0.69/0.75 WORST_CASE(?,O(n^2)) 0.69/0.75 0.69/0.75 Preprocessing Cost Relations 0.69/0.75 ===================================== 0.69/0.75 0.69/0.75 #### Computed strongly connected components 0.69/0.75 0. recursive : [eval_perfect1_bb3_in/4,eval_perfect1_bb4_in/4] 0.69/0.75 1. recursive : [eval_perfect1_12/14,eval_perfect1_13/14,eval_perfect1_14/14,eval_perfect1_15/14,eval_perfect1_16/14,eval_perfect1_17/14,eval_perfect1_bb2_in/14,eval_perfect1_bb3_in_loop_cont/15,eval_perfect1_bb5_in/14] 0.69/0.75 2. non_recursive : [eval_perfect1_stop/9] 0.69/0.75 3. non_recursive : [eval_perfect1_bb7_in/9] 0.69/0.75 4. non_recursive : [eval_perfect1_bb6_in/9] 0.69/0.75 5. non_recursive : [exit_location/1] 0.69/0.75 6. non_recursive : [eval_perfect1_bb2_in_loop_cont/10] 0.69/0.75 7. non_recursive : [eval_perfect1_8/9] 0.69/0.75 8. non_recursive : [eval_perfect1_7/9] 0.69/0.75 9. non_recursive : [eval_perfect1_6/9] 0.69/0.75 10. non_recursive : [eval_perfect1_5/9] 0.69/0.75 11. non_recursive : [eval_perfect1_4/9] 0.69/0.75 12. non_recursive : [eval_perfect1_3/9] 0.69/0.75 13. non_recursive : [eval_perfect1_2/9] 0.69/0.75 14. non_recursive : [eval_perfect1_bb1_in/9] 0.69/0.75 15. non_recursive : [eval_perfect1_1/9] 0.69/0.75 16. non_recursive : [eval_perfect1_0/9] 0.69/0.75 17. non_recursive : [eval_perfect1_bb0_in/9] 0.69/0.75 18. non_recursive : [eval_perfect1_start/9] 0.69/0.75 0.69/0.75 #### Obtained direct recursion through partial evaluation 0.69/0.75 0. SCC is partially evaluated into eval_perfect1_bb3_in/4 0.69/0.75 1. SCC is partially evaluated into eval_perfect1_bb2_in/14 0.69/0.75 2. SCC is completely evaluated into other SCCs 0.69/0.75 3. SCC is completely evaluated into other SCCs 0.69/0.75 4. SCC is partially evaluated into eval_perfect1_bb6_in/9 0.69/0.75 5. SCC is completely evaluated into other SCCs 0.69/0.75 6. SCC is partially evaluated into eval_perfect1_bb2_in_loop_cont/10 0.69/0.75 7. SCC is partially evaluated into eval_perfect1_8/9 0.69/0.75 8. SCC is completely evaluated into other SCCs 0.69/0.75 9. SCC is completely evaluated into other SCCs 0.69/0.75 10. SCC is completely evaluated into other SCCs 0.69/0.75 11. SCC is completely evaluated into other SCCs 0.69/0.75 12. SCC is completely evaluated into other SCCs 0.69/0.75 13. SCC is completely evaluated into other SCCs 0.69/0.75 14. SCC is completely evaluated into other SCCs 0.69/0.75 15. SCC is partially evaluated into eval_perfect1_1/9 0.69/0.75 16. SCC is completely evaluated into other SCCs 0.69/0.75 17. SCC is completely evaluated into other SCCs 0.69/0.75 18. SCC is partially evaluated into eval_perfect1_start/9 0.69/0.75 0.69/0.75 Control-Flow Refinement of Cost Relations 0.69/0.75 ===================================== 0.69/0.75 0.69/0.75 ### Specialization of cost equations eval_perfect1_bb3_in/4 0.69/0.75 * CE 15 is refined into CE [19] 0.69/0.75 * CE 14 is refined into CE [20] 0.69/0.75 * CE 13 is refined into CE [21] 0.69/0.75 0.69/0.75 0.69/0.75 ### Cost equations --> "Loop" of eval_perfect1_bb3_in/4 0.69/0.75 * CEs [21] --> Loop 19 0.69/0.75 * CEs [19] --> Loop 20 0.69/0.75 * CEs [20] --> Loop 21 0.69/0.75 0.69/0.75 ### Ranking functions of CR eval_perfect1_bb3_in(V_y1_0,V_y2_1,B,C) 0.69/0.75 * RF of phase [19]: [-V_y1_0+V_y2_1+1,V_y2_1] 0.69/0.75 0.69/0.75 #### Partial ranking functions of CR eval_perfect1_bb3_in(V_y1_0,V_y2_1,B,C) 0.69/0.75 * Partial RF of phase [19]: 0.69/0.75 - RF of loop [19:1]: 0.69/0.75 -V_y1_0+V_y2_1+1 0.69/0.75 V_y2_1 0.69/0.75 0.69/0.75 0.69/0.75 ### Specialization of cost equations eval_perfect1_bb2_in/14 0.69/0.75 * CE 9 is refined into CE [22] 0.69/0.75 * CE 8 is refined into CE [23,24] 0.69/0.75 * CE 10 is refined into CE [25] 0.69/0.75 * CE 7 is refined into CE [26] 0.69/0.75 * CE 6 is discarded (unfeasible) 0.69/0.75 * CE 5 is refined into CE [27] 0.69/0.75 0.69/0.75 0.69/0.75 ### Cost equations --> "Loop" of eval_perfect1_bb2_in/14 0.69/0.75 * CEs [26] --> Loop 22 0.69/0.75 * CEs [27] --> Loop 23 0.69/0.75 * CEs [22] --> Loop 24 0.69/0.75 * CEs [23,24] --> Loop 25 0.69/0.75 * CEs [25] --> Loop 26 0.69/0.75 0.69/0.75 ### Ranking functions of CR eval_perfect1_bb2_in(V__y3_0,V_6,V_7,V_x,V_y1_0,V_y2_1,V_y3_0,B,C,D,E,F,G,H) 0.69/0.75 * RF of phase [22,23]: [V_y1_0] 0.69/0.75 0.69/0.75 #### Partial ranking functions of CR eval_perfect1_bb2_in(V__y3_0,V_6,V_7,V_x,V_y1_0,V_y2_1,V_y3_0,B,C,D,E,F,G,H) 0.69/0.75 * Partial RF of phase [22,23]: 0.69/0.75 - RF of loop [22:1]: 0.69/0.75 V_y1_0-1 0.69/0.75 - RF of loop [23:1]: 0.69/0.75 V_y1_0 0.69/0.75 0.69/0.75 0.69/0.75 ### Specialization of cost equations eval_perfect1_bb6_in/9 0.69/0.75 * CE 17 is refined into CE [28] 0.69/0.75 * CE 16 is refined into CE [29] 0.69/0.75 * CE 18 is refined into CE [30] 0.69/0.75 0.69/0.75 0.69/0.75 ### Cost equations --> "Loop" of eval_perfect1_bb6_in/9 0.69/0.75 * CEs [28] --> Loop 27 0.69/0.75 * CEs [29] --> Loop 28 0.69/0.75 * CEs [30] --> Loop 29 0.69/0.75 0.69/0.75 ### Ranking functions of CR eval_perfect1_bb6_in(V__y3_0,V_1,V_6,V_7,V_x,V_y1_0,V_y2_1,V_y3_0,B) 0.69/0.75 0.69/0.75 #### Partial ranking functions of CR eval_perfect1_bb6_in(V__y3_0,V_1,V_6,V_7,V_x,V_y1_0,V_y2_1,V_y3_0,B) 0.69/0.75 0.69/0.75 0.69/0.75 ### Specialization of cost equations eval_perfect1_bb2_in_loop_cont/10 0.69/0.75 * CE 11 is refined into CE [31,32,33] 0.69/0.75 * CE 12 is refined into CE [34] 0.69/0.75 0.69/0.75 0.69/0.75 ### Cost equations --> "Loop" of eval_perfect1_bb2_in_loop_cont/10 0.69/0.75 * CEs [33] --> Loop 30 0.69/0.75 * CEs [32] --> Loop 31 0.69/0.75 * CEs [31] --> Loop 32 0.69/0.75 * CEs [34] --> Loop 33 0.69/0.75 0.69/0.75 ### Ranking functions of CR eval_perfect1_bb2_in_loop_cont(A,B,C,D,E,F,G,H,I,J) 0.69/0.75 0.69/0.75 #### Partial ranking functions of CR eval_perfect1_bb2_in_loop_cont(A,B,C,D,E,F,G,H,I,J) 0.69/0.75 0.69/0.75 0.69/0.75 ### Specialization of cost equations eval_perfect1_8/9 0.69/0.75 * CE 4 is refined into CE [35,36,37,38,39,40] 0.69/0.75 0.69/0.75 0.69/0.75 ### Cost equations --> "Loop" of eval_perfect1_8/9 0.69/0.75 * CEs [37] --> Loop 34 0.69/0.75 * CEs [35,36,38,39,40] --> Loop 35 0.69/0.75 0.69/0.75 ### Ranking functions of CR eval_perfect1_8(V__y3_0,V_1,V_6,V_7,V_x,V_y1_0,V_y2_1,V_y3_0,B) 0.69/0.75 0.69/0.75 #### Partial ranking functions of CR eval_perfect1_8(V__y3_0,V_1,V_6,V_7,V_x,V_y1_0,V_y2_1,V_y3_0,B) 0.69/0.75 0.69/0.75 0.69/0.75 ### Specialization of cost equations eval_perfect1_1/9 0.69/0.75 * CE 3 is refined into CE [41,42] 0.69/0.75 * CE 2 is refined into CE [43] 0.69/0.75 0.69/0.75 0.69/0.75 ### Cost equations --> "Loop" of eval_perfect1_1/9 0.69/0.75 * CEs [42] --> Loop 36 0.69/0.75 * CEs [41] --> Loop 37 0.69/0.75 * CEs [43] --> Loop 38 0.69/0.75 0.69/0.75 ### Ranking functions of CR eval_perfect1_1(V__y3_0,V_1,V_6,V_7,V_x,V_y1_0,V_y2_1,V_y3_0,B) 0.69/0.75 0.69/0.75 #### Partial ranking functions of CR eval_perfect1_1(V__y3_0,V_1,V_6,V_7,V_x,V_y1_0,V_y2_1,V_y3_0,B) 0.69/0.75 0.69/0.75 0.69/0.75 ### Specialization of cost equations eval_perfect1_start/9 0.69/0.75 * CE 1 is refined into CE [44,45,46] 0.69/0.75 0.69/0.75 0.69/0.75 ### Cost equations --> "Loop" of eval_perfect1_start/9 0.69/0.75 * CEs [46] --> Loop 39 0.69/0.75 * CEs [45] --> Loop 40 0.69/0.75 * CEs [44] --> Loop 41 0.69/0.75 0.69/0.75 ### Ranking functions of CR eval_perfect1_start(V__y3_0,V_1,V_6,V_7,V_x,V_y1_0,V_y2_1,V_y3_0,B) 0.69/0.75 0.69/0.75 #### Partial ranking functions of CR eval_perfect1_start(V__y3_0,V_1,V_6,V_7,V_x,V_y1_0,V_y2_1,V_y3_0,B) 0.69/0.75 0.69/0.75 0.69/0.75 Computing Bounds 0.69/0.75 ===================================== 0.69/0.75 0.69/0.75 #### Cost of chains of eval_perfect1_bb3_in(V_y1_0,V_y2_1,B,C): 0.69/0.75 * Chain [[19],21]: 1*it(19)+0 0.69/0.75 Such that:it(19) =< -V_y1_0+V_y2_1+1 0.69/0.75 0.69/0.75 with precondition: [B=2,C>=0,V_y1_0>=C+1,V_y2_1>=V_y1_0+C] 0.69/0.75 0.69/0.75 * Chain [[19],20]: 1*it(19)+0 0.69/0.75 Such that:it(19) =< -V_y1_0+V_y2_1+1 0.69/0.75 0.69/0.75 with precondition: [B=3,V_y1_0>=1,V_y2_1>=V_y1_0] 0.69/0.75 0.69/0.75 * Chain [20]: 0 0.69/0.75 with precondition: [B=3,V_y1_0>=1] 0.69/0.75 0.69/0.75 0.69/0.75 #### Cost of chains of eval_perfect1_bb2_in(V__y3_0,V_6,V_7,V_x,V_y1_0,V_y2_1,V_y3_0,B,C,D,E,F,G,H): 0.69/0.75 * Chain [[22,23],26]: 2*it(22)+1*s(5)+1*s(6)+0 0.69/0.75 Such that:aux(1) =< V_x 0.69/0.75 aux(5) =< V_y1_0 0.69/0.75 it(22) =< aux(5) 0.69/0.75 aux(2) =< aux(1) 0.69/0.75 s(5) =< it(22)*aux(1) 0.69/0.75 s(6) =< it(22)*aux(2) 0.69/0.75 0.69/0.75 with precondition: [B=3,V_y1_0>=1,V_x>=V_y1_0+1,V_x>=V_y3_0] 0.69/0.75 0.69/0.75 * Chain [[22,23],25]: 2*it(22)+1*s(5)+1*s(6)+1*s(7)+0 0.69/0.75 Such that:aux(6) =< V_x 0.69/0.75 aux(7) =< V_y1_0 0.69/0.75 s(7) =< aux(6) 0.69/0.75 it(22) =< aux(7) 0.69/0.75 aux(2) =< aux(6) 0.69/0.75 s(5) =< it(22)*aux(6) 0.69/0.75 s(6) =< it(22)*aux(2) 0.69/0.75 0.69/0.75 with precondition: [B=3,V_y1_0>=2,V_x>=V_y1_0+1,V_x>=V_y3_0] 0.69/0.75 0.69/0.75 * Chain [[22,23],24]: 2*it(22)+1*s(5)+1*s(6)+0 0.69/0.75 Such that:aux(1) =< V_x 0.69/0.75 aux(8) =< V_y1_0 0.69/0.75 it(22) =< aux(8) 0.69/0.75 aux(2) =< aux(1) 0.69/0.75 s(5) =< it(22)*aux(1) 0.69/0.75 s(6) =< it(22)*aux(2) 0.69/0.75 0.69/0.75 with precondition: [B=4,E=0,F=0,G=0,C=D,C=H,V_y1_0>=1,V_x>=V_y1_0+1,V_x>=V_y3_0,V_y3_0>=C+1] 0.69/0.75 0.69/0.75 * Chain [26]: 0 0.69/0.75 with precondition: [B=3,V_x>=2,V_x>=V_y1_0+1,V_x>=V_y3_0,V_x+V_y1_0>=V_y3_0+1] 0.69/0.75 0.69/0.75 * Chain [25]: 1*s(7)+0 0.69/0.75 Such that:s(7) =< V_x-V_y1_0+1 0.69/0.75 0.69/0.75 with precondition: [B=3,V_y1_0>=1,V_x>=V_y1_0+1,V_x>=V_y3_0] 0.69/0.75 0.69/0.75 0.69/0.75 #### Cost of chains of eval_perfect1_bb6_in(V__y3_0,V_1,V_6,V_7,V_x,V_y1_0,V_y2_1,V_y3_0,B): 0.69/0.75 * Chain [29]: 0 0.69/0.75 with precondition: [V_y3_0=0,V_1+1=V_x,V_1>=1] 0.69/0.75 0.69/0.75 * Chain [28]: 0 0.69/0.75 with precondition: [V_1+1=V_x,0>=V_y3_0+1,V_1>=1] 0.69/0.75 0.69/0.75 * Chain [27]: 0 0.69/0.75 with precondition: [V_1+1=V_x,V_1>=1,V_y3_0>=1] 0.69/0.75 0.69/0.75 0.69/0.75 #### Cost of chains of eval_perfect1_bb2_in_loop_cont(A,B,C,D,E,F,G,H,I,J): 0.69/0.75 * Chain [33]: 0 0.69/0.75 with precondition: [A=3,F=C+1,F>=2] 0.69/0.75 0.69/0.75 * Chain [32]: 0 0.69/0.75 with precondition: [A=4,I=0,F=C+1,F>=2] 0.69/0.75 0.69/0.75 * Chain [31]: 0 0.69/0.75 with precondition: [A=4,F=C+1,0>=I+1,F>=2] 0.69/0.75 0.69/0.75 * Chain [30]: 0 0.69/0.75 with precondition: [A=4,F=C+1,F>=2,I>=1] 0.69/0.75 0.69/0.75 0.69/0.75 #### Cost of chains of eval_perfect1_8(V__y3_0,V_1,V_6,V_7,V_x,V_y1_0,V_y2_1,V_y3_0,B): 0.69/0.75 * Chain [35]: 1*s(16)+8*s(18)+4*s(20)+4*s(21)+0 0.69/0.75 Such that:s(16) =< 2 0.69/0.75 aux(9) =< V_1 0.69/0.75 aux(10) =< V_1+1 0.69/0.75 s(18) =< aux(9) 0.69/0.75 s(19) =< aux(10) 0.69/0.75 s(20) =< s(18)*aux(10) 0.69/0.75 s(21) =< s(18)*s(19) 0.69/0.75 0.69/0.75 with precondition: [V_x=V_1+1,V_x>=2] 0.69/0.75 0.69/0.75 * Chain [34]: 1*s(42)+2*s(43)+1*s(45)+1*s(46)+0 0.69/0.75 Such that:s(41) =< V_1 0.69/0.75 s(40) =< V_1+1 0.69/0.75 s(42) =< s(40) 0.69/0.75 s(43) =< s(41) 0.69/0.75 s(44) =< s(40) 0.69/0.75 s(45) =< s(43)*s(40) 0.69/0.75 s(46) =< s(43)*s(44) 0.69/0.75 0.69/0.75 with precondition: [V_x=V_1+1,V_x>=3] 0.69/0.75 0.69/0.75 0.69/0.75 #### Cost of chains of eval_perfect1_1(V__y3_0,V_1,V_6,V_7,V_x,V_y1_0,V_y2_1,V_y3_0,B): 0.69/0.75 * Chain [38]: 0 0.69/0.75 with precondition: [1>=V_x] 0.69/0.75 0.69/0.75 * Chain [37]: 1*s(47)+8*s(50)+4*s(52)+4*s(53)+0 0.69/0.75 Such that:s(47) =< 2 0.69/0.75 aux(11) =< V_x 0.69/0.75 s(50) =< aux(11) 0.69/0.75 s(51) =< aux(11) 0.69/0.75 s(52) =< s(50)*aux(11) 0.69/0.75 s(53) =< s(50)*s(51) 0.69/0.75 0.69/0.75 with precondition: [V_x>=2] 0.69/0.75 0.69/0.75 * Chain [36]: 3*s(56)+1*s(59)+1*s(60)+0 0.69/0.75 Such that:aux(12) =< V_x 0.69/0.75 s(56) =< aux(12) 0.69/0.75 s(58) =< aux(12) 0.69/0.75 s(59) =< s(56)*aux(12) 0.69/0.75 s(60) =< s(56)*s(58) 0.69/0.75 0.69/0.75 with precondition: [V_x>=3] 0.69/0.75 0.69/0.75 0.69/0.75 #### Cost of chains of eval_perfect1_start(V__y3_0,V_1,V_6,V_7,V_x,V_y1_0,V_y2_1,V_y3_0,B): 0.69/0.75 * Chain [41]: 0 0.69/0.75 with precondition: [1>=V_x] 0.69/0.75 0.69/0.75 * Chain [40]: 1*s(61)+8*s(63)+4*s(65)+4*s(66)+0 0.69/0.75 Such that:s(61) =< 2 0.69/0.75 s(62) =< V_x 0.69/0.75 s(63) =< s(62) 0.69/0.75 s(64) =< s(62) 0.69/0.75 s(65) =< s(63)*s(62) 0.69/0.75 s(66) =< s(63)*s(64) 0.69/0.75 0.69/0.75 with precondition: [V_x>=2] 0.69/0.75 0.69/0.75 * Chain [39]: 3*s(68)+1*s(70)+1*s(71)+0 0.69/0.75 Such that:s(67) =< V_x 0.69/0.75 s(68) =< s(67) 0.69/0.75 s(69) =< s(67) 0.69/0.75 s(70) =< s(68)*s(67) 0.69/0.75 s(71) =< s(68)*s(69) 0.69/0.75 0.69/0.75 with precondition: [V_x>=3] 0.69/0.75 0.69/0.75 0.69/0.75 Closed-form bounds of eval_perfect1_start(V__y3_0,V_1,V_6,V_7,V_x,V_y1_0,V_y2_1,V_y3_0,B): 0.69/0.75 ------------------------------------- 0.69/0.75 * Chain [41] with precondition: [1>=V_x] 0.69/0.75 - Upper bound: 0 0.69/0.75 - Complexity: constant 0.69/0.75 * Chain [40] with precondition: [V_x>=2] 0.69/0.75 - Upper bound: 8*V_x+2+8*V_x*V_x 0.69/0.75 - Complexity: n^2 0.69/0.75 * Chain [39] with precondition: [V_x>=3] 0.69/0.75 - Upper bound: 2*V_x*V_x+3*V_x 0.69/0.75 - Complexity: n^2 0.69/0.75 0.69/0.75 ### Maximum cost of eval_perfect1_start(V__y3_0,V_1,V_6,V_7,V_x,V_y1_0,V_y2_1,V_y3_0,B): nat(V_x)*5+2+nat(V_x)*6*nat(V_x)+(nat(V_x)*2*nat(V_x)+nat(V_x)*3) 0.69/0.75 Asymptotic class: n^2 0.69/0.75 * Total analysis performed in 645 ms. 0.69/0.75 0.76/0.85 EOF