0.85/0.91 WORST_CASE(?,O(n^1)) 0.85/0.91 0.85/0.91 Preprocessing Cost Relations 0.85/0.91 ===================================== 0.85/0.91 0.85/0.91 #### Computed strongly connected components 0.85/0.91 0. recursive : [eval_speedNestedMultiple_6/6,eval_speedNestedMultiple_7/6,eval_speedNestedMultiple_bb2_in/6,eval_speedNestedMultiple_bb3_in/6,eval_speedNestedMultiple_bb4_in/6] 0.85/0.91 1. recursive : [eval_speedNestedMultiple_11/13,eval_speedNestedMultiple_12/13,eval_speedNestedMultiple__critedge_in/13,eval_speedNestedMultiple_bb1_in/13,eval_speedNestedMultiple_bb2_in_loop_cont/14] 0.85/0.91 2. non_recursive : [eval_speedNestedMultiple_stop/10] 0.85/0.91 3. non_recursive : [eval_speedNestedMultiple_bb5_in/10] 0.85/0.91 4. non_recursive : [exit_location/1] 0.85/0.91 5. non_recursive : [eval_speedNestedMultiple_bb1_in_loop_cont/11] 0.85/0.91 6. non_recursive : [eval_speedNestedMultiple_5/10] 0.85/0.91 7. non_recursive : [eval_speedNestedMultiple_4/10] 0.85/0.91 8. non_recursive : [eval_speedNestedMultiple_3/10] 0.85/0.91 9. non_recursive : [eval_speedNestedMultiple_2/10] 0.85/0.91 10. non_recursive : [eval_speedNestedMultiple_1/10] 0.85/0.91 11. non_recursive : [eval_speedNestedMultiple_0/10] 0.85/0.91 12. non_recursive : [eval_speedNestedMultiple_bb0_in/10] 0.85/0.91 13. non_recursive : [eval_speedNestedMultiple_start/10] 0.85/0.91 0.85/0.91 #### Obtained direct recursion through partial evaluation 0.85/0.91 0. SCC is partially evaluated into eval_speedNestedMultiple_bb2_in/6 0.85/0.91 1. SCC is partially evaluated into eval_speedNestedMultiple_bb1_in/13 0.85/0.91 2. SCC is completely evaluated into other SCCs 0.85/0.91 3. SCC is completely evaluated into other SCCs 0.85/0.91 4. SCC is completely evaluated into other SCCs 0.85/0.91 5. SCC is partially evaluated into eval_speedNestedMultiple_bb1_in_loop_cont/11 0.85/0.91 6. SCC is partially evaluated into eval_speedNestedMultiple_5/10 0.85/0.91 7. SCC is completely evaluated into other SCCs 0.85/0.91 8. SCC is completely evaluated into other SCCs 0.85/0.91 9. SCC is completely evaluated into other SCCs 0.85/0.91 10. SCC is completely evaluated into other SCCs 0.85/0.91 11. SCC is completely evaluated into other SCCs 0.85/0.91 12. SCC is completely evaluated into other SCCs 0.85/0.91 13. SCC is partially evaluated into eval_speedNestedMultiple_start/10 0.85/0.91 0.85/0.91 Control-Flow Refinement of Cost Relations 0.85/0.91 ===================================== 0.85/0.91 0.85/0.91 ### Specialization of cost equations eval_speedNestedMultiple_bb2_in/6 0.85/0.91 * CE 12 is refined into CE [13] 0.85/0.91 * CE 9 is refined into CE [14] 0.85/0.91 * CE 11 is refined into CE [15] 0.85/0.91 * CE 10 is refined into CE [16] 0.85/0.91 0.85/0.91 0.85/0.91 ### Cost equations --> "Loop" of eval_speedNestedMultiple_bb2_in/6 0.85/0.91 * CEs [16] --> Loop 13 0.85/0.91 * CEs [13] --> Loop 14 0.85/0.91 * CEs [14] --> Loop 15 0.85/0.91 * CEs [15] --> Loop 16 0.85/0.91 0.85/0.91 ### Ranking functions of CR eval_speedNestedMultiple_bb2_in(V__1,V_2,V_m,B,C,D) 0.85/0.91 * RF of phase [13]: [-V__1+V_m] 0.85/0.91 0.85/0.91 #### Partial ranking functions of CR eval_speedNestedMultiple_bb2_in(V__1,V_2,V_m,B,C,D) 0.85/0.91 * Partial RF of phase [13]: 0.85/0.91 - RF of loop [13:1]: 0.85/0.91 -V__1+V_m 0.85/0.91 0.85/0.91 0.85/0.91 ### Specialization of cost equations eval_speedNestedMultiple_bb1_in/13 0.85/0.91 * CE 5 is refined into CE [17] 0.85/0.91 * CE 3 is refined into CE [18,19] 0.85/0.91 * CE 6 is refined into CE [20] 0.85/0.91 * CE 4 is refined into CE [21,22,23,24] 0.85/0.91 0.85/0.91 0.85/0.91 ### Cost equations --> "Loop" of eval_speedNestedMultiple_bb1_in/13 0.85/0.91 * CEs [24] --> Loop 17 0.85/0.91 * CEs [23] --> Loop 18 0.85/0.91 * CEs [22] --> Loop 19 0.85/0.91 * CEs [21] --> Loop 20 0.85/0.91 * CEs [17] --> Loop 21 0.85/0.91 * CEs [19] --> Loop 22 0.85/0.91 * CEs [18] --> Loop 23 0.85/0.91 * CEs [20] --> Loop 24 0.85/0.91 0.85/0.91 ### Ranking functions of CR eval_speedNestedMultiple_bb1_in(V__0,V__01,V__1,V_2,V_5,V_m,V_n,B,C,D,E,F,G) 0.85/0.91 * RF of phase [17,19]: [-V__0+V_n] 0.85/0.91 * RF of phase [20]: [-V__0+V_n] 0.85/0.91 0.85/0.91 #### Partial ranking functions of CR eval_speedNestedMultiple_bb1_in(V__0,V__01,V__1,V_2,V_5,V_m,V_n,B,C,D,E,F,G) 0.85/0.91 * Partial RF of phase [17,19]: 0.85/0.91 - RF of loop [17:1]: 0.85/0.91 -V__01+V_m-1 0.85/0.91 - RF of loop [17:1,19:1]: 0.85/0.91 -V__0+V_n 0.85/0.91 * Partial RF of phase [20]: 0.85/0.91 - RF of loop [20:1]: 0.85/0.91 -V__0+V_n 0.85/0.91 0.85/0.91 0.85/0.91 ### Specialization of cost equations eval_speedNestedMultiple_bb1_in_loop_cont/11 0.85/0.91 * CE 7 is refined into CE [25] 0.85/0.91 * CE 8 is refined into CE [26] 0.85/0.91 0.85/0.91 0.85/0.91 ### Cost equations --> "Loop" of eval_speedNestedMultiple_bb1_in_loop_cont/11 0.85/0.91 * CEs [25] --> Loop 25 0.85/0.91 * CEs [26] --> Loop 26 0.85/0.91 0.85/0.91 ### Ranking functions of CR eval_speedNestedMultiple_bb1_in_loop_cont(A,B,C,D,E,F,G,H,I,J,K) 0.85/0.91 0.85/0.91 #### Partial ranking functions of CR eval_speedNestedMultiple_bb1_in_loop_cont(A,B,C,D,E,F,G,H,I,J,K) 0.85/0.91 0.85/0.91 0.85/0.91 ### Specialization of cost equations eval_speedNestedMultiple_5/10 0.85/0.91 * CE 2 is refined into CE [27,28,29,30,31,32,33,34,35,36,37,38,39,40] 0.85/0.91 0.85/0.91 0.85/0.91 ### Cost equations --> "Loop" of eval_speedNestedMultiple_5/10 0.85/0.91 * CEs [34] --> Loop 27 0.85/0.91 * CEs [33,39] --> Loop 28 0.85/0.91 * CEs [31,38] --> Loop 29 0.85/0.91 * CEs [29,40] --> Loop 30 0.85/0.91 * CEs [28] --> Loop 31 0.85/0.91 * CEs [36] --> Loop 32 0.85/0.91 * CEs [32] --> Loop 33 0.85/0.91 * CEs [30,37] --> Loop 34 0.85/0.91 * CEs [35] --> Loop 35 0.85/0.91 * CEs [27] --> Loop 36 0.85/0.91 0.85/0.91 ### Ranking functions of CR eval_speedNestedMultiple_5(V__0,V__01,V__1,V_2,V_5,V_m,V_n,V_x,V_y,B) 0.85/0.91 0.85/0.91 #### Partial ranking functions of CR eval_speedNestedMultiple_5(V__0,V__01,V__1,V_2,V_5,V_m,V_n,V_x,V_y,B) 0.85/0.91 0.85/0.91 0.85/0.91 ### Specialization of cost equations eval_speedNestedMultiple_start/10 0.85/0.91 * CE 1 is refined into CE [41,42,43,44,45,46,47,48,49,50] 0.85/0.91 0.85/0.91 0.85/0.91 ### Cost equations --> "Loop" of eval_speedNestedMultiple_start/10 0.85/0.91 * CEs [50] --> Loop 37 0.85/0.91 * CEs [49] --> Loop 38 0.85/0.91 * CEs [48] --> Loop 39 0.85/0.91 * CEs [47] --> Loop 40 0.85/0.91 * CEs [46] --> Loop 41 0.85/0.91 * CEs [45] --> Loop 42 0.85/0.91 * CEs [44] --> Loop 43 0.85/0.91 * CEs [43] --> Loop 44 0.85/0.91 * CEs [42] --> Loop 45 0.85/0.91 * CEs [41] --> Loop 46 0.85/0.91 0.85/0.91 ### Ranking functions of CR eval_speedNestedMultiple_start(V__0,V__01,V__1,V_2,V_5,V_m,V_n,V_x,V_y,B) 0.85/0.91 0.85/0.91 #### Partial ranking functions of CR eval_speedNestedMultiple_start(V__0,V__01,V__1,V_2,V_5,V_m,V_n,V_x,V_y,B) 0.85/0.91 0.85/0.91 0.85/0.91 Computing Bounds 0.85/0.91 ===================================== 0.85/0.91 0.85/0.91 #### Cost of chains of eval_speedNestedMultiple_bb2_in(V__1,V_2,V_m,B,C,D): 0.85/0.91 * Chain [[13],16]: 1*it(13)+0 0.85/0.91 Such that:it(13) =< -V__1+C 0.85/0.91 0.85/0.91 with precondition: [B=2,V_m=C,D>=1,V_m>=V__1+1] 0.85/0.91 0.85/0.91 * Chain [[13],15]: 1*it(13)+0 0.85/0.91 Such that:it(13) =< -V__1+C 0.85/0.91 0.85/0.91 with precondition: [B=2,0>=D,C>=V__1+1,V_m>=C+1] 0.85/0.91 0.85/0.91 * Chain [[13],14]: 1*it(13)+0 0.85/0.91 Such that:it(13) =< -V__1+V_m 0.85/0.91 0.85/0.91 with precondition: [B=3,V_m>=V__1+1] 0.85/0.91 0.85/0.91 * Chain [16]: 0 0.85/0.91 with precondition: [B=2,D=V_2,V__1=C,V__1>=V_m] 0.85/0.91 0.85/0.91 * Chain [15]: 0 0.85/0.91 with precondition: [B=2,V__1=C,0>=D,V_m>=V__1+1] 0.85/0.91 0.85/0.91 * Chain [14]: 0 0.85/0.91 with precondition: [B=3] 0.85/0.91 0.85/0.91 0.85/0.91 #### Cost of chains of eval_speedNestedMultiple_bb1_in(V__0,V__01,V__1,V_2,V_5,V_m,V_n,B,C,D,E,F,G): 0.85/0.91 * Chain [[20],24]: 1*it(20)+0 0.85/0.91 Such that:it(20) =< -V__0+V_n 0.85/0.91 0.85/0.91 with precondition: [B=3,V_n>=V__0+1,V__01>=V_m] 0.85/0.91 0.85/0.91 * Chain [[20],23]: 1*it(20)+0 0.85/0.91 Such that:it(20) =< -V__0+V_n 0.85/0.91 0.85/0.91 with precondition: [B=3,V_n>=V__0+2,V__01>=V_m] 0.85/0.91 0.85/0.91 * Chain [[20],21]: 1*it(20)+0 0.85/0.91 Such that:it(20) =< -V__0+C 0.85/0.91 0.85/0.91 with precondition: [B=4,V_n=C,V__01=D,V__01=E,V_2=F,V_n=G,V_n>=V__0+1,V__01>=V_m] 0.85/0.91 0.85/0.91 * Chain [[17,19],24]: 1*it(17)+1*it(19)+1*s(3)+0 0.85/0.91 Such that:aux(5) =< -V__0+V_n 0.85/0.91 aux(6) =< -V__01+V_m 0.85/0.91 it(17) =< aux(5) 0.85/0.91 it(19) =< aux(5) 0.85/0.91 it(17) =< aux(6) 0.85/0.91 s(3) =< aux(6) 0.85/0.91 0.85/0.91 with precondition: [B=3,V_n>=V__0+1,V_m>=V__01+1] 0.85/0.91 0.85/0.91 * Chain [[17,19],23]: 1*it(17)+1*it(19)+1*s(3)+0 0.85/0.91 Such that:aux(7) =< -V__0+V_n 0.85/0.91 aux(8) =< -V__01+V_m 0.85/0.91 it(17) =< aux(7) 0.85/0.91 it(19) =< aux(7) 0.85/0.91 it(17) =< aux(8) 0.85/0.91 s(3) =< aux(8) 0.85/0.91 0.85/0.91 with precondition: [B=3,V_n>=V__0+2,V_m>=V__01+1] 0.85/0.92 0.85/0.92 * Chain [[17,19],22]: 1*it(17)+1*it(19)+2*s(3)+0 0.85/0.92 Such that:aux(9) =< -V__0+V_n 0.85/0.92 aux(10) =< -V__01+V_m 0.85/0.92 s(3) =< aux(10) 0.85/0.92 it(17) =< aux(9) 0.85/0.92 it(19) =< aux(9) 0.85/0.92 it(17) =< aux(10) 0.85/0.92 0.85/0.92 with precondition: [B=3,V_n>=V__0+2,V_m>=V__01+1] 0.85/0.92 0.85/0.92 * Chain [[17,19],21]: 1*it(17)+1*it(19)+1*s(3)+0 0.85/0.92 Such that:aux(3) =< -V__01+V_m 0.85/0.92 aux(4) =< -V__01+E 0.85/0.92 aux(11) =< -V__0+V_n 0.85/0.92 it(17) =< aux(11) 0.85/0.92 it(19) =< aux(11) 0.85/0.92 it(17) =< aux(3) 0.85/0.92 s(3) =< aux(3) 0.85/0.92 it(17) =< aux(4) 0.85/0.92 s(3) =< aux(4) 0.85/0.92 0.85/0.92 with precondition: [B=4,V_n=C,D=E,V_n=G,0>=F,V_n>=V__0+1,D>=V__01,V_m>=D+1] 0.85/0.92 0.85/0.92 * Chain [[17,19],18,[20],24]: 1*it(17)+2*it(19)+2*s(3)+1 0.85/0.92 Such that:aux(12) =< -V__0+V_n 0.85/0.92 aux(13) =< -V__01+V_m 0.85/0.92 it(19) =< aux(12) 0.85/0.92 s(3) =< aux(13) 0.85/0.92 it(17) =< aux(12) 0.85/0.92 it(17) =< aux(13) 0.85/0.92 0.85/0.92 with precondition: [B=3,V_n>=V__0+3,V_m>=V__01+1] 0.85/0.92 0.85/0.92 * Chain [[17,19],18,[20],23]: 1*it(17)+2*it(19)+2*s(3)+1 0.85/0.92 Such that:aux(14) =< -V__0+V_n 0.85/0.92 aux(15) =< -V__01+V_m 0.85/0.92 it(19) =< aux(14) 0.85/0.92 s(3) =< aux(15) 0.85/0.92 it(17) =< aux(14) 0.85/0.92 it(17) =< aux(15) 0.85/0.92 0.85/0.92 with precondition: [B=3,V_n>=V__0+4,V_m>=V__01+1] 0.85/0.92 0.85/0.92 * Chain [[17,19],18,[20],21]: 1*it(17)+2*it(19)+2*s(3)+1 0.85/0.92 Such that:aux(16) =< -V__0+V_n 0.85/0.92 aux(17) =< -V__01+V_m 0.85/0.92 it(19) =< aux(16) 0.85/0.92 s(3) =< aux(17) 0.85/0.92 it(17) =< aux(16) 0.85/0.92 it(17) =< aux(17) 0.85/0.92 0.85/0.92 with precondition: [B=4,V_n=C,V_m=D,V_m=E,V_n=G,F>=1,V_n>=V__0+3,V_m>=V__01+1] 0.85/0.92 0.85/0.92 * Chain [[17,19],18,24]: 1*it(17)+1*it(19)+2*s(3)+1 0.85/0.92 Such that:aux(18) =< -V__0+V_n 0.85/0.92 aux(19) =< -V__01+V_m 0.85/0.92 s(3) =< aux(19) 0.85/0.92 it(17) =< aux(18) 0.85/0.92 it(19) =< aux(18) 0.85/0.92 it(17) =< aux(19) 0.85/0.92 0.85/0.92 with precondition: [B=3,V_n>=V__0+2,V_m>=V__01+1] 0.85/0.92 0.85/0.92 * Chain [[17,19],18,23]: 1*it(17)+1*it(19)+2*s(3)+1 0.85/0.92 Such that:aux(20) =< -V__0+V_n 0.85/0.92 aux(21) =< -V__01+V_m 0.85/0.92 s(3) =< aux(21) 0.85/0.92 it(17) =< aux(20) 0.85/0.92 it(19) =< aux(20) 0.85/0.92 it(17) =< aux(21) 0.85/0.92 0.85/0.92 with precondition: [B=3,V_n>=V__0+3,V_m>=V__01+1] 0.85/0.92 0.85/0.92 * Chain [[17,19],18,21]: 1*it(17)+1*it(19)+2*s(3)+1 0.85/0.92 Such that:aux(22) =< -V__0+V_n 0.85/0.92 aux(23) =< -V__01+V_m 0.85/0.92 s(3) =< aux(23) 0.85/0.92 it(17) =< aux(22) 0.85/0.92 it(19) =< aux(22) 0.85/0.92 it(17) =< aux(23) 0.85/0.92 0.85/0.92 with precondition: [B=4,V_n=C,V_m=D,V_m=E,V_n=G,F>=1,V_n>=V__0+2,V_m>=V__01+1] 0.85/0.92 0.85/0.92 * Chain [24]: 0 0.85/0.92 with precondition: [B=3] 0.85/0.92 0.85/0.92 * Chain [23]: 0 0.85/0.92 with precondition: [B=3,V_n>=V__0+1] 0.85/0.92 0.85/0.92 * Chain [22]: 1*s(4)+0 0.85/0.92 Such that:s(4) =< -V__01+V_m 0.85/0.92 0.85/0.92 with precondition: [B=3,V_n>=V__0+1,V_m>=V__01+1] 0.85/0.92 0.85/0.92 * Chain [21]: 0 0.85/0.92 with precondition: [B=4,D=V__01,E=V__1,F=V_2,G=V_5,V__0=C,V__0>=V_n] 0.85/0.92 0.85/0.92 * Chain [18,[20],24]: 1*it(20)+1*s(5)+1 0.85/0.92 Such that:it(20) =< -V__0+V_n 0.85/0.92 s(5) =< -V__01+V_m 0.85/0.92 0.85/0.92 with precondition: [B=3,V_n>=V__0+2,V_m>=V__01+1] 0.85/0.92 0.85/0.92 * Chain [18,[20],23]: 1*it(20)+1*s(5)+1 0.85/0.92 Such that:it(20) =< -V__0+V_n 0.85/0.92 s(5) =< -V__01+V_m 0.85/0.92 0.85/0.92 with precondition: [B=3,V_n>=V__0+3,V_m>=V__01+1] 0.85/0.92 0.85/0.92 * Chain [18,[20],21]: 1*it(20)+1*s(5)+1 0.85/0.92 Such that:it(20) =< -V__0+V_n 0.85/0.92 s(5) =< -V__01+D 0.85/0.92 0.85/0.92 with precondition: [B=4,V_n=C,V_m=D,V_m=E,V_n=G,F>=1,V_n>=V__0+2,V_m>=V__01+1] 0.85/0.92 0.85/0.92 * Chain [18,24]: 1*s(5)+1 0.85/0.92 Such that:s(5) =< -V__01+V_m 0.85/0.92 0.85/0.92 with precondition: [B=3,V_n>=V__0+1,V_m>=V__01+1] 0.85/0.92 0.85/0.92 * Chain [18,23]: 1*s(5)+1 0.85/0.92 Such that:s(5) =< -V__01+V_m 0.85/0.92 0.85/0.92 with precondition: [B=3,V_n>=V__0+2,V_m>=V__01+1] 0.85/0.92 0.85/0.92 * Chain [18,21]: 1*s(5)+1 0.85/0.92 Such that:s(5) =< -V__01+V_m 0.85/0.92 0.85/0.92 with precondition: [B=4,C=V__0+1,C=V_n,V_m=D,V_m=E,C=G,F>=1,V_m>=V__01+1] 0.85/0.92 0.85/0.92 0.85/0.92 #### Cost of chains of eval_speedNestedMultiple_bb1_in_loop_cont(A,B,C,D,E,F,G,H,I,J,K): 0.85/0.92 * Chain [26]: 0 0.85/0.92 with precondition: [A=3] 0.85/0.92 0.85/0.92 * Chain [25]: 0 0.85/0.92 with precondition: [A=4] 0.85/0.92 0.85/0.92 0.85/0.92 #### Cost of chains of eval_speedNestedMultiple_5(V__0,V__01,V__1,V_2,V_5,V_m,V_n,V_x,V_y,B): 0.85/0.92 * Chain [36]: 0 0.85/0.92 with precondition: [] 0.85/0.92 0.85/0.92 * Chain [35]: 1*s(50)+1 0.85/0.92 Such that:s(50) =< V_m-V_y 0.85/0.92 0.85/0.92 with precondition: [V_x+1=V_n,V_m>=V_y+1] 0.85/0.92 0.85/0.92 * Chain [34]: 2*s(51)+0 0.85/0.92 Such that:aux(30) =< V_n-V_x 0.85/0.92 s(51) =< aux(30) 0.85/0.92 0.85/0.92 with precondition: [V_y>=V_m,V_n>=V_x+1] 0.85/0.92 0.85/0.92 * Chain [33]: 1*s(53)+0 0.85/0.92 Such that:s(53) =< V_n-V_x 0.85/0.92 0.85/0.92 with precondition: [V_y>=V_m,V_n>=V_x+2] 0.85/0.92 0.85/0.92 * Chain [32]: 0 0.85/0.92 with precondition: [V_x>=V_n] 0.85/0.92 0.85/0.92 * Chain [31]: 0 0.85/0.92 with precondition: [V_n>=V_x+1] 0.85/0.92 0.85/0.92 * Chain [30]: 4*s(56)+2*s(57)+2*s(58)+1 0.85/0.92 Such that:aux(32) =< V_m-V_y 0.85/0.92 aux(33) =< V_n-V_x 0.85/0.92 s(56) =< aux(32) 0.85/0.92 s(57) =< aux(33) 0.85/0.92 s(58) =< aux(33) 0.85/0.92 s(57) =< aux(32) 0.85/0.92 0.85/0.92 with precondition: [V_n>=V_x+1,V_m>=V_y+1] 0.85/0.92 0.85/0.92 * Chain [29]: 6*s(67)+10*s(68)+4*s(69)+1 0.85/0.92 Such that:aux(35) =< V_m-V_y 0.85/0.92 aux(36) =< V_n-V_x 0.85/0.92 s(67) =< aux(36) 0.85/0.92 s(68) =< aux(35) 0.85/0.92 s(69) =< aux(36) 0.85/0.92 s(69) =< aux(35) 0.85/0.92 0.85/0.92 with precondition: [V_n>=V_x+2,V_m>=V_y+1] 0.85/0.92 0.85/0.92 * Chain [28]: 6*s(78)+7*s(79)+3*s(80)+1 0.85/0.92 Such that:aux(37) =< V_m-V_y 0.85/0.92 aux(38) =< V_n-V_x 0.85/0.92 s(78) =< aux(38) 0.85/0.92 s(79) =< aux(37) 0.85/0.92 s(80) =< aux(38) 0.85/0.92 s(80) =< aux(37) 0.85/0.92 0.85/0.92 with precondition: [V_n>=V_x+3,V_m>=V_y+1] 0.85/0.92 0.85/0.92 * Chain [27]: 2*s(88)+2*s(89)+1*s(90)+1 0.85/0.92 Such that:s(87) =< V_m-V_y 0.85/0.92 s(86) =< V_n-V_x 0.85/0.92 s(88) =< s(86) 0.85/0.92 s(89) =< s(87) 0.85/0.92 s(90) =< s(86) 0.85/0.92 s(90) =< s(87) 0.85/0.92 0.85/0.92 with precondition: [V_n>=V_x+4,V_m>=V_y+1] 0.85/0.92 0.85/0.92 0.85/0.92 #### Cost of chains of eval_speedNestedMultiple_start(V__0,V__01,V__1,V_2,V_5,V_m,V_n,V_x,V_y,B): 0.85/0.92 * Chain [46]: 0 0.85/0.92 with precondition: [] 0.85/0.92 0.85/0.92 * Chain [45]: 1*s(91)+1 0.85/0.92 Such that:s(91) =< V_m-V_y 0.85/0.92 0.85/0.92 with precondition: [V_x+1=V_n,V_m>=V_y+1] 0.85/0.92 0.85/0.92 * Chain [44]: 2*s(93)+0 0.85/0.92 Such that:s(92) =< V_n-V_x 0.85/0.92 s(93) =< s(92) 0.85/0.92 0.85/0.92 with precondition: [V_y>=V_m,V_n>=V_x+1] 0.85/0.92 0.85/0.92 * Chain [43]: 1*s(94)+0 0.85/0.92 Such that:s(94) =< V_n-V_x 0.85/0.92 0.85/0.92 with precondition: [V_y>=V_m,V_n>=V_x+2] 0.85/0.92 0.85/0.92 * Chain [42]: 0 0.85/0.92 with precondition: [V_x>=V_n] 0.85/0.92 0.85/0.92 * Chain [41]: 0 0.85/0.92 with precondition: [V_n>=V_x+1] 0.85/0.92 0.85/0.92 * Chain [40]: 4*s(97)+2*s(98)+2*s(99)+1 0.85/0.92 Such that:s(95) =< V_m-V_y 0.85/0.92 s(96) =< V_n-V_x 0.85/0.92 s(97) =< s(95) 0.85/0.92 s(98) =< s(96) 0.85/0.92 s(99) =< s(96) 0.85/0.92 s(98) =< s(95) 0.85/0.92 0.85/0.92 with precondition: [V_n>=V_x+1,V_m>=V_y+1] 0.85/0.92 0.85/0.92 * Chain [39]: 6*s(102)+10*s(103)+4*s(104)+1 0.85/0.92 Such that:s(100) =< V_m-V_y 0.85/0.92 s(101) =< V_n-V_x 0.85/0.92 s(102) =< s(101) 0.85/0.92 s(103) =< s(100) 0.85/0.92 s(104) =< s(101) 0.85/0.92 s(104) =< s(100) 0.85/0.92 0.85/0.92 with precondition: [V_n>=V_x+2,V_m>=V_y+1] 0.85/0.92 0.85/0.92 * Chain [38]: 6*s(107)+7*s(108)+3*s(109)+1 0.85/0.92 Such that:s(105) =< V_m-V_y 0.85/0.92 s(106) =< V_n-V_x 0.85/0.92 s(107) =< s(106) 0.85/0.92 s(108) =< s(105) 0.85/0.92 s(109) =< s(106) 0.85/0.92 s(109) =< s(105) 0.85/0.92 0.85/0.92 with precondition: [V_n>=V_x+3,V_m>=V_y+1] 0.85/0.92 0.85/0.92 * Chain [37]: 2*s(112)+2*s(113)+1*s(114)+1 0.85/0.92 Such that:s(110) =< V_m-V_y 0.85/0.92 s(111) =< V_n-V_x 0.85/0.92 s(112) =< s(111) 0.85/0.92 s(113) =< s(110) 0.85/0.92 s(114) =< s(111) 0.85/0.92 s(114) =< s(110) 0.85/0.92 0.85/0.92 with precondition: [V_n>=V_x+4,V_m>=V_y+1] 0.85/0.92 0.85/0.92 0.85/0.92 Closed-form bounds of eval_speedNestedMultiple_start(V__0,V__01,V__1,V_2,V_5,V_m,V_n,V_x,V_y,B): 0.85/0.92 ------------------------------------- 0.85/0.92 * Chain [46] with precondition: [] 0.85/0.92 - Upper bound: 0 0.85/0.92 - Complexity: constant 0.85/0.92 * Chain [45] with precondition: [V_x+1=V_n,V_m>=V_y+1] 0.85/0.92 - Upper bound: V_m-V_y+1 0.85/0.92 - Complexity: n 0.85/0.92 * Chain [44] with precondition: [V_y>=V_m,V_n>=V_x+1] 0.85/0.92 - Upper bound: 2*V_n-2*V_x 0.85/0.92 - Complexity: n 0.85/0.92 * Chain [43] with precondition: [V_y>=V_m,V_n>=V_x+2] 0.85/0.92 - Upper bound: V_n-V_x 0.85/0.92 - Complexity: n 0.85/0.92 * Chain [42] with precondition: [V_x>=V_n] 0.85/0.92 - Upper bound: 0 0.85/0.92 - Complexity: constant 0.85/0.92 * Chain [41] with precondition: [V_n>=V_x+1] 0.85/0.92 - Upper bound: 0 0.85/0.92 - Complexity: constant 0.85/0.92 * Chain [40] with precondition: [V_n>=V_x+1,V_m>=V_y+1] 0.85/0.92 - Upper bound: 4*V_m+4*V_n-4*V_x-4*V_y+1 0.85/0.92 - Complexity: n 0.85/0.92 * Chain [39] with precondition: [V_n>=V_x+2,V_m>=V_y+1] 0.85/0.92 - Upper bound: 10*V_m+10*V_n-10*V_x-10*V_y+1 0.85/0.92 - Complexity: n 0.85/0.92 * Chain [38] with precondition: [V_n>=V_x+3,V_m>=V_y+1] 0.85/0.92 - Upper bound: 7*V_m+9*V_n-9*V_x-7*V_y+1 0.85/0.92 - Complexity: n 0.85/0.92 * Chain [37] with precondition: [V_n>=V_x+4,V_m>=V_y+1] 0.85/0.92 - Upper bound: 2*V_m+3*V_n-3*V_x-2*V_y+1 0.85/0.92 - Complexity: n 0.85/0.92 0.85/0.92 ### Maximum cost of eval_speedNestedMultiple_start(V__0,V__01,V__1,V_2,V_5,V_m,V_n,V_x,V_y,B): max([nat(V_m-V_y)+1,nat(V_n-V_x)*5+nat(V_m-V_y)*3+(nat(V_m-V_y)*3+nat(V_n-V_x))+(nat(V_m-V_y)*2+nat(V_n-V_x))+(nat(V_m-V_y)*2+1+nat(V_n-V_x))+nat(V_n-V_x)+nat(V_n-V_x)]) 0.85/0.92 Asymptotic class: n 0.85/0.92 * Total analysis performed in 796 ms. 0.85/0.92 0.91/1.02 EOF