1.49/1.49 WORST_CASE(?,O(n^2)) 1.49/1.49 1.49/1.49 Preprocessing Cost Relations 1.49/1.49 ===================================== 1.49/1.49 1.49/1.49 #### Computed strongly connected components 1.49/1.49 0. recursive : [eval_rank1_8/6,eval_rank1_9/6,eval_rank1_bb3_in/6,eval_rank1_bb4_in/6,eval_rank1_bb5_in/6] 1.49/1.49 1. recursive : [eval_rank1_13/18,eval_rank1_14/18,eval_rank1_6/18,eval_rank1_7/18,eval_rank1__critedge_in/18,eval_rank1_bb1_in/18,eval_rank1_bb2_in/18,eval_rank1_bb3_in_loop_cont/19,eval_rank1_bb6_in/18] 1.49/1.49 2. non_recursive : [eval_rank1_stop/10] 1.49/1.49 3. non_recursive : [eval_rank1_bb7_in/10] 1.49/1.49 4. non_recursive : [exit_location/1] 1.49/1.49 5. non_recursive : [eval_rank1_bb1_in_loop_cont/11] 1.49/1.49 6. non_recursive : [eval_rank1_5/10] 1.49/1.49 7. non_recursive : [eval_rank1_4/10] 1.49/1.49 8. non_recursive : [eval_rank1_3/10] 1.49/1.49 9. non_recursive : [eval_rank1_2/10] 1.49/1.49 10. non_recursive : [eval_rank1_1/10] 1.49/1.49 11. non_recursive : [eval_rank1_0/10] 1.49/1.49 12. non_recursive : [eval_rank1_bb0_in/10] 1.49/1.49 13. non_recursive : [eval_rank1_start/10] 1.49/1.49 1.49/1.49 #### Obtained direct recursion through partial evaluation 1.49/1.49 0. SCC is partially evaluated into eval_rank1_bb3_in/6 1.49/1.49 1. SCC is partially evaluated into eval_rank1_bb1_in/18 1.49/1.49 2. SCC is completely evaluated into other SCCs 1.49/1.49 3. SCC is completely evaluated into other SCCs 1.49/1.49 4. SCC is completely evaluated into other SCCs 1.49/1.49 5. SCC is partially evaluated into eval_rank1_bb1_in_loop_cont/11 1.49/1.49 6. SCC is partially evaluated into eval_rank1_5/10 1.49/1.49 7. SCC is completely evaluated into other SCCs 1.49/1.49 8. SCC is completely evaluated into other SCCs 1.49/1.49 9. SCC is completely evaluated into other SCCs 1.49/1.49 10. SCC is completely evaluated into other SCCs 1.49/1.49 11. SCC is completely evaluated into other SCCs 1.49/1.49 12. SCC is completely evaluated into other SCCs 1.49/1.49 13. SCC is partially evaluated into eval_rank1_start/10 1.49/1.49 1.49/1.49 Control-Flow Refinement of Cost Relations 1.49/1.49 ===================================== 1.49/1.49 1.49/1.49 ### Specialization of cost equations eval_rank1_bb3_in/6 1.49/1.49 * CE 14 is refined into CE [15] 1.49/1.49 * CE 11 is refined into CE [16] 1.49/1.49 * CE 13 is refined into CE [17] 1.49/1.49 * CE 12 is refined into CE [18] 1.49/1.49 1.49/1.49 1.49/1.49 ### Cost equations --> "Loop" of eval_rank1_bb3_in/6 1.49/1.49 * CEs [18] --> Loop 15 1.49/1.49 * CEs [15] --> Loop 16 1.49/1.49 * CEs [16] --> Loop 17 1.49/1.49 * CEs [17] --> Loop 18 1.49/1.49 1.49/1.49 ### Ranking functions of CR eval_rank1_bb3_in(V_5,V_m,V_y_1,B,C,D) 1.49/1.49 * RF of phase [15]: [V_m-V_y_1+1] 1.49/1.49 1.49/1.49 #### Partial ranking functions of CR eval_rank1_bb3_in(V_5,V_m,V_y_1,B,C,D) 1.49/1.49 * Partial RF of phase [15]: 1.49/1.49 - RF of loop [15:1]: 1.49/1.49 V_m-V_y_1+1 1.49/1.49 1.49/1.49 1.49/1.49 ### Specialization of cost equations eval_rank1_bb1_in/18 1.49/1.49 * CE 7 is refined into CE [19] 1.49/1.49 * CE 6 is refined into CE [20] 1.49/1.49 * CE 5 is refined into CE [21,22] 1.49/1.49 * CE 8 is refined into CE [23] 1.49/1.49 * CE 3 is refined into CE [24] 1.49/1.49 * CE 4 is refined into CE [25,26,27,28] 1.49/1.49 1.49/1.49 1.49/1.49 ### Cost equations --> "Loop" of eval_rank1_bb1_in/18 1.49/1.49 * CEs [24] --> Loop 19 1.49/1.49 * CEs [28] --> Loop 20 1.49/1.49 * CEs [27] --> Loop 21 1.49/1.49 * CEs [25] --> Loop 22 1.49/1.49 * CEs [26] --> Loop 23 1.49/1.49 * CEs [19] --> Loop 24 1.49/1.49 * CEs [20] --> Loop 25 1.49/1.49 * CEs [23] --> Loop 26 1.49/1.49 * CEs [22] --> Loop 27 1.49/1.49 * CEs [21] --> Loop 28 1.49/1.49 1.49/1.49 ### Ranking functions of CR eval_rank1_bb1_in(V_2,V_5,V_8,V_m,V_x_0,V_x_1,V_y_0,V_y_1,V_y_2,B,C,D,E,F,G,H,I,J) 1.49/1.49 1.49/1.49 #### Partial ranking functions of CR eval_rank1_bb1_in(V_2,V_5,V_8,V_m,V_x_0,V_x_1,V_y_0,V_y_1,V_y_2,B,C,D,E,F,G,H,I,J) 1.49/1.49 * Partial RF of phase [19,20,21,22,23]: 1.49/1.49 - RF of loop [19:1,21:1]: 1.49/1.49 V_y_0+1 depends on loops [20:1,23:1] 1.49/1.49 - RF of loop [20:1,21:1,22:1,23:1]: 1.49/1.49 V_x_0+1 1.49/1.49 - RF of loop [22:1]: 1.49/1.49 -V_m+V_y_0 depends on loops [20:1,23:1] 1.49/1.49 V_y_0 depends on loops [20:1,23:1] 1.49/1.49 1.49/1.49 1.49/1.49 ### Specialization of cost equations eval_rank1_bb1_in_loop_cont/11 1.49/1.49 * CE 9 is refined into CE [29] 1.49/1.49 * CE 10 is refined into CE [30] 1.49/1.49 1.49/1.49 1.49/1.49 ### Cost equations --> "Loop" of eval_rank1_bb1_in_loop_cont/11 1.49/1.49 * CEs [29] --> Loop 29 1.49/1.49 * CEs [30] --> Loop 30 1.49/1.49 1.49/1.49 ### Ranking functions of CR eval_rank1_bb1_in_loop_cont(A,B,C,D,E,F,G,H,I,J,K) 1.49/1.49 1.49/1.49 #### Partial ranking functions of CR eval_rank1_bb1_in_loop_cont(A,B,C,D,E,F,G,H,I,J,K) 1.49/1.49 1.49/1.49 1.49/1.49 ### Specialization of cost equations eval_rank1_5/10 1.49/1.49 * CE 2 is refined into CE [31,32,33,34,35,36,37] 1.49/1.49 1.49/1.49 1.49/1.49 ### Cost equations --> "Loop" of eval_rank1_5/10 1.49/1.49 * CEs [33] --> Loop 31 1.49/1.49 * CEs [31,32,35,36] --> Loop 32 1.49/1.49 * CEs [37] --> Loop 33 1.49/1.49 * CEs [34] --> Loop 34 1.49/1.49 1.49/1.49 ### Ranking functions of CR eval_rank1_5(V_2,V_5,V_8,V_m,V_x_0,V_x_1,V_y_0,V_y_1,V_y_2,B) 1.49/1.49 1.49/1.49 #### Partial ranking functions of CR eval_rank1_5(V_2,V_5,V_8,V_m,V_x_0,V_x_1,V_y_0,V_y_1,V_y_2,B) 1.49/1.49 1.49/1.49 1.49/1.49 ### Specialization of cost equations eval_rank1_start/10 1.49/1.50 * CE 1 is refined into CE [38,39,40,41] 1.49/1.50 1.49/1.50 1.49/1.50 ### Cost equations --> "Loop" of eval_rank1_start/10 1.49/1.50 * CEs [41] --> Loop 35 1.49/1.50 * CEs [40] --> Loop 36 1.49/1.50 * CEs [39] --> Loop 37 1.49/1.50 * CEs [38] --> Loop 38 1.49/1.50 1.49/1.50 ### Ranking functions of CR eval_rank1_start(V_2,V_5,V_8,V_m,V_x_0,V_x_1,V_y_0,V_y_1,V_y_2,B) 1.49/1.50 1.49/1.50 #### Partial ranking functions of CR eval_rank1_start(V_2,V_5,V_8,V_m,V_x_0,V_x_1,V_y_0,V_y_1,V_y_2,B) 1.49/1.50 1.49/1.50 1.49/1.50 Computing Bounds 1.49/1.50 ===================================== 1.49/1.50 1.49/1.50 #### Cost of chains of eval_rank1_bb3_in(V_5,V_m,V_y_1,B,C,D): 1.49/1.50 * Chain [[15],18]: 1*it(15)+0 1.49/1.50 Such that:it(15) =< -V_y_1+D 1.49/1.50 1.49/1.50 with precondition: [B=2,V_m+1=D,V_y_1>=0,C>=1,V_m>=V_y_1] 1.49/1.50 1.49/1.50 * Chain [[15],17]: 1*it(15)+0 1.49/1.50 Such that:it(15) =< -V_y_1+D 1.49/1.50 1.49/1.50 with precondition: [B=2,0>=C,V_y_1>=0,D>=V_y_1+1,V_m>=D] 1.49/1.50 1.49/1.50 * Chain [[15],16]: 1*it(15)+0 1.49/1.50 Such that:it(15) =< V_m-V_y_1+1 1.49/1.50 1.49/1.50 with precondition: [B=3,V_y_1>=0,V_m>=V_y_1] 1.49/1.50 1.49/1.50 * Chain [18]: 0 1.49/1.50 with precondition: [B=2,C=V_5,V_y_1=D,V_m>=0,V_y_1>=V_m+1] 1.49/1.50 1.49/1.50 * Chain [17]: 0 1.49/1.50 with precondition: [B=2,V_y_1=D,0>=C,V_y_1>=0,V_m>=V_y_1] 1.49/1.50 1.49/1.50 * Chain [16]: 0 1.49/1.50 with precondition: [B=3,V_m>=0,V_y_1>=0] 1.49/1.50 1.49/1.50 1.49/1.50 #### Cost of chains of eval_rank1_bb1_in(V_2,V_5,V_8,V_m,V_x_0,V_x_1,V_y_0,V_y_1,V_y_2,B,C,D,E,F,G,H,I,J): 1.49/1.50 * Chain [[19,20,21,22,23],28]: 1*it(19)+2*it(20)+2*it(21)+1*s(5)+1*s(6)+0 1.49/1.50 Such that:aux(51) =< V_m 1.49/1.50 aux(52) =< V_m+V_x_0 1.49/1.50 aux(36) =< V_m+V_x_0-V_y_0+1 1.49/1.50 aux(52) =< V_m+2*V_x_0 1.49/1.50 aux(54) =< V_x_0 1.49/1.50 aux(53) =< V_x_0+1 1.49/1.50 aux(56) =< V_y_0 1.49/1.50 aux(55) =< V_y_0+1 1.49/1.50 it(20) =< aux(53) 1.49/1.50 it(21) =< aux(53) 1.49/1.50 it(20) =< aux(54) 1.49/1.50 it(21) =< aux(54) 1.49/1.50 aux(38) =< aux(51)+1 1.49/1.50 aux(12) =< aux(51) 1.49/1.50 aux(11) =< it(20)*aux(51) 1.49/1.50 aux(1) =< it(20)*aux(51) 1.49/1.50 s(5) =< it(20)*aux(51) 1.49/1.50 aux(13) =< it(20)*aux(12) 1.49/1.50 aux(4) =< aux(11) 1.49/1.50 aux(1) =< it(20)*aux(12) 1.49/1.50 aux(4) =< aux(13) 1.49/1.50 aux(2) =< it(20)*aux(38) 1.49/1.50 s(6) =< it(20)*aux(38) 1.49/1.50 it(19) =< aux(2)+aux(1)+aux(55) 1.49/1.50 it(21) =< aux(2)+aux(1)+aux(55) 1.49/1.50 it(19) =< aux(2)+aux(4)+aux(56) 1.49/1.50 it(21) =< aux(2)+aux(4)+aux(56) 1.49/1.50 s(6) =< it(19)+aux(52) 1.49/1.50 s(6) =< it(19)+aux(36) 1.49/1.50 1.49/1.50 with precondition: [B=3,V_x_0>=0,V_y_0>=0,V_m>=V_x_0,V_x_0+V_y_0>=1] 1.49/1.50 1.49/1.50 * Chain [[19,20,21,22,23],27]: 1*it(19)+2*it(20)+2*it(21)+1*s(5)+1*s(6)+1*s(7)+0 1.49/1.50 Such that:aux(51) =< V_m 1.49/1.50 s(7) =< V_m+1 1.49/1.50 aux(52) =< V_m+V_x_0-V_y_0 1.49/1.50 aux(36) =< V_m+V_x_0-V_y_0+1 1.49/1.50 aux(52) =< V_m+2*V_x_0 1.49/1.50 aux(54) =< V_x_0 1.49/1.50 aux(53) =< V_x_0+1 1.49/1.50 aux(56) =< V_y_0 1.49/1.50 aux(55) =< V_y_0+1 1.49/1.50 it(20) =< aux(53) 1.49/1.50 it(21) =< aux(53) 1.49/1.50 it(20) =< aux(54) 1.49/1.50 it(21) =< aux(54) 1.49/1.50 aux(38) =< aux(51)+1 1.49/1.50 aux(12) =< aux(51) 1.49/1.50 aux(11) =< it(20)*aux(51) 1.49/1.50 aux(1) =< it(20)*aux(51) 1.49/1.50 s(5) =< it(20)*aux(51) 1.49/1.50 aux(13) =< it(20)*aux(12) 1.49/1.50 aux(4) =< aux(11) 1.49/1.50 aux(1) =< it(20)*aux(12) 1.49/1.50 aux(4) =< aux(13) 1.49/1.50 aux(2) =< it(20)*aux(38) 1.49/1.50 s(6) =< it(20)*aux(38) 1.49/1.50 it(19) =< aux(2)+aux(1)+aux(55) 1.49/1.50 it(21) =< aux(2)+aux(1)+aux(55) 1.49/1.50 it(19) =< aux(2)+aux(4)+aux(56) 1.49/1.50 it(21) =< aux(2)+aux(4)+aux(56) 1.49/1.50 s(6) =< it(19)+aux(52) 1.49/1.50 s(6) =< it(19)+aux(36) 1.49/1.50 1.49/1.50 with precondition: [B=3,V_x_0>=0,V_y_0>=0,V_m>=V_x_0,V_x_0+V_y_0>=1] 1.49/1.50 1.49/1.50 * Chain [[19,20,21,22,23],26]: 1*it(19)+2*it(20)+2*it(21)+1*s(5)+1*s(6)+0 1.49/1.50 Such that:aux(51) =< V_m 1.49/1.50 aux(52) =< V_m+V_x_0+1 1.49/1.50 aux(36) =< V_m+V_x_0-V_y_0+1 1.49/1.50 aux(57) =< V_x_0+1 1.49/1.50 aux(58) =< V_y_0+1 1.49/1.50 it(20) =< aux(57) 1.49/1.50 it(21) =< aux(57) 1.49/1.50 aux(38) =< aux(51)+1 1.49/1.50 aux(12) =< aux(51) 1.49/1.50 aux(11) =< it(20)*aux(51) 1.49/1.50 aux(1) =< it(20)*aux(51) 1.49/1.50 s(5) =< it(20)*aux(51) 1.49/1.50 aux(13) =< it(20)*aux(12) 1.49/1.50 aux(4) =< aux(11) 1.49/1.50 aux(1) =< it(20)*aux(12) 1.49/1.50 aux(4) =< aux(13) 1.49/1.50 aux(2) =< it(20)*aux(38) 1.49/1.50 s(6) =< it(20)*aux(38) 1.49/1.50 it(19) =< aux(2)+aux(1)+aux(58) 1.49/1.50 it(21) =< aux(2)+aux(1)+aux(58) 1.49/1.50 it(19) =< aux(2)+aux(4)+aux(58) 1.49/1.50 it(21) =< aux(2)+aux(4)+aux(58) 1.49/1.50 s(6) =< it(19)+aux(52) 1.49/1.50 s(6) =< it(19)+aux(36) 1.49/1.50 1.49/1.50 with precondition: [B=3,V_x_0>=0,V_y_0>=0,V_m>=V_x_0] 1.49/1.50 1.49/1.50 * Chain [[19,20,21,22,23],25]: 1*it(19)+2*it(20)+2*it(21)+1*s(5)+1*s(6)+0 1.49/1.50 Such that:aux(51) =< V_m 1.49/1.50 aux(36) =< V_m+V_x_0-V_y_0+1 1.49/1.50 aux(52) =< V_m-V_y_0+H+1 1.49/1.50 aux(52) =< V_x_0-V_y_0+J 1.49/1.50 aux(55) =< V_y_0+1 1.49/1.50 aux(56) =< V_y_0-J+1 1.49/1.50 aux(59) =< V_x_0+1 1.49/1.50 it(20) =< aux(59) 1.49/1.50 it(21) =< aux(59) 1.49/1.50 aux(38) =< aux(51)+1 1.49/1.50 aux(12) =< aux(51) 1.49/1.50 aux(11) =< it(20)*aux(51) 1.49/1.50 aux(1) =< it(20)*aux(51) 1.49/1.50 s(5) =< it(20)*aux(51) 1.49/1.50 aux(13) =< it(20)*aux(12) 1.49/1.50 aux(4) =< aux(11) 1.49/1.50 aux(1) =< it(20)*aux(12) 1.49/1.50 aux(4) =< aux(13) 1.49/1.50 aux(2) =< it(20)*aux(38) 1.49/1.50 s(6) =< it(20)*aux(38) 1.49/1.50 it(19) =< aux(2)+aux(1)+aux(55) 1.49/1.50 it(21) =< aux(2)+aux(1)+aux(55) 1.49/1.50 it(19) =< aux(2)+aux(4)+aux(56) 1.49/1.50 it(21) =< aux(2)+aux(4)+aux(56) 1.49/1.50 s(6) =< it(19)+aux(52) 1.49/1.50 s(6) =< it(19)+aux(36) 1.49/1.50 1.49/1.50 with precondition: [B=4,E+1=0,F+1=0,G+1=0,H+1=I,H+1=J,V_x_0>=0,V_y_0>=0,C>=1,H+1>=0,V_m>=V_x_0] 1.49/1.50 1.49/1.50 * Chain [[19,20,21,22,23],24]: 1*it(19)+2*it(20)+2*it(21)+1*s(5)+1*s(6)+0 1.49/1.50 Such that:aux(51) =< V_m 1.49/1.50 aux(36) =< V_m+V_x_0-V_y_0+1 1.49/1.50 aux(52) =< V_m-V_y_0-G 1.49/1.50 aux(53) =< V_x_0+1 1.49/1.50 aux(52) =< V_x_0-V_y_0-G 1.49/1.50 aux(54) =< V_x_0-F 1.49/1.50 aux(60) =< V_y_0+1 1.49/1.50 it(20) =< aux(53) 1.49/1.50 it(21) =< aux(53) 1.49/1.50 it(20) =< aux(54) 1.49/1.50 it(21) =< aux(54) 1.49/1.50 aux(38) =< aux(51)+1 1.49/1.50 aux(12) =< aux(51) 1.49/1.50 aux(11) =< it(20)*aux(51) 1.49/1.50 aux(1) =< it(20)*aux(51) 1.49/1.50 s(5) =< it(20)*aux(51) 1.49/1.50 aux(13) =< it(20)*aux(12) 1.49/1.50 aux(4) =< aux(11) 1.49/1.50 aux(1) =< it(20)*aux(12) 1.49/1.50 aux(4) =< aux(13) 1.49/1.50 aux(2) =< it(20)*aux(38) 1.49/1.50 s(6) =< it(20)*aux(38) 1.49/1.50 it(19) =< aux(2)+aux(1)+aux(60) 1.49/1.50 it(21) =< aux(2)+aux(1)+aux(60) 1.49/1.50 it(19) =< aux(2)+aux(4)+aux(60) 1.49/1.50 it(21) =< aux(2)+aux(4)+aux(60) 1.49/1.50 s(6) =< it(19)+aux(52) 1.49/1.50 s(6) =< it(19)+aux(36) 1.49/1.50 1.49/1.50 with precondition: [B=4,H+1=0,J=0,F=G,V_x_0>=0,V_y_0>=0,F+1>=0,V_m>=V_x_0,V_x_0>=F] 1.49/1.50 1.49/1.50 * Chain [28]: 0 1.49/1.50 with precondition: [B=3,V_x_0>=0,V_y_0>=0,V_m>=V_x_0] 1.49/1.50 1.49/1.50 * Chain [27]: 1*s(7)+0 1.49/1.50 Such that:s(7) =< V_m-V_y_0+1 1.49/1.50 1.49/1.50 with precondition: [B=3,V_x_0>=0,V_y_0>=0,V_m>=V_x_0,V_m>=V_y_0] 1.49/1.50 1.49/1.50 * Chain [26]: 0 1.49/1.50 with precondition: [B=3,V_y_0+1>=0,V_m>=V_x_0] 1.49/1.50 1.49/1.50 * Chain [25]: 0 1.49/1.50 with precondition: [B=4,C=V_2,D=V_5,E=V_8,G=V_x_1,I=V_y_1,J=V_y_2,V_x_0=F,V_y_0=H,0>=V_x_0+1,V_y_0+1>=0,V_m>=V_x_0] 1.49/1.50 1.49/1.50 1.49/1.50 #### Cost of chains of eval_rank1_bb1_in_loop_cont(A,B,C,D,E,F,G,H,I,J,K): 1.49/1.50 * Chain [30]: 0 1.49/1.50 with precondition: [A=3] 1.49/1.50 1.49/1.50 * Chain [29]: 0 1.49/1.50 with precondition: [A=4] 1.49/1.50 1.49/1.50 1.49/1.50 #### Cost of chains of eval_rank1_5(V_2,V_5,V_8,V_m,V_x_0,V_x_1,V_y_0,V_y_1,V_y_2,B): 1.49/1.50 * Chain [34]: 0 1.49/1.50 with precondition: [] 1.49/1.50 1.49/1.50 * Chain [33]: 0 1.49/1.50 with precondition: [0>=V_m+1] 1.49/1.50 1.49/1.50 * Chain [32]: 7*s(69)+6*s(70)+3*s(75)+2*s(79)+3*s(80)+1*s(116)+0 1.49/1.50 Such that:aux(71) =< 1 1.49/1.50 aux(72) =< V_m 1.49/1.50 aux(73) =< V_m+1 1.49/1.50 aux(74) =< 2*V_m+1 1.49/1.50 s(69) =< aux(73) 1.49/1.50 s(70) =< aux(73) 1.49/1.50 s(71) =< aux(72)+1 1.49/1.50 s(72) =< aux(72) 1.49/1.50 s(73) =< s(69)*aux(72) 1.49/1.50 s(74) =< s(69)*aux(72) 1.49/1.50 s(75) =< s(69)*aux(72) 1.49/1.50 s(76) =< s(69)*s(72) 1.49/1.50 s(77) =< s(73) 1.49/1.50 s(74) =< s(69)*s(72) 1.49/1.50 s(77) =< s(76) 1.49/1.50 s(78) =< s(69)*s(71) 1.49/1.50 s(79) =< s(69)*s(71) 1.49/1.50 s(80) =< s(78)+s(74)+aux(71) 1.49/1.50 s(70) =< s(78)+s(74)+aux(71) 1.49/1.50 s(80) =< s(78)+s(77)+aux(71) 1.49/1.50 s(70) =< s(78)+s(77)+aux(71) 1.49/1.50 s(79) =< s(80)+aux(74) 1.49/1.50 s(116) =< s(69)*s(71) 1.49/1.50 s(116) =< s(80)+aux(73) 1.49/1.50 s(116) =< s(80)+aux(74) 1.49/1.50 1.49/1.50 with precondition: [V_m>=0] 1.49/1.50 1.49/1.50 * Chain [31]: 1*s(118)+4*s(128)+4*s(129)+2*s(134)+2*s(138)+2*s(139)+0 1.49/1.50 Such that:s(127) =< 1 1.49/1.50 s(122) =< 2*V_m+1 1.49/1.50 s(123) =< 3*V_m 1.49/1.50 aux(75) =< V_m 1.49/1.50 aux(76) =< V_m+1 1.49/1.50 aux(77) =< 2*V_m 1.49/1.50 s(118) =< aux(76) 1.49/1.50 s(119) =< aux(77) 1.49/1.50 s(119) =< s(123) 1.49/1.50 s(128) =< aux(76) 1.49/1.50 s(129) =< aux(76) 1.49/1.50 s(128) =< aux(75) 1.49/1.50 s(129) =< aux(75) 1.49/1.50 s(130) =< aux(75)+1 1.49/1.50 s(131) =< aux(75) 1.49/1.50 s(132) =< s(128)*aux(75) 1.49/1.50 s(133) =< s(128)*aux(75) 1.49/1.50 s(134) =< s(128)*aux(75) 1.49/1.50 s(135) =< s(128)*s(131) 1.49/1.50 s(136) =< s(132) 1.49/1.50 s(133) =< s(128)*s(131) 1.49/1.50 s(136) =< s(135) 1.49/1.50 s(137) =< s(128)*s(130) 1.49/1.50 s(138) =< s(128)*s(130) 1.49/1.50 s(139) =< s(137)+s(133)+s(127) 1.49/1.50 s(129) =< s(137)+s(133)+s(127) 1.49/1.50 s(139) =< s(137)+s(136) 1.49/1.50 s(129) =< s(137)+s(136) 1.49/1.50 s(138) =< s(139)+s(119) 1.49/1.50 s(138) =< s(139)+s(122) 1.49/1.50 1.49/1.50 with precondition: [V_m>=1] 1.49/1.50 1.49/1.50 1.49/1.50 #### Cost of chains of eval_rank1_start(V_2,V_5,V_8,V_m,V_x_0,V_x_1,V_y_0,V_y_1,V_y_2,B): 1.49/1.50 * Chain [38]: 0 1.49/1.50 with precondition: [] 1.49/1.50 1.49/1.50 * Chain [37]: 0 1.49/1.50 with precondition: [0>=V_m+1] 1.49/1.50 1.49/1.50 * Chain [36]: 7*s(145)+6*s(146)+3*s(151)+2*s(155)+3*s(156)+1*s(157)+0 1.49/1.50 Such that:s(141) =< 1 1.49/1.50 s(142) =< V_m 1.49/1.50 s(143) =< V_m+1 1.49/1.50 s(144) =< 2*V_m+1 1.49/1.50 s(145) =< s(143) 1.49/1.50 s(146) =< s(143) 1.49/1.50 s(147) =< s(142)+1 1.49/1.50 s(148) =< s(142) 1.49/1.50 s(149) =< s(145)*s(142) 1.49/1.50 s(150) =< s(145)*s(142) 1.49/1.50 s(151) =< s(145)*s(142) 1.49/1.50 s(152) =< s(145)*s(148) 1.49/1.50 s(153) =< s(149) 1.49/1.50 s(150) =< s(145)*s(148) 1.49/1.50 s(153) =< s(152) 1.49/1.50 s(154) =< s(145)*s(147) 1.49/1.50 s(155) =< s(145)*s(147) 1.49/1.50 s(156) =< s(154)+s(150)+s(141) 1.49/1.50 s(146) =< s(154)+s(150)+s(141) 1.49/1.50 s(156) =< s(154)+s(153)+s(141) 1.49/1.50 s(146) =< s(154)+s(153)+s(141) 1.49/1.50 s(155) =< s(156)+s(144) 1.49/1.50 s(157) =< s(145)*s(147) 1.49/1.50 s(157) =< s(156)+s(143) 1.49/1.50 s(157) =< s(156)+s(144) 1.49/1.50 1.49/1.50 with precondition: [V_m>=0] 1.49/1.50 1.49/1.50 * Chain [35]: 1*s(164)+4*s(166)+4*s(167)+2*s(172)+2*s(176)+2*s(177)+0 1.49/1.50 Such that:s(158) =< 1 1.49/1.50 s(161) =< V_m 1.49/1.50 s(162) =< V_m+1 1.49/1.50 s(163) =< 2*V_m 1.49/1.50 s(159) =< 2*V_m+1 1.49/1.50 s(160) =< 3*V_m 1.49/1.50 s(164) =< s(162) 1.49/1.50 s(165) =< s(163) 1.49/1.50 s(165) =< s(160) 1.49/1.50 s(166) =< s(162) 1.49/1.50 s(167) =< s(162) 1.49/1.50 s(166) =< s(161) 1.49/1.50 s(167) =< s(161) 1.49/1.50 s(168) =< s(161)+1 1.49/1.50 s(169) =< s(161) 1.49/1.50 s(170) =< s(166)*s(161) 1.49/1.50 s(171) =< s(166)*s(161) 1.49/1.50 s(172) =< s(166)*s(161) 1.49/1.50 s(173) =< s(166)*s(169) 1.49/1.50 s(174) =< s(170) 1.49/1.50 s(171) =< s(166)*s(169) 1.49/1.50 s(174) =< s(173) 1.49/1.50 s(175) =< s(166)*s(168) 1.49/1.50 s(176) =< s(166)*s(168) 1.49/1.50 s(177) =< s(175)+s(171)+s(158) 1.49/1.50 s(167) =< s(175)+s(171)+s(158) 1.49/1.50 s(177) =< s(175)+s(174) 1.49/1.50 s(167) =< s(175)+s(174) 1.49/1.50 s(176) =< s(177)+s(165) 1.49/1.50 s(176) =< s(177)+s(159) 1.49/1.50 1.49/1.50 with precondition: [V_m>=1] 1.49/1.50 1.49/1.50 1.49/1.50 Closed-form bounds of eval_rank1_start(V_2,V_5,V_8,V_m,V_x_0,V_x_1,V_y_0,V_y_1,V_y_2,B): 1.49/1.50 ------------------------------------- 1.49/1.50 * Chain [38] with precondition: [] 1.49/1.50 - Upper bound: 0 1.49/1.50 - Complexity: constant 1.49/1.50 * Chain [37] with precondition: [0>=V_m+1] 1.49/1.50 - Upper bound: 0 1.49/1.50 - Complexity: constant 1.49/1.50 * Chain [36] with precondition: [V_m>=0] 1.49/1.50 - Upper bound: (V_m+1)*(12*V_m)+3+(19*V_m+19) 1.49/1.50 - Complexity: n^2 1.49/1.50 * Chain [35] with precondition: [V_m>=1] 1.49/1.50 - Upper bound: (V_m+1)*(8*V_m)+2+(13*V_m+13) 1.49/1.50 - Complexity: n^2 1.49/1.50 1.49/1.50 ### Maximum cost of eval_rank1_start(V_2,V_5,V_8,V_m,V_x_0,V_x_1,V_y_0,V_y_1,V_y_2,B): nat(V_m)*8*nat(V_m+1)+2+nat(V_m+1)*13+(nat(V_m)*4*nat(V_m+1)+1+nat(V_m+1)*6) 1.49/1.50 Asymptotic class: n^2 1.49/1.50 * Total analysis performed in 1314 ms. 1.49/1.50 1.50/1.60 EOF