0.62/0.67 WORST_CASE(?,O(n^2)) 0.62/0.67 0.62/0.67 Preprocessing Cost Relations 0.62/0.67 ===================================== 0.62/0.67 0.62/0.67 #### Computed strongly connected components 0.62/0.67 0. recursive : [eval_perfect_bb2_in/4,eval_perfect_bb3_in/4] 0.62/0.67 1. recursive : [eval_perfect_10/14,eval_perfect_11/14,eval_perfect_7/14,eval_perfect_8/14,eval_perfect_9/14,eval_perfect_bb1_in/14,eval_perfect_bb2_in_loop_cont/15,eval_perfect_bb4_in/14] 0.62/0.67 2. non_recursive : [eval_perfect_stop/8] 0.62/0.67 3. non_recursive : [eval_perfect_bb6_in/8] 0.62/0.67 4. non_recursive : [eval_perfect_bb5_in/8] 0.62/0.67 5. non_recursive : [exit_location/1] 0.62/0.67 6. non_recursive : [eval_perfect_bb1_in_loop_cont/9] 0.62/0.67 7. non_recursive : [eval_perfect_1/8] 0.62/0.67 8. non_recursive : [eval_perfect_0/8] 0.62/0.67 9. non_recursive : [eval_perfect_bb0_in/8] 0.62/0.67 10. non_recursive : [eval_perfect_start/8] 0.62/0.67 0.62/0.67 #### Obtained direct recursion through partial evaluation 0.62/0.67 0. SCC is partially evaluated into eval_perfect_bb2_in/4 0.62/0.67 1. SCC is partially evaluated into eval_perfect_bb1_in/14 0.62/0.67 2. SCC is completely evaluated into other SCCs 0.62/0.67 3. SCC is completely evaluated into other SCCs 0.62/0.67 4. SCC is partially evaluated into eval_perfect_bb5_in/8 0.62/0.67 5. SCC is completely evaluated into other SCCs 0.62/0.67 6. SCC is partially evaluated into eval_perfect_bb1_in_loop_cont/9 0.62/0.67 7. SCC is partially evaluated into eval_perfect_1/8 0.62/0.67 8. SCC is completely evaluated into other SCCs 0.62/0.67 9. SCC is completely evaluated into other SCCs 0.62/0.67 10. SCC is partially evaluated into eval_perfect_start/8 0.62/0.67 0.62/0.67 Control-Flow Refinement of Cost Relations 0.62/0.67 ===================================== 0.62/0.67 0.62/0.67 ### Specialization of cost equations eval_perfect_bb2_in/4 0.62/0.67 * CE 14 is refined into CE [18] 0.62/0.67 * CE 13 is refined into CE [19] 0.62/0.67 * CE 12 is refined into CE [20] 0.62/0.67 0.62/0.67 0.62/0.67 ### Cost equations --> "Loop" of eval_perfect_bb2_in/4 0.62/0.67 * CEs [20] --> Loop 18 0.62/0.67 * CEs [18] --> Loop 19 0.62/0.67 * CEs [19] --> Loop 20 0.62/0.67 0.62/0.67 ### Ranking functions of CR eval_perfect_bb2_in(V_1,V_y2_1,B,C) 0.62/0.67 * RF of phase [18]: [-V_1+V_y2_1+1,V_y2_1] 0.62/0.67 0.62/0.67 #### Partial ranking functions of CR eval_perfect_bb2_in(V_1,V_y2_1,B,C) 0.62/0.67 * Partial RF of phase [18]: 0.62/0.67 - RF of loop [18:1]: 0.62/0.67 -V_1+V_y2_1+1 0.62/0.67 V_y2_1 0.62/0.67 0.62/0.67 0.62/0.67 ### Specialization of cost equations eval_perfect_bb1_in/14 0.62/0.67 * CE 8 is refined into CE [21] 0.62/0.67 * CE 7 is refined into CE [22,23] 0.62/0.67 * CE 9 is refined into CE [24] 0.62/0.67 * CE 6 is refined into CE [25] 0.62/0.67 * CE 5 is discarded (unfeasible) 0.62/0.67 * CE 4 is refined into CE [26] 0.62/0.67 0.62/0.67 0.62/0.67 ### Cost equations --> "Loop" of eval_perfect_bb1_in/14 0.62/0.67 * CEs [25] --> Loop 21 0.62/0.67 * CEs [26] --> Loop 22 0.62/0.67 * CEs [21] --> Loop 23 0.62/0.67 * CEs [22,23] --> Loop 24 0.62/0.67 * CEs [24] --> Loop 25 0.62/0.67 0.62/0.67 ### Ranking functions of CR eval_perfect_bb1_in(V__y3_0,V_1,V_6,V_x,V_y1_0_sink,V_y2_1,V_y3_0,B,C,D,E,F,G,H) 0.62/0.67 * RF of phase [21,22]: [V_y1_0_sink-1] 0.62/0.67 0.62/0.67 #### Partial ranking functions of CR eval_perfect_bb1_in(V__y3_0,V_1,V_6,V_x,V_y1_0_sink,V_y2_1,V_y3_0,B,C,D,E,F,G,H) 0.62/0.67 * Partial RF of phase [21,22]: 0.62/0.67 - RF of loop [21:1]: 0.62/0.67 V_y1_0_sink-2 0.62/0.67 - RF of loop [22:1]: 0.62/0.67 V_y1_0_sink-1 0.62/0.67 0.62/0.67 0.62/0.67 ### Specialization of cost equations eval_perfect_bb5_in/8 0.62/0.67 * CE 16 is refined into CE [27] 0.62/0.67 * CE 15 is refined into CE [28] 0.62/0.67 * CE 17 is refined into CE [29] 0.62/0.67 0.62/0.67 0.62/0.67 ### Cost equations --> "Loop" of eval_perfect_bb5_in/8 0.62/0.67 * CEs [27] --> Loop 26 0.62/0.67 * CEs [28] --> Loop 27 0.62/0.67 * CEs [29] --> Loop 28 0.62/0.67 0.62/0.67 ### Ranking functions of CR eval_perfect_bb5_in(V__y3_0,V_1,V_6,V_x,V_y1_0_sink,V_y2_1,V_y3_0,B) 0.62/0.67 0.62/0.67 #### Partial ranking functions of CR eval_perfect_bb5_in(V__y3_0,V_1,V_6,V_x,V_y1_0_sink,V_y2_1,V_y3_0,B) 0.62/0.67 0.62/0.67 0.62/0.67 ### Specialization of cost equations eval_perfect_bb1_in_loop_cont/9 0.62/0.67 * CE 10 is refined into CE [30,31,32] 0.62/0.67 * CE 11 is refined into CE [33] 0.62/0.67 0.62/0.67 0.62/0.67 ### Cost equations --> "Loop" of eval_perfect_bb1_in_loop_cont/9 0.62/0.67 * CEs [32] --> Loop 29 0.62/0.67 * CEs [31] --> Loop 30 0.62/0.67 * CEs [30] --> Loop 31 0.62/0.67 * CEs [33] --> Loop 32 0.62/0.67 0.62/0.67 ### Ranking functions of CR eval_perfect_bb1_in_loop_cont(A,B,C,D,E,F,G,H,I) 0.62/0.67 0.62/0.67 #### Partial ranking functions of CR eval_perfect_bb1_in_loop_cont(A,B,C,D,E,F,G,H,I) 0.62/0.67 0.62/0.67 0.62/0.67 ### Specialization of cost equations eval_perfect_1/8 0.62/0.67 * CE 3 is refined into CE [34,35,36,37,38,39] 0.62/0.67 * CE 2 is refined into CE [40] 0.62/0.67 0.62/0.67 0.62/0.67 ### Cost equations --> "Loop" of eval_perfect_1/8 0.62/0.67 * CEs [36] --> Loop 33 0.62/0.67 * CEs [34,35,37,38,39] --> Loop 34 0.62/0.67 * CEs [40] --> Loop 35 0.62/0.67 0.62/0.67 ### Ranking functions of CR eval_perfect_1(V__y3_0,V_1,V_6,V_x,V_y1_0_sink,V_y2_1,V_y3_0,B) 0.62/0.67 0.62/0.67 #### Partial ranking functions of CR eval_perfect_1(V__y3_0,V_1,V_6,V_x,V_y1_0_sink,V_y2_1,V_y3_0,B) 0.62/0.67 0.62/0.67 0.62/0.67 ### Specialization of cost equations eval_perfect_start/8 0.62/0.67 * CE 1 is refined into CE [41,42,43] 0.62/0.67 0.62/0.67 0.62/0.67 ### Cost equations --> "Loop" of eval_perfect_start/8 0.62/0.67 * CEs [43] --> Loop 36 0.62/0.67 * CEs [42] --> Loop 37 0.62/0.67 * CEs [41] --> Loop 38 0.62/0.67 0.62/0.67 ### Ranking functions of CR eval_perfect_start(V__y3_0,V_1,V_6,V_x,V_y1_0_sink,V_y2_1,V_y3_0,B) 0.62/0.67 0.62/0.67 #### Partial ranking functions of CR eval_perfect_start(V__y3_0,V_1,V_6,V_x,V_y1_0_sink,V_y2_1,V_y3_0,B) 0.62/0.67 0.62/0.67 0.62/0.67 Computing Bounds 0.62/0.67 ===================================== 0.62/0.67 0.62/0.67 #### Cost of chains of eval_perfect_bb2_in(V_1,V_y2_1,B,C): 0.62/0.67 * Chain [[18],20]: 1*it(18)+0 0.62/0.67 Such that:it(18) =< -V_1+V_y2_1+1 0.62/0.67 0.62/0.67 with precondition: [B=2,C>=0,V_1>=C+1,V_y2_1>=V_1+C] 0.62/0.67 0.62/0.67 * Chain [[18],19]: 1*it(18)+0 0.62/0.67 Such that:it(18) =< -V_1+V_y2_1+1 0.62/0.67 0.62/0.67 with precondition: [B=3,V_1>=1,V_y2_1>=V_1] 0.62/0.67 0.62/0.67 * Chain [19]: 0 0.62/0.67 with precondition: [B=3,V_1>=1] 0.62/0.67 0.62/0.67 0.62/0.67 #### Cost of chains of eval_perfect_bb1_in(V__y3_0,V_1,V_6,V_x,V_y1_0_sink,V_y2_1,V_y3_0,B,C,D,E,F,G,H): 0.62/0.67 * Chain [[21,22],25]: 2*it(21)+1*s(5)+1*s(6)+0 0.62/0.67 Such that:aux(1) =< V_x 0.62/0.67 aux(5) =< V_y1_0_sink 0.62/0.67 it(21) =< aux(5) 0.62/0.67 aux(2) =< aux(1) 0.62/0.67 s(5) =< it(21)*aux(1) 0.62/0.67 s(6) =< it(21)*aux(2) 0.62/0.67 0.62/0.67 with precondition: [B=3,V_y1_0_sink>=2,V_x>=V_y1_0_sink,V_x>=V_y3_0] 0.62/0.67 0.62/0.67 * Chain [[21,22],24]: 2*it(21)+1*s(5)+1*s(6)+1*s(7)+0 0.62/0.67 Such that:aux(6) =< V_x 0.62/0.67 aux(7) =< V_y1_0_sink 0.62/0.67 s(7) =< aux(6) 0.62/0.67 it(21) =< aux(7) 0.62/0.67 aux(2) =< aux(6) 0.62/0.67 s(5) =< it(21)*aux(6) 0.62/0.67 s(6) =< it(21)*aux(2) 0.62/0.67 0.62/0.67 with precondition: [B=3,V_y1_0_sink>=3,V_x>=V_y1_0_sink,V_x>=V_y3_0] 0.62/0.67 0.62/0.67 * Chain [[21,22],23]: 2*it(21)+1*s(5)+1*s(6)+0 0.62/0.67 Such that:aux(1) =< V_x 0.62/0.67 aux(8) =< V_y1_0_sink 0.62/0.67 it(21) =< aux(8) 0.62/0.67 aux(2) =< aux(1) 0.62/0.67 s(5) =< it(21)*aux(1) 0.62/0.67 s(6) =< it(21)*aux(2) 0.62/0.67 0.62/0.67 with precondition: [B=4,D=1,F=1,G=0,C=E,C=H,V_y1_0_sink>=2,V_x>=V_y1_0_sink,V_x>=V_y3_0,V_y3_0>=C+1] 0.62/0.67 0.62/0.67 * Chain [25]: 0 0.62/0.67 with precondition: [B=3,V_x>=2,V_x>=V_y1_0_sink,V_x>=V_y3_0,V_x+V_y1_0_sink>=V_y3_0+2] 0.62/0.67 0.62/0.67 * Chain [24]: 1*s(7)+0 0.62/0.67 Such that:s(7) =< V_x-V_y1_0_sink+2 0.62/0.67 0.62/0.67 with precondition: [B=3,V_y1_0_sink>=2,V_x>=V_y1_0_sink,V_x>=V_y3_0] 0.62/0.67 0.62/0.67 0.62/0.67 #### Cost of chains of eval_perfect_bb5_in(V__y3_0,V_1,V_6,V_x,V_y1_0_sink,V_y2_1,V_y3_0,B): 0.62/0.67 * Chain [28]: 0 0.62/0.67 with precondition: [V_y3_0=0,V_x>=2] 0.62/0.67 0.62/0.67 * Chain [27]: 0 0.62/0.67 with precondition: [0>=V_y3_0+1,V_x>=2] 0.62/0.67 0.62/0.67 * Chain [26]: 0 0.62/0.67 with precondition: [V_x>=2,V_y3_0>=1] 0.62/0.67 0.62/0.67 0.62/0.67 #### Cost of chains of eval_perfect_bb1_in_loop_cont(A,B,C,D,E,F,G,H,I): 0.62/0.67 * Chain [32]: 0 0.62/0.67 with precondition: [A=3,E>=2] 0.62/0.67 0.62/0.67 * Chain [31]: 0 0.62/0.67 with precondition: [A=4,H=0,E>=2] 0.62/0.67 0.62/0.67 * Chain [30]: 0 0.62/0.67 with precondition: [A=4,0>=H+1,E>=2] 0.62/0.67 0.62/0.67 * Chain [29]: 0 0.62/0.67 with precondition: [A=4,E>=2,H>=1] 0.62/0.67 0.62/0.67 0.62/0.67 #### Cost of chains of eval_perfect_1(V__y3_0,V_1,V_6,V_x,V_y1_0_sink,V_y2_1,V_y3_0,B): 0.62/0.67 * Chain [35]: 0 0.62/0.67 with precondition: [1>=V_x] 0.62/0.67 0.62/0.67 * Chain [34]: 1*s(16)+8*s(18)+4*s(20)+4*s(21)+0 0.62/0.67 Such that:s(16) =< 2 0.62/0.67 aux(13) =< V_x 0.62/0.67 s(18) =< aux(13) 0.62/0.67 s(19) =< aux(13) 0.62/0.67 s(20) =< s(18)*aux(13) 0.62/0.67 s(21) =< s(18)*s(19) 0.62/0.67 0.62/0.67 with precondition: [V_x>=2] 0.62/0.67 0.62/0.67 * Chain [33]: 3*s(42)+1*s(45)+1*s(46)+0 0.62/0.67 Such that:aux(14) =< V_x 0.62/0.67 s(42) =< aux(14) 0.62/0.67 s(44) =< aux(14) 0.62/0.67 s(45) =< s(42)*aux(14) 0.62/0.67 s(46) =< s(42)*s(44) 0.62/0.67 0.62/0.67 with precondition: [V_x>=3] 0.62/0.67 0.62/0.67 0.62/0.67 #### Cost of chains of eval_perfect_start(V__y3_0,V_1,V_6,V_x,V_y1_0_sink,V_y2_1,V_y3_0,B): 0.62/0.67 * Chain [38]: 0 0.62/0.67 with precondition: [1>=V_x] 0.62/0.67 0.62/0.67 * Chain [37]: 1*s(47)+8*s(49)+4*s(51)+4*s(52)+0 0.62/0.67 Such that:s(47) =< 2 0.62/0.67 s(48) =< V_x 0.62/0.67 s(49) =< s(48) 0.62/0.67 s(50) =< s(48) 0.62/0.67 s(51) =< s(49)*s(48) 0.62/0.67 s(52) =< s(49)*s(50) 0.62/0.67 0.62/0.67 with precondition: [V_x>=2] 0.62/0.67 0.62/0.67 * Chain [36]: 3*s(54)+1*s(56)+1*s(57)+0 0.62/0.67 Such that:s(53) =< V_x 0.62/0.67 s(54) =< s(53) 0.62/0.67 s(55) =< s(53) 0.62/0.67 s(56) =< s(54)*s(53) 0.62/0.67 s(57) =< s(54)*s(55) 0.62/0.67 0.62/0.67 with precondition: [V_x>=3] 0.62/0.67 0.62/0.67 0.62/0.67 Closed-form bounds of eval_perfect_start(V__y3_0,V_1,V_6,V_x,V_y1_0_sink,V_y2_1,V_y3_0,B): 0.62/0.67 ------------------------------------- 0.62/0.67 * Chain [38] with precondition: [1>=V_x] 0.62/0.67 - Upper bound: 0 0.62/0.67 - Complexity: constant 0.62/0.67 * Chain [37] with precondition: [V_x>=2] 0.62/0.67 - Upper bound: 8*V_x+2+8*V_x*V_x 0.62/0.67 - Complexity: n^2 0.62/0.67 * Chain [36] with precondition: [V_x>=3] 0.62/0.67 - Upper bound: 2*V_x*V_x+3*V_x 0.62/0.67 - Complexity: n^2 0.62/0.67 0.62/0.67 ### Maximum cost of eval_perfect_start(V__y3_0,V_1,V_6,V_x,V_y1_0_sink,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) 0.62/0.67 Asymptotic class: n^2 0.62/0.67 * Total analysis performed in 555 ms. 0.62/0.67 0.69/0.77 EOF