Preprocessing Cost Relations 0.59/0.60 ===================================== 0.59/0.60 0.59/0.60 #### Computed strongly connected components 0.59/0.60 0. recursive : [eval_start_6/10,eval_start_7/10,eval_start_bb2_in/10,eval_start_bb3_in/10] 0.59/0.60 1. recursive : [eval_start_bb1_in/10,eval_start_bb2_in_loop_cont/11] 0.59/0.60 2. non_recursive : [eval_start_stop/6] 0.59/0.60 3. non_recursive : [eval_start_bb4_in/6] 0.59/0.60 4. non_recursive : [exit_location/1] 0.59/0.60 5. non_recursive : [eval_start_bb1_in_loop_cont/7] 0.59/0.60 6. non_recursive : [eval_start_3/6] 0.59/0.60 7. non_recursive : [eval_start_2/6] 0.59/0.60 8. non_recursive : [eval_start_1/6] 0.59/0.60 9. non_recursive : [eval_start_0/6] 0.59/0.60 10. non_recursive : [eval_start_bb0_in/6] 0.59/0.60 11. non_recursive : [eval_start_start/6] 0.59/0.60 0.59/0.60 #### Obtained direct recursion through partial evaluation 0.59/0.60 0. SCC is partially evaluated into eval_start_bb2_in/10 0.59/0.60 1. SCC is partially evaluated into eval_start_bb1_in/10 0.59/0.60 2. SCC is completely evaluated into other SCCs 0.59/0.60 3. SCC is completely evaluated into other SCCs 0.59/0.60 4. SCC is completely evaluated into other SCCs 0.59/0.60 5. SCC is partially evaluated into eval_start_bb1_in_loop_cont/7 0.59/0.60 6. SCC is partially evaluated into eval_start_3/6 0.59/0.60 7. SCC is completely evaluated into other SCCs 0.59/0.60 8. SCC is completely evaluated into other SCCs 0.59/0.60 9. SCC is completely evaluated into other SCCs 0.59/0.60 10. SCC is completely evaluated into other SCCs 0.59/0.60 11. SCC is partially evaluated into eval_start_start/6 0.59/0.60 0.59/0.60 Control-Flow Refinement of Cost Relations 0.59/0.60 ===================================== 0.59/0.60 0.59/0.60 ### Specialization of cost equations eval_start_bb2_in/10 0.59/0.60 * CE 12 is refined into CE [13] 0.59/0.60 * CE 10 is refined into CE [14] 0.59/0.60 * CE 11 is refined into CE [15] 0.59/0.60 * CE 9 is refined into CE [16] 0.59/0.60 0.59/0.60 0.59/0.60 ### Cost equations --> "Loop" of eval_start_bb2_in/10 0.59/0.60 * CEs [16] --> Loop 13 0.59/0.60 * CEs [13] --> Loop 14 0.59/0.60 * CEs [14] --> Loop 15 0.59/0.60 * CEs [15] --> Loop 16 0.59/0.60 0.59/0.60 ### Ranking functions of CR eval_start_bb2_in(V_1,V_3,V_n,V_x_0,V_x_0_sink,B,C,D,E,F) 0.59/0.60 * RF of phase [13]: [V_n-V_x_0_sink-1] 0.59/0.60 0.59/0.60 #### Partial ranking functions of CR eval_start_bb2_in(V_1,V_3,V_n,V_x_0,V_x_0_sink,B,C,D,E,F) 0.59/0.60 * Partial RF of phase [13]: 0.59/0.60 - RF of loop [13:1]: 0.59/0.60 V_n-V_x_0_sink-1 0.59/0.60 0.59/0.60 0.59/0.60 ### Specialization of cost equations eval_start_bb1_in/10 0.59/0.60 * CE 5 is refined into CE [17] 0.59/0.60 * CE 3 is refined into CE [18,19] 0.59/0.60 * CE 6 is refined into CE [20] 0.59/0.60 * CE 4 is refined into CE [21,22,23,24] 0.59/0.60 0.59/0.60 0.59/0.60 ### Cost equations --> "Loop" of eval_start_bb1_in/10 0.59/0.60 * CEs [24] --> Loop 17 0.59/0.60 * CEs [23] --> Loop 18 0.59/0.60 * CEs [21] --> Loop 19 0.59/0.60 * CEs [22] --> Loop 20 0.59/0.60 * CEs [17] --> Loop 21 0.59/0.60 * CEs [19] --> Loop 22 0.59/0.60 * CEs [18] --> Loop 23 0.59/0.60 * CEs [20] --> Loop 24 0.59/0.60 0.59/0.60 ### Ranking functions of CR eval_start_bb1_in(V_1,V_3,V_n,V_x_0,V_x_0_sink,B,C,D,E,F) 0.59/0.60 * RF of phase [17,18]: [V_n-V_x_0-1] 0.59/0.60 0.59/0.60 #### Partial ranking functions of CR eval_start_bb1_in(V_1,V_3,V_n,V_x_0,V_x_0_sink,B,C,D,E,F) 0.59/0.60 * Partial RF of phase [17,18]: 0.59/0.60 - RF of loop [17:1]: 0.59/0.60 V_n/2-V_x_0/2-1 0.59/0.60 - RF of loop [18:1]: 0.59/0.60 V_n-V_x_0-1 0.59/0.60 0.59/0.60 0.59/0.60 ### Specialization of cost equations eval_start_bb1_in_loop_cont/7 0.59/0.60 * CE 7 is refined into CE [25] 0.59/0.60 * CE 8 is refined into CE [26] 0.59/0.60 0.59/0.60 0.59/0.60 ### Cost equations --> "Loop" of eval_start_bb1_in_loop_cont/7 0.59/0.60 * CEs [25] --> Loop 25 0.59/0.60 * CEs [26] --> Loop 26 0.59/0.60 0.59/0.60 ### Ranking functions of CR eval_start_bb1_in_loop_cont(A,B,C,D,E,F,G) 0.59/0.60 0.59/0.60 #### Partial ranking functions of CR eval_start_bb1_in_loop_cont(A,B,C,D,E,F,G) 0.59/0.60 0.59/0.60 0.59/0.60 ### Specialization of cost equations eval_start_3/6 0.59/0.60 * CE 2 is refined into CE [27,28,29,30,31,32,33,34,35,36] 0.59/0.60 0.59/0.60 0.59/0.60 ### Cost equations --> "Loop" of eval_start_3/6 0.59/0.60 * CEs [31,34] --> Loop 27 0.59/0.60 * CEs [30,33,35] --> Loop 28 0.59/0.60 * CEs [29] --> Loop 29 0.59/0.60 * CEs [32] --> Loop 30 0.59/0.60 * CEs [27,36] --> Loop 31 0.59/0.60 * CEs [28] --> Loop 32 0.59/0.60 0.59/0.60 ### Ranking functions of CR eval_start_3(V_1,V_3,V_n,V_x_0,V_x_0_sink,B) 0.59/0.60 0.59/0.60 #### Partial ranking functions of CR eval_start_3(V_1,V_3,V_n,V_x_0,V_x_0_sink,B) 0.59/0.60 0.59/0.60 0.59/0.60 ### Specialization of cost equations eval_start_start/6 0.59/0.60 * CE 1 is refined into CE [37,38,39,40,41,42] 0.59/0.60 0.59/0.60 0.59/0.60 ### Cost equations --> "Loop" of eval_start_start/6 0.59/0.60 * CEs [42] --> Loop 33 0.59/0.60 * CEs [41] --> Loop 34 0.59/0.60 * CEs [40] --> Loop 35 0.59/0.60 * CEs [39] --> Loop 36 0.59/0.60 * CEs [38] --> Loop 37 0.59/0.60 * CEs [37] --> Loop 38 0.59/0.60 0.59/0.60 ### Ranking functions of CR eval_start_start(V_1,V_3,V_n,V_x_0,V_x_0_sink,B) 0.59/0.60 0.59/0.60 #### Partial ranking functions of CR eval_start_start(V_1,V_3,V_n,V_x_0,V_x_0_sink,B) 0.59/0.60 0.59/0.60 0.59/0.60 Computing Bounds 0.59/0.60 ===================================== 0.59/0.60 0.59/0.60 #### Cost of chains of eval_start_bb2_in(V_1,V_3,V_n,V_x_0,V_x_0_sink,B,C,D,E,F): 0.59/0.60 * Chain [[13],16]: 1*it(13)+0 0.59/0.60 Such that:it(13) =< V_n-V_x_0_sink 0.59/0.60 0.59/0.60 with precondition: [B=2,V_n=C+1,V_n=E,V_n=F+1,0>=D,V_x_0_sink>=V_x_0,V_n>=V_x_0_sink+2] 0.59/0.60 0.59/0.60 * Chain [[13],15]: 1*it(13)+0 0.59/0.60 Such that:it(13) =< -V_x_0_sink+C 0.59/0.60 0.59/0.60 with precondition: [B=2,C=E,C=F+1,D>=1,V_x_0_sink>=V_x_0,C>=V_x_0_sink+2,V_n>=C+1] 0.59/0.60 0.59/0.60 * Chain [[13],14]: 1*it(13)+0 0.59/0.60 Such that:it(13) =< V_n-V_x_0_sink 0.59/0.60 0.59/0.60 with precondition: [B=3,V_x_0_sink>=V_x_0,V_n>=V_x_0_sink+2] 0.59/0.60 0.59/0.60 * Chain [16]: 0 0.59/0.60 with precondition: [B=2,C=V_1,D=V_3,V_x_0_sink+1=V_n,V_x_0_sink+1=E,V_x_0_sink=F,V_x_0_sink>=V_x_0] 0.59/0.60 0.59/0.60 * Chain [15]: 0 0.59/0.60 with precondition: [B=2,V_x_0_sink+1=C,V_x_0_sink+1=E,V_x_0_sink=F,D>=1,V_x_0_sink>=V_x_0,V_n>=V_x_0_sink+2] 0.59/0.60 0.59/0.60 * Chain [14]: 0 0.59/0.60 with precondition: [B=3,V_x_0_sink>=V_x_0,V_n>=V_x_0_sink+1] 0.59/0.60 0.59/0.60 0.59/0.60 #### Cost of chains of eval_start_bb1_in(V_1,V_3,V_n,V_x_0,V_x_0_sink,B,C,D,E,F): 0.59/0.60 * Chain [[17,18],24]: 1*it(17)+2*it(18)+0 0.59/0.60 Such that:it(17) =< V_n/2-V_x_0/2 0.59/0.60 aux(3) =< V_n-V_x_0 0.59/0.60 it(17) =< aux(3) 0.59/0.60 it(18) =< aux(3) 0.59/0.60 0.59/0.60 with precondition: [B=3,V_x_0>=0,V_n>=V_x_0+2] 0.59/0.60 0.59/0.60 * Chain [[17,18],23]: 1*it(17)+2*it(18)+0 0.59/0.60 Such that:it(17) =< V_n/2-V_x_0/2 0.59/0.60 aux(4) =< V_n-V_x_0 0.59/0.60 it(17) =< aux(4) 0.59/0.60 it(18) =< aux(4) 0.59/0.60 0.59/0.60 with precondition: [B=3,V_x_0>=0,V_n>=V_x_0+2] 0.59/0.60 0.59/0.60 * Chain [[17,18],22]: 1*it(17)+3*it(18)+0 0.59/0.60 Such that:it(17) =< V_n/2-V_x_0/2 0.59/0.60 aux(5) =< V_n-V_x_0 0.59/0.60 it(17) =< aux(5) 0.59/0.60 it(18) =< aux(5) 0.59/0.60 0.59/0.60 with precondition: [B=3,V_x_0>=0,V_n>=V_x_0+3] 0.59/0.60 0.59/0.60 * Chain [[17,18],20,24]: 1*it(17)+3*it(18)+1 0.59/0.60 Such that:it(17) =< V_n/2-V_x_0/2 0.59/0.60 aux(6) =< V_n-V_x_0 0.59/0.60 it(17) =< aux(6) 0.59/0.60 it(18) =< aux(6) 0.59/0.60 0.59/0.60 with precondition: [B=3,V_x_0>=0,V_n>=V_x_0+3] 0.59/0.60 0.59/0.60 * Chain [[17,18],20,21]: 1*it(17)+2*it(18)+1*s(5)+1 0.59/0.60 Such that:aux(2) =< -V_x_0+C 0.59/0.60 it(17) =< -V_x_0/2+C/2 0.59/0.60 aux(7) =< -V_x_0+C+1 0.59/0.60 aux(2) =< aux(7) 0.59/0.60 it(17) =< aux(7) 0.59/0.60 s(5) =< aux(7) 0.59/0.60 it(18) =< aux(7) 0.59/0.60 it(17) =< aux(2) 0.59/0.60 it(18) =< aux(2) 0.59/0.60 0.59/0.60 with precondition: [B=4,C+1=V_n,C+1=E,C=F,0>=D,V_x_0>=0,C>=V_x_0+2] 0.59/0.60 0.59/0.60 * Chain [[17,18],19,24]: 1*it(17)+2*it(18)+1 0.59/0.60 Such that:it(17) =< V_n/2-V_x_0/2 0.59/0.60 aux(8) =< V_n-V_x_0 0.59/0.60 it(17) =< aux(8) 0.59/0.60 it(18) =< aux(8) 0.59/0.60 0.59/0.60 with precondition: [B=3,V_x_0>=0,V_n>=V_x_0+2] 0.59/0.60 0.59/0.60 * Chain [[17,18],19,21]: 1*it(17)+2*it(18)+1 0.59/0.60 Such that:aux(2) =< -V_x_0+C 0.59/0.60 aux(1) =< -V_x_0+C+1 0.59/0.60 it(17) =< -V_x_0/2+C/2 0.59/0.60 it(17) =< aux(1) 0.59/0.60 it(18) =< aux(1) 0.59/0.60 it(17) =< aux(2) 0.59/0.60 it(18) =< aux(2) 0.59/0.60 0.59/0.60 with precondition: [B=4,C+1=V_n,C+1=E,C=F,V_x_0>=0,D>=1,C>=V_x_0+1] 0.59/0.60 0.59/0.60 * Chain [24]: 0 0.59/0.60 with precondition: [B=3,V_x_0>=0] 0.59/0.60 0.59/0.60 * Chain [23]: 0 0.59/0.60 with precondition: [B=3,V_x_0>=0,V_n>=V_x_0+1] 0.59/0.60 0.59/0.60 * Chain [22]: 1*s(4)+0 0.59/0.60 Such that:s(4) =< V_n-V_x_0 0.59/0.60 0.59/0.60 with precondition: [B=3,V_x_0>=0,V_n>=V_x_0+2] 0.59/0.60 0.59/0.60 * Chain [21]: 0 0.59/0.60 with precondition: [B=4,C=V_1,D=V_3,F=V_x_0_sink,V_x_0=E,V_x_0>=0,V_x_0>=V_n] 0.59/0.60 0.59/0.60 * Chain [20,24]: 1*s(5)+1 0.59/0.60 Such that:s(5) =< V_n-V_x_0 0.59/0.60 0.59/0.60 with precondition: [B=3,V_x_0>=0,V_n>=V_x_0+2] 0.59/0.60 0.59/0.60 * Chain [20,21]: 1*s(5)+1 0.59/0.60 Such that:s(5) =< -V_x_0+C+1 0.59/0.60 0.59/0.60 with precondition: [B=4,C+1=V_n,C+1=E,C=F,0>=D,V_x_0>=0,C>=V_x_0+1] 0.59/0.60 0.59/0.60 * Chain [19,24]: 1 0.59/0.60 with precondition: [B=3,V_x_0+1=V_n,V_x_0>=0] 0.59/0.60 0.59/0.60 * Chain [19,21]: 1 0.59/0.60 with precondition: [B=4,V_n=V_x_0+1,V_1=C,V_3=D,V_n=E,V_n=F+1,V_n>=1] 0.59/0.60 0.59/0.60 0.59/0.60 #### Cost of chains of eval_start_bb1_in_loop_cont(A,B,C,D,E,F,G): 0.59/0.60 * Chain [26]: 0 0.59/0.60 with precondition: [A=3] 0.59/0.60 0.59/0.60 * Chain [25]: 0 0.59/0.60 with precondition: [A=4] 0.59/0.60 0.59/0.60 0.59/0.60 #### Cost of chains of eval_start_3(V_1,V_3,V_n,V_x_0,V_x_0_sink,B): 0.59/0.60 * Chain [32]: 0 0.59/0.60 with precondition: [] 0.59/0.60 0.59/0.60 * Chain [31]: 1 0.59/0.60 with precondition: [V_n=1] 0.59/0.60 0.59/0.60 * Chain [30]: 0 0.59/0.60 with precondition: [0>=V_n] 0.59/0.60 0.59/0.60 * Chain [29]: 0 0.59/0.60 with precondition: [V_n>=1] 0.59/0.60 0.59/0.60 * Chain [28]: 11*s(25)+4*s(26)+1 0.59/0.60 Such that:aux(14) =< V_n 0.59/0.60 aux(15) =< V_n/2 0.59/0.60 s(25) =< aux(14) 0.59/0.60 s(26) =< aux(15) 0.59/0.60 s(26) =< aux(14) 0.59/0.60 0.59/0.60 with precondition: [V_n>=2] 0.59/0.60 0.59/0.60 * Chain [27]: 3*s(34)+9*s(35)+1 0.59/0.60 Such that:aux(17) =< V_n 0.59/0.60 aux(18) =< V_n/2 0.59/0.60 s(34) =< aux(18) 0.59/0.60 s(34) =< aux(17) 0.59/0.60 s(35) =< aux(17) 0.59/0.60 0.59/0.60 with precondition: [V_n>=3] 0.59/0.60 0.59/0.60 0.59/0.60 #### Cost of chains of eval_start_start(V_1,V_3,V_n,V_x_0,V_x_0_sink,B): 0.59/0.60 * Chain [38]: 0 0.59/0.60 with precondition: [] 0.59/0.60 0.59/0.60 * Chain [37]: 1 0.59/0.60 with precondition: [V_n=1] 0.59/0.60 0.59/0.60 * Chain [36]: 0 0.59/0.60 with precondition: [0>=V_n] 0.59/0.60 0.59/0.60 * Chain [35]: 0 0.59/0.60 with precondition: [V_n>=1] 0.59/0.60 0.59/0.60 * Chain [34]: 11*s(43)+4*s(44)+1 0.59/0.60 Such that:s(41) =< V_n 0.59/0.60 s(42) =< V_n/2 0.59/0.60 s(43) =< s(41) 0.59/0.60 s(44) =< s(42) 0.59/0.60 s(44) =< s(41) 0.59/0.60 0.59/0.60 with precondition: [V_n>=2] 0.59/0.60 0.59/0.60 * Chain [33]: 3*s(47)+9*s(48)+1 0.59/0.60 Such that:s(45) =< V_n 0.59/0.60 s(46) =< V_n/2 0.59/0.60 s(47) =< s(46) 0.59/0.60 s(47) =< s(45) 0.59/0.60 s(48) =< s(45) 0.59/0.60 0.59/0.60 with precondition: [V_n>=3] 0.59/0.60 0.59/0.60 0.59/0.60 Closed-form bounds of eval_start_start(V_1,V_3,V_n,V_x_0,V_x_0_sink,B): 0.59/0.60 ------------------------------------- 0.59/0.60 * Chain [38] with precondition: [] 0.59/0.60 - Upper bound: 0 0.59/0.60 - Complexity: constant 0.59/0.60 * Chain [37] with precondition: [V_n=1] 0.59/0.60 - Upper bound: 1 0.59/0.60 - Complexity: constant 0.59/0.60 * Chain [36] with precondition: [0>=V_n] 0.59/0.60 - Upper bound: 0 0.59/0.60 - Complexity: constant 0.59/0.60 * Chain [35] with precondition: [V_n>=1] 0.59/0.60 - Upper bound: 0 0.59/0.60 - Complexity: constant 0.59/0.60 * Chain [34] with precondition: [V_n>=2] 0.59/0.60 - Upper bound: 13*V_n+1 0.59/0.60 - Complexity: n 0.59/0.60 * Chain [33] with precondition: [V_n>=3] 0.59/0.60 - Upper bound: 21/2*V_n+1 0.59/0.60 - Complexity: n 0.59/0.60 0.59/0.60 ### Maximum cost of eval_start_start(V_1,V_3,V_n,V_x_0,V_x_0_sink,B): nat(V_n/2)*3+nat(V_n)*9+(nat(V_n)*2+nat(V_n/2))+1 0.59/0.60 Asymptotic class: n 0.59/0.60 * Total analysis performed in 512 ms. 0.59/0.60 0.60/0.70 EOF