1.14/1.21 WORST_CASE(?,O(n^4)) 1.14/1.21 1.14/1.21 Preprocessing Cost Relations 1.14/1.21 ===================================== 1.14/1.21 1.14/1.21 #### Computed strongly connected components 1.14/1.21 0. recursive : [evalfbb3in/4,evalfbb4in/4] 1.14/1.21 1. recursive : [evalfbb4in_loop_cont/7,evalfbb5in/6,evalfbb6in/6] 1.14/1.21 2. recursive : [evalfbb6in_loop_cont/11,evalfbb7in/10,evalfbb8in/10] 1.14/1.21 3. recursive : [evalfbb10in/10,evalfbb8in_loop_cont/11] 1.14/1.21 4. non_recursive : [evalfstop/6] 1.14/1.21 5. non_recursive : [evalfreturnin/6] 1.14/1.21 6. non_recursive : [exit_location/1] 1.14/1.21 7. non_recursive : [evalfbb10in_loop_cont/7] 1.14/1.21 8. non_recursive : [evalfentryin/6] 1.14/1.21 9. non_recursive : [evalfstart/6] 1.14/1.21 1.14/1.21 #### Obtained direct recursion through partial evaluation 1.14/1.21 0. SCC is partially evaluated into evalfbb4in/4 1.14/1.21 1. SCC is partially evaluated into evalfbb6in/6 1.14/1.21 2. SCC is partially evaluated into evalfbb8in/10 1.14/1.21 3. SCC is partially evaluated into evalfbb10in/10 1.14/1.21 4. SCC is completely evaluated into other SCCs 1.14/1.21 5. SCC is completely evaluated into other SCCs 1.14/1.21 6. SCC is completely evaluated into other SCCs 1.14/1.21 7. SCC is partially evaluated into evalfbb10in_loop_cont/7 1.14/1.21 8. SCC is partially evaluated into evalfentryin/6 1.14/1.21 9. SCC is partially evaluated into evalfstart/6 1.14/1.21 1.14/1.21 Control-Flow Refinement of Cost Relations 1.14/1.21 ===================================== 1.14/1.21 1.14/1.21 ### Specialization of cost equations evalfbb4in/4 1.14/1.21 * CE 19 is refined into CE [20] 1.14/1.21 * CE 18 is refined into CE [21] 1.14/1.21 * CE 17 is refined into CE [22] 1.14/1.21 1.14/1.21 1.14/1.21 ### Cost equations --> "Loop" of evalfbb4in/4 1.14/1.21 * CEs [22] --> Loop 20 1.14/1.21 * CEs [20] --> Loop 21 1.14/1.21 * CEs [21] --> Loop 22 1.14/1.21 1.14/1.21 ### Ranking functions of CR evalfbb4in(D,E,F,G) 1.14/1.21 * RF of phase [20]: [D-E+1] 1.14/1.21 1.14/1.21 #### Partial ranking functions of CR evalfbb4in(D,E,F,G) 1.14/1.21 * Partial RF of phase [20]: 1.14/1.21 - RF of loop [20:1]: 1.14/1.21 D-E+1 1.14/1.21 1.14/1.21 1.14/1.21 ### Specialization of cost equations evalfbb6in/6 1.14/1.21 * CE 15 is refined into CE [23] 1.14/1.21 * CE 13 is refined into CE [24,25] 1.14/1.21 * CE 16 is refined into CE [26] 1.14/1.21 * CE 14 is refined into CE [27] 1.14/1.21 1.14/1.21 1.14/1.21 ### Cost equations --> "Loop" of evalfbb6in/6 1.14/1.21 * CEs [27] --> Loop 23 1.14/1.21 * CEs [23] --> Loop 24 1.14/1.21 * CEs [24,25] --> Loop 25 1.14/1.21 * CEs [26] --> Loop 26 1.14/1.21 1.14/1.21 ### Ranking functions of CR evalfbb6in(B,D,E,F,G,H) 1.14/1.21 * RF of phase [23]: [B-D+1] 1.14/1.21 1.14/1.21 #### Partial ranking functions of CR evalfbb6in(B,D,E,F,G,H) 1.14/1.21 * Partial RF of phase [23]: 1.14/1.21 - RF of loop [23:1]: 1.14/1.21 B-D+1 1.14/1.21 1.14/1.21 1.14/1.21 ### Specialization of cost equations evalfbb8in/10 1.14/1.21 * CE 11 is refined into CE [28] 1.14/1.21 * CE 9 is refined into CE [29,30,31] 1.14/1.21 * CE 12 is refined into CE [32] 1.14/1.21 * CE 10 is refined into CE [33,34] 1.14/1.21 1.14/1.21 1.14/1.21 ### Cost equations --> "Loop" of evalfbb8in/10 1.14/1.21 * CEs [34] --> Loop 27 1.14/1.21 * CEs [33] --> Loop 28 1.14/1.21 * CEs [28] --> Loop 29 1.14/1.21 * CEs [31] --> Loop 30 1.14/1.21 * CEs [30] --> Loop 31 1.14/1.21 * CEs [29] --> Loop 32 1.14/1.21 * CEs [32] --> Loop 33 1.14/1.21 1.14/1.21 ### Ranking functions of CR evalfbb8in(A,B,C,D,E,F,G,H,I,J) 1.14/1.21 * RF of phase [27]: [A-C+1,B-C] 1.14/1.21 * RF of phase [28]: [A-C+1,B-C+1] 1.14/1.21 1.14/1.21 #### Partial ranking functions of CR evalfbb8in(A,B,C,D,E,F,G,H,I,J) 1.14/1.21 * Partial RF of phase [27]: 1.14/1.21 - RF of loop [27:1]: 1.14/1.21 A-C+1 1.14/1.21 B-C 1.14/1.21 * Partial RF of phase [28]: 1.14/1.21 - RF of loop [28:1]: 1.14/1.21 A-C+1 1.14/1.21 B-C+1 1.14/1.21 1.14/1.21 1.14/1.21 ### Specialization of cost equations evalfbb10in/10 1.14/1.21 * CE 5 is refined into CE [35] 1.14/1.21 * CE 3 is refined into CE [36,37,38,39,40,41,42,43] 1.14/1.21 * CE 6 is refined into CE [44] 1.14/1.21 * CE 4 is refined into CE [45,46,47] 1.14/1.21 1.14/1.21 1.14/1.21 ### Cost equations --> "Loop" of evalfbb10in/10 1.14/1.21 * CEs [45] --> Loop 34 1.14/1.21 * CEs [47] --> Loop 35 1.14/1.21 * CEs [46] --> Loop 36 1.14/1.21 * CEs [35] --> Loop 37 1.14/1.21 * CEs [38] --> Loop 38 1.14/1.21 * CEs [43] --> Loop 39 1.14/1.21 * CEs [41] --> Loop 40 1.14/1.21 * CEs [42] --> Loop 41 1.14/1.21 * CEs [40] --> Loop 42 1.14/1.21 * CEs [39] --> Loop 43 1.14/1.21 * CEs [37] --> Loop 44 1.14/1.21 * CEs [36] --> Loop 45 1.14/1.21 * CEs [44] --> Loop 46 1.14/1.21 1.14/1.21 ### Ranking functions of CR evalfbb10in(A,B,C,D,E,F,G,H,I,J) 1.14/1.21 * RF of phase [35]: [-A+B] 1.14/1.21 1.14/1.21 #### Partial ranking functions of CR evalfbb10in(A,B,C,D,E,F,G,H,I,J) 1.14/1.21 * Partial RF of phase [35]: 1.14/1.21 - RF of loop [35:1]: 1.14/1.21 -A+B 1.14/1.21 1.14/1.21 1.14/1.21 ### Specialization of cost equations evalfbb10in_loop_cont/7 1.14/1.21 * CE 7 is refined into CE [48] 1.14/1.21 * CE 8 is refined into CE [49] 1.14/1.21 1.14/1.21 1.14/1.21 ### Cost equations --> "Loop" of evalfbb10in_loop_cont/7 1.14/1.21 * CEs [48] --> Loop 47 1.14/1.21 * CEs [49] --> Loop 48 1.14/1.21 1.14/1.21 ### Ranking functions of CR evalfbb10in_loop_cont(A,B,C,D,E,F,G) 1.14/1.21 1.14/1.21 #### Partial ranking functions of CR evalfbb10in_loop_cont(A,B,C,D,E,F,G) 1.14/1.21 1.14/1.21 1.14/1.21 ### Specialization of cost equations evalfentryin/6 1.14/1.21 * CE 2 is refined into CE [50,51,52,53,54,55,56,57,58] 1.14/1.21 1.14/1.21 1.14/1.21 ### Cost equations --> "Loop" of evalfentryin/6 1.14/1.21 * CEs [55] --> Loop 49 1.14/1.21 * CEs [54] --> Loop 50 1.14/1.21 * CEs [53,58] --> Loop 51 1.14/1.21 * CEs [52] --> Loop 52 1.14/1.21 * CEs [57] --> Loop 53 1.14/1.21 * CEs [50,56] --> Loop 54 1.14/1.21 * CEs [51] --> Loop 55 1.14/1.21 1.14/1.21 ### Ranking functions of CR evalfentryin(A,B,C,D,E,F) 1.14/1.21 1.14/1.21 #### Partial ranking functions of CR evalfentryin(A,B,C,D,E,F) 1.14/1.21 1.14/1.21 1.14/1.21 ### Specialization of cost equations evalfstart/6 1.14/1.21 * CE 1 is refined into CE [59,60,61,62,63,64,65] 1.14/1.21 1.14/1.21 1.14/1.21 ### Cost equations --> "Loop" of evalfstart/6 1.14/1.21 * CEs [65] --> Loop 56 1.14/1.21 * CEs [64] --> Loop 57 1.14/1.21 * CEs [63] --> Loop 58 1.14/1.21 * CEs [62] --> Loop 59 1.14/1.21 * CEs [61] --> Loop 60 1.14/1.21 * CEs [60] --> Loop 61 1.14/1.21 * CEs [59] --> Loop 62 1.14/1.21 1.14/1.21 ### Ranking functions of CR evalfstart(A,B,C,D,E,F) 1.14/1.21 1.14/1.21 #### Partial ranking functions of CR evalfstart(A,B,C,D,E,F) 1.14/1.21 1.14/1.21 1.14/1.21 Computing Bounds 1.14/1.21 ===================================== 1.14/1.21 1.14/1.21 #### Cost of chains of evalfbb4in(D,E,F,G): 1.14/1.21 * Chain [[20],22]: 1*it(20)+0 1.14/1.21 Such that:it(20) =< -E+G 1.14/1.21 1.14/1.21 with precondition: [F=2,D+1=G,D>=2,E>=1,D>=E] 1.14/1.21 1.14/1.21 * Chain [[20],21]: 1*it(20)+0 1.14/1.21 Such that:it(20) =< D-E+1 1.14/1.21 1.14/1.21 with precondition: [F=3,D>=2,E>=1,D>=E] 1.14/1.21 1.14/1.21 * Chain [21]: 0 1.14/1.21 with precondition: [F=3,D>=2,E>=1] 1.14/1.21 1.14/1.21 1.14/1.21 #### Cost of chains of evalfbb6in(B,D,E,F,G,H): 1.14/1.21 * Chain [[23],26]: 1*it(23)+1*s(3)+0 1.14/1.21 Such that:aux(1) =< B+1 1.14/1.21 it(23) =< B-D+1 1.14/1.21 s(3) =< it(23)*aux(1) 1.14/1.21 1.14/1.21 with precondition: [F=3,D>=2,B>=D] 1.14/1.21 1.14/1.21 * Chain [[23],25]: 1*it(23)+1*s(3)+1*s(4)+0 1.14/1.21 Such that:s(4) =< B 1.14/1.21 aux(1) =< B+1 1.14/1.21 it(23) =< B-D 1.14/1.21 s(3) =< it(23)*aux(1) 1.14/1.21 1.14/1.21 with precondition: [F=3,D>=2,B>=D+1] 1.14/1.21 1.14/1.21 * Chain [[23],24]: 1*it(23)+1*s(3)+0 1.14/1.21 Such that:it(23) =< -D+G 1.14/1.21 aux(1) =< G 1.14/1.21 s(3) =< it(23)*aux(1) 1.14/1.21 1.14/1.21 with precondition: [F=4,B+1=G,B+1=H,D>=2,B>=D] 1.14/1.21 1.14/1.21 * Chain [26]: 0 1.14/1.21 with precondition: [F=3,D>=2,B+1>=D] 1.14/1.21 1.14/1.21 * Chain [25]: 1*s(4)+0 1.14/1.21 Such that:s(4) =< D 1.14/1.21 1.14/1.21 with precondition: [F=3,D>=2,B>=D] 1.14/1.21 1.14/1.21 * Chain [24]: 0 1.14/1.21 with precondition: [F=4,B+1=D,H=E,B+1=G,B>=1] 1.14/1.21 1.14/1.21 1.14/1.21 #### Cost of chains of evalfbb8in(A,B,C,D,E,F,G,H,I,J): 1.14/1.21 * Chain [[28],33]: 1*it(28)+0 1.14/1.21 Such that:it(28) =< A-C+1 1.14/1.21 1.14/1.21 with precondition: [F=3,A=B,C>=1,A>=C] 1.14/1.21 1.14/1.21 * Chain [[28],32]: 1*it(28)+0 1.14/1.21 Such that:it(28) =< A-C 1.14/1.21 1.14/1.21 with precondition: [F=3,A=B,C>=1,A>=C+1] 1.14/1.21 1.14/1.21 * Chain [[28],29]: 1*it(28)+0 1.14/1.21 Such that:it(28) =< -C+H 1.14/1.21 1.14/1.21 with precondition: [F=5,A=B,A+1=G,A+1=H,A+1=I,E=J,C>=1,A>=C] 1.14/1.21 1.14/1.21 * Chain [[27],33]: 1*it(27)+1*s(15)+1*s(16)+0 1.14/1.21 Such that:aux(2) =< -A+B 1.14/1.21 it(27) =< A-C+1 1.14/1.21 s(13) =< B+1 1.14/1.21 aux(3) =< B-C 1.14/1.21 aux(2) =< aux(3) 1.14/1.21 it(27) =< aux(3) 1.14/1.21 s(15) =< it(27)*aux(2) 1.14/1.21 s(16) =< s(15)*s(13) 1.14/1.21 1.14/1.21 with precondition: [F=3,C>=1,B>=A+1,A>=C] 1.14/1.21 1.14/1.21 * Chain [[27],32]: 1*it(27)+1*s(15)+1*s(16)+0 1.14/1.21 Such that:aux(2) =< -A+B 1.14/1.21 it(27) =< A-C 1.14/1.21 s(13) =< B+1 1.14/1.21 aux(3) =< B-C 1.14/1.21 aux(2) =< aux(3) 1.14/1.21 it(27) =< aux(3) 1.14/1.21 s(15) =< it(27)*aux(2) 1.14/1.21 s(16) =< s(15)*s(13) 1.14/1.21 1.14/1.21 with precondition: [F=3,C>=1,B>=A+1,A>=C+1] 1.14/1.21 1.14/1.21 * Chain [[27],31]: 1*it(27)+1*s(15)+1*s(16)+1*s(18)+1*s(19)+1*s(20)+0 1.14/1.21 Such that:s(19) =< A+1 1.14/1.21 it(27) =< A-C 1.14/1.21 aux(3) =< B-C 1.14/1.21 aux(4) =< -A+B 1.14/1.21 aux(5) =< B+1 1.14/1.21 aux(2) =< aux(4) 1.14/1.21 s(18) =< aux(4) 1.14/1.21 s(20) =< s(18)*aux(5) 1.14/1.21 aux(2) =< aux(3) 1.14/1.21 it(27) =< aux(3) 1.14/1.21 s(15) =< it(27)*aux(2) 1.14/1.21 s(16) =< s(15)*aux(5) 1.14/1.21 1.14/1.21 with precondition: [F=3,C>=1,B>=A+1,A>=C+1] 1.14/1.21 1.14/1.21 * Chain [[27],30]: 1*it(27)+1*s(15)+1*s(16)+1*s(21)+1*s(23)+1*s(24)+0 1.14/1.21 Such that:it(27) =< A-C 1.14/1.21 s(21) =< B 1.14/1.21 aux(3) =< B-C 1.14/1.21 aux(6) =< -A+B 1.14/1.21 aux(7) =< B+1 1.14/1.21 aux(2) =< aux(6) 1.14/1.21 s(23) =< aux(6) 1.14/1.21 s(24) =< s(23)*aux(7) 1.14/1.21 aux(2) =< aux(3) 1.14/1.21 it(27) =< aux(3) 1.14/1.21 s(15) =< it(27)*aux(2) 1.14/1.21 s(16) =< s(15)*aux(7) 1.14/1.21 1.14/1.21 with precondition: [F=3,C>=1,B>=A+2,A>=C+1] 1.14/1.21 1.14/1.21 * Chain [[27],29]: 1*it(27)+1*s(15)+1*s(16)+0 1.14/1.21 Such that:it(27) =< -C+H 1.14/1.21 aux(3) =< -C+I 1.14/1.21 aux(2) =< -H+I 1.14/1.21 s(13) =< I 1.14/1.21 aux(2) =< aux(3) 1.14/1.21 it(27) =< aux(3) 1.14/1.21 s(15) =< it(27)*aux(2) 1.14/1.21 s(16) =< s(15)*s(13) 1.14/1.21 1.14/1.21 with precondition: [F=5,A+1=G,A+1=H,B+1=I,B+1=J,C>=1,B>=A+1,A>=C] 1.14/1.21 1.14/1.21 * Chain [33]: 0 1.14/1.21 with precondition: [F=3,C>=1,B>=A] 1.14/1.21 1.14/1.21 * Chain [32]: 0 1.14/1.21 with precondition: [F=3,C>=1,B>=A,A>=C] 1.14/1.21 1.14/1.21 * Chain [31]: 1*s(18)+1*s(19)+1*s(20)+0 1.14/1.21 Such that:s(18) =< -A+B 1.14/1.21 s(19) =< A+1 1.14/1.21 s(17) =< B+1 1.14/1.21 s(20) =< s(18)*s(17) 1.14/1.21 1.14/1.21 with precondition: [F=3,C>=1,B>=A+1,A>=C] 1.14/1.21 1.14/1.21 * Chain [30]: 1*s(21)+1*s(23)+1*s(24)+0 1.14/1.21 Such that:s(23) =< -A+B 1.14/1.21 s(21) =< B 1.14/1.21 s(22) =< B+1 1.14/1.21 s(24) =< s(23)*s(22) 1.14/1.21 1.14/1.21 with precondition: [F=3,C>=1,B>=A+2,A>=C] 1.14/1.21 1.14/1.21 * Chain [29]: 0 1.14/1.21 with precondition: [F=5,I=D,J=E,A+1=G,C=H,C>=1,B>=A,C>=A+1] 1.14/1.21 1.14/1.21 1.14/1.21 #### Cost of chains of evalfbb10in(A,B,C,D,E,F,G,H,I,J): 1.14/1.21 * Chain [[35],46]: 1*it(35)+1*s(63)+1*s(64)+1*s(65)+0 1.14/1.21 Such that:it(35) =< -A+B 1.14/1.21 aux(16) =< B 1.14/1.21 aux(15) =< aux(16) 1.14/1.21 s(59) =< aux(16) 1.14/1.21 aux(15) =< s(59)+1 1.14/1.21 aux(14) =< s(59)+1 1.14/1.21 s(58) =< s(59)+2 1.14/1.21 s(63) =< it(35)*aux(15) 1.14/1.21 s(66) =< it(35)*aux(14) 1.14/1.21 s(59) =< aux(14) 1.14/1.21 s(63) =< s(66) 1.14/1.21 s(64) =< s(63)*s(59) 1.14/1.21 s(65) =< s(64)*s(58) 1.14/1.21 1.14/1.21 with precondition: [F=3,A>=1,B>=A+1] 1.14/1.21 1.14/1.21 * Chain [[35],45]: 1*it(35)+1*s(63)+1*s(64)+1*s(65)+1*s(67)+0 1.14/1.21 Such that:it(35) =< -A+B 1.14/1.21 aux(17) =< B 1.14/1.21 s(67) =< aux(17) 1.14/1.21 aux(15) =< aux(17) 1.14/1.21 s(59) =< aux(17) 1.14/1.21 aux(15) =< s(59)+1 1.14/1.21 aux(14) =< s(59)+1 1.14/1.21 s(58) =< s(59)+2 1.14/1.21 s(63) =< it(35)*aux(15) 1.14/1.21 s(66) =< it(35)*aux(14) 1.14/1.21 s(59) =< aux(14) 1.14/1.21 s(63) =< s(66) 1.14/1.21 s(64) =< s(63)*s(59) 1.14/1.21 s(65) =< s(64)*s(58) 1.14/1.21 1.14/1.21 with precondition: [F=3,A>=1,B>=A+1] 1.14/1.21 1.14/1.21 * Chain [[35],44]: 1*it(35)+1*s(63)+1*s(64)+1*s(65)+1*s(68)+0 1.14/1.21 Such that:it(35) =< -A+B 1.14/1.21 aux(18) =< B 1.14/1.21 s(68) =< aux(18) 1.14/1.21 aux(15) =< aux(18) 1.14/1.21 s(59) =< aux(18) 1.14/1.21 aux(15) =< s(59)+1 1.14/1.21 aux(14) =< s(59)+1 1.14/1.21 s(58) =< s(59)+2 1.14/1.21 s(63) =< it(35)*aux(15) 1.14/1.21 s(66) =< it(35)*aux(14) 1.14/1.21 s(59) =< aux(14) 1.14/1.21 s(63) =< s(66) 1.14/1.21 s(64) =< s(63)*s(59) 1.14/1.21 s(65) =< s(64)*s(58) 1.14/1.21 1.14/1.21 with precondition: [F=3,A>=1,B>=A+1] 1.14/1.21 1.14/1.21 * Chain [[35],43]: 1*it(35)+1*s(63)+1*s(64)+1*s(65)+0 1.14/1.21 Such that:it(35) =< -A+B 1.14/1.21 aux(16) =< B 1.14/1.21 aux(15) =< aux(16) 1.14/1.21 s(59) =< aux(16) 1.14/1.21 aux(15) =< s(59)+1 1.14/1.21 aux(14) =< s(59)+1 1.14/1.21 s(58) =< s(59)+2 1.14/1.21 s(63) =< it(35)*aux(15) 1.14/1.21 s(66) =< it(35)*aux(14) 1.14/1.21 s(59) =< aux(14) 1.14/1.21 s(63) =< s(66) 1.14/1.21 s(64) =< s(63)*s(59) 1.14/1.21 s(65) =< s(64)*s(58) 1.14/1.21 1.14/1.21 with precondition: [F=3,A>=1,B>=A+1] 1.14/1.21 1.14/1.21 * Chain [[35],42]: 1*it(35)+1*s(63)+1*s(64)+1*s(65)+1*s(69)+1*s(70)+1*s(74)+1*s(76)+1*s(77)+1*s(78)+0 1.14/1.21 Such that:it(35) =< -A+B 1.14/1.21 aux(19) =< B 1.14/1.21 aux(20) =< B+1 1.14/1.21 s(69) =< aux(19) 1.14/1.21 s(70) =< aux(19) 1.14/1.21 s(72) =< aux(19) 1.14/1.21 s(69) =< aux(20) 1.14/1.21 s(72) =< aux(20) 1.14/1.21 s(74) =< s(72) 1.14/1.21 s(75) =< s(72) 1.14/1.21 s(76) =< s(74)*aux(20) 1.14/1.21 s(75) =< aux(19) 1.14/1.21 s(77) =< s(70)*s(75) 1.14/1.21 s(78) =< s(77)*aux(20) 1.14/1.21 aux(15) =< aux(19) 1.14/1.21 s(59) =< aux(19) 1.14/1.21 aux(15) =< s(59)+1 1.14/1.21 aux(14) =< s(59)+1 1.14/1.21 s(58) =< s(59)+2 1.14/1.21 s(63) =< it(35)*aux(15) 1.14/1.21 s(66) =< it(35)*aux(14) 1.14/1.21 s(59) =< aux(14) 1.14/1.21 s(63) =< s(66) 1.14/1.21 s(64) =< s(63)*s(59) 1.14/1.21 s(65) =< s(64)*s(58) 1.14/1.21 1.14/1.21 with precondition: [F=3,A>=1,B>=A+2] 1.14/1.21 1.14/1.21 * Chain [[35],41]: 2*it(35)+1*s(63)+1*s(64)+1*s(65)+1*s(80)+1*s(82)+0 1.14/1.21 Such that:s(81) =< B+1 1.14/1.21 aux(21) =< -A+B 1.14/1.21 aux(22) =< B 1.14/1.21 it(35) =< aux(21) 1.14/1.21 s(80) =< aux(22) 1.14/1.21 s(82) =< it(35)*s(81) 1.14/1.21 aux(15) =< aux(22) 1.14/1.21 s(59) =< aux(22) 1.14/1.21 aux(15) =< s(59)+1 1.14/1.21 aux(14) =< s(59)+1 1.14/1.21 s(58) =< s(59)+2 1.14/1.21 s(63) =< it(35)*aux(15) 1.14/1.21 s(66) =< it(35)*aux(14) 1.14/1.21 s(59) =< aux(14) 1.14/1.21 s(63) =< s(66) 1.14/1.21 s(64) =< s(63)*s(59) 1.14/1.21 s(65) =< s(64)*s(58) 1.14/1.21 1.14/1.21 with precondition: [F=3,A>=1,B>=A+3] 1.14/1.21 1.14/1.21 * Chain [[35],40]: 1*it(35)+1*s(63)+1*s(64)+1*s(65)+1*s(83)+2*s(89)+2*s(90)+2*s(91)+1*s(92)+1*s(93)+0 1.14/1.21 Such that:it(35) =< -A+B 1.14/1.21 aux(23) =< B 1.14/1.21 aux(24) =< B+1 1.14/1.21 s(83) =< aux(23) 1.14/1.21 s(84) =< aux(23) 1.14/1.21 s(83) =< aux(24) 1.14/1.21 s(84) =< aux(24) 1.14/1.21 s(88) =< s(84) 1.14/1.21 s(89) =< aux(23) 1.14/1.21 s(88) =< aux(23) 1.14/1.21 s(90) =< s(89)*s(88) 1.14/1.21 s(91) =< s(90)*aux(24) 1.14/1.21 s(92) =< s(84) 1.14/1.21 s(93) =< s(92)*aux(24) 1.14/1.21 aux(15) =< aux(23) 1.14/1.21 s(59) =< aux(23) 1.14/1.21 aux(15) =< s(59)+1 1.14/1.21 aux(14) =< s(59)+1 1.14/1.21 s(58) =< s(59)+2 1.14/1.21 s(63) =< it(35)*aux(15) 1.14/1.21 s(66) =< it(35)*aux(14) 1.14/1.21 s(59) =< aux(14) 1.14/1.21 s(63) =< s(66) 1.14/1.21 s(64) =< s(63)*s(59) 1.14/1.21 s(65) =< s(64)*s(58) 1.14/1.21 1.14/1.21 with precondition: [F=3,A>=1,B>=A+2] 1.14/1.21 1.14/1.21 * Chain [[35],39]: 1*it(35)+1*s(63)+1*s(64)+1*s(65)+2*s(94)+1*s(100)+1*s(101)+1*s(102)+1*s(103)+0 1.14/1.21 Such that:s(98) =< B+1 1.14/1.21 aux(26) =< -A+B 1.14/1.21 aux(27) =< B 1.14/1.21 it(35) =< aux(26) 1.14/1.21 s(97) =< aux(26) 1.14/1.21 s(94) =< aux(27) 1.14/1.21 s(97) =< aux(27) 1.14/1.21 s(99) =< s(97) 1.14/1.21 s(100) =< s(97) 1.14/1.21 s(101) =< s(100)*s(98) 1.14/1.21 s(99) =< aux(27) 1.14/1.21 s(102) =< s(94)*s(99) 1.14/1.21 s(103) =< s(102)*s(98) 1.14/1.21 aux(15) =< aux(27) 1.14/1.21 s(59) =< aux(27) 1.14/1.21 aux(15) =< s(59)+1 1.14/1.21 aux(14) =< s(59)+1 1.14/1.21 s(58) =< s(59)+2 1.14/1.21 s(63) =< it(35)*aux(15) 1.14/1.21 s(66) =< it(35)*aux(14) 1.14/1.21 s(59) =< aux(14) 1.14/1.21 s(63) =< s(66) 1.14/1.21 s(64) =< s(63)*s(59) 1.14/1.21 s(65) =< s(64)*s(58) 1.14/1.21 1.14/1.21 with precondition: [F=3,A>=1,B>=A+3] 1.14/1.21 1.14/1.21 * Chain [[35],38]: 1*it(35)+1*s(63)+1*s(64)+1*s(65)+0 1.14/1.21 Such that:it(35) =< -A+B 1.14/1.21 aux(16) =< B 1.14/1.21 aux(15) =< aux(16) 1.14/1.21 s(59) =< aux(16) 1.14/1.21 aux(15) =< s(59)+1 1.14/1.21 aux(14) =< s(59)+1 1.14/1.21 s(58) =< s(59)+2 1.14/1.21 s(63) =< it(35)*aux(15) 1.14/1.21 s(66) =< it(35)*aux(14) 1.14/1.21 s(59) =< aux(14) 1.14/1.21 s(63) =< s(66) 1.14/1.21 s(64) =< s(63)*s(59) 1.14/1.21 s(65) =< s(64)*s(58) 1.14/1.21 1.14/1.21 with precondition: [F=3,A>=1,B>=A+1] 1.14/1.21 1.14/1.21 * Chain [[35],34,46]: 1*it(35)+1*s(63)+1*s(64)+1*s(65)+1*s(104)+1 1.14/1.21 Such that:it(35) =< -A+B 1.14/1.21 aux(28) =< B 1.14/1.21 s(104) =< aux(28) 1.14/1.21 aux(15) =< aux(28) 1.14/1.21 s(59) =< aux(28) 1.14/1.21 aux(15) =< s(59)+1 1.14/1.21 aux(14) =< s(59)+1 1.14/1.21 s(58) =< s(59)+2 1.14/1.21 s(63) =< it(35)*aux(15) 1.14/1.21 s(66) =< it(35)*aux(14) 1.14/1.21 s(59) =< aux(14) 1.14/1.21 s(63) =< s(66) 1.14/1.21 s(64) =< s(63)*s(59) 1.14/1.21 s(65) =< s(64)*s(58) 1.14/1.21 1.14/1.21 with precondition: [F=3,A>=1,B>=A+1] 1.14/1.21 1.14/1.21 * Chain [[35],34,37]: 1*it(35)+1*s(63)+1*s(64)+1*s(65)+1*s(104)+1 1.14/1.21 Such that:it(35) =< -A+G 1.14/1.21 aux(29) =< G 1.14/1.21 s(104) =< aux(29) 1.14/1.21 aux(15) =< aux(29) 1.14/1.21 s(59) =< aux(29) 1.14/1.21 aux(15) =< s(59)+1 1.14/1.21 aux(14) =< s(59)+1 1.14/1.21 s(58) =< s(59)+2 1.14/1.21 s(63) =< it(35)*aux(15) 1.14/1.21 s(66) =< it(35)*aux(14) 1.14/1.21 s(59) =< aux(14) 1.14/1.21 s(63) =< s(66) 1.14/1.21 s(64) =< s(63)*s(59) 1.14/1.21 s(65) =< s(64)*s(58) 1.14/1.21 1.14/1.21 with precondition: [F=6,B+1=G,B+1=H,B+1=I,B+1=J,A>=1,B>=A+1] 1.14/1.21 1.14/1.21 * Chain [46]: 0 1.14/1.21 with precondition: [F=3,A>=1] 1.14/1.21 1.14/1.21 * Chain [45]: 1*s(67)+0 1.14/1.21 Such that:s(67) =< B 1.14/1.21 1.14/1.21 with precondition: [F=3,A=B,A>=1] 1.14/1.21 1.14/1.21 * Chain [43]: 0 1.14/1.21 with precondition: [F=3,A>=1,B>=A] 1.14/1.21 1.14/1.21 * Chain [42]: 1*s(69)+1*s(70)+1*s(74)+1*s(76)+1*s(77)+1*s(78)+0 1.14/1.21 Such that:s(72) =< -A+B 1.14/1.21 s(70) =< A 1.14/1.21 s(69) =< A+1 1.14/1.21 s(71) =< B 1.14/1.21 s(73) =< B+1 1.14/1.21 s(74) =< s(72) 1.14/1.21 s(75) =< s(72) 1.14/1.21 s(76) =< s(74)*s(73) 1.14/1.21 s(75) =< s(71) 1.14/1.21 s(70) =< s(71) 1.14/1.21 s(77) =< s(70)*s(75) 1.14/1.21 s(78) =< s(77)*s(73) 1.14/1.21 1.14/1.21 with precondition: [F=3,A>=1,B>=A+1] 1.14/1.21 1.14/1.21 * Chain [41]: 1*s(79)+1*s(80)+1*s(82)+0 1.14/1.21 Such that:s(79) =< -A+B 1.14/1.21 s(80) =< B 1.14/1.21 s(81) =< B+1 1.14/1.21 s(82) =< s(79)*s(81) 1.14/1.21 1.14/1.21 with precondition: [F=3,A>=1,B>=A+2] 1.14/1.21 1.14/1.21 * Chain [38]: 0 1.14/1.21 with precondition: [F=3,A>=1,B>=A] 1.14/1.21 1.14/1.21 * Chain [37]: 0 1.14/1.21 with precondition: [F=6,H=C,I=D,J=E,A=G,A>=1,A>=B+1] 1.14/1.21 1.14/1.21 * Chain [34,46]: 1*s(104)+1 1.14/1.21 Such that:s(104) =< A 1.14/1.21 1.14/1.21 with precondition: [F=3,A=B,A>=1] 1.14/1.21 1.14/1.21 * Chain [34,37]: 1*s(104)+1 1.14/1.21 Such that:s(104) =< G 1.14/1.21 1.14/1.21 with precondition: [F=6,A=B,A+1=G,A+1=H,A+1=I,E=J,A>=1] 1.14/1.21 1.14/1.21 1.14/1.21 #### Cost of chains of evalfbb10in_loop_cont(A,B,C,D,E,F,G): 1.14/1.21 * Chain [48]: 0 1.14/1.21 with precondition: [A=3] 1.14/1.21 1.14/1.21 * Chain [47]: 0 1.14/1.21 with precondition: [A=6] 1.14/1.21 1.14/1.21 1.14/1.21 #### Cost of chains of evalfentryin(A,B,C,D,E,F): 1.14/1.21 * Chain [55]: 0 1.14/1.21 with precondition: [] 1.14/1.21 1.14/1.21 * Chain [54]: 5 1.14/1.21 with precondition: [B=1] 1.14/1.21 1.14/1.21 * Chain [53]: 0 1.14/1.21 with precondition: [0>=B] 1.14/1.21 1.14/1.21 * Chain [52]: 0 1.14/1.21 with precondition: [B>=1] 1.14/1.21 1.14/1.21 * Chain [51]: 1*s(258)+1*s(259)+11*s(263)+1*s(265)+1*s(266)+1*s(267)+1*s(273)+1*s(275)+1*s(276)+1*s(281)+1*s(283)+1*s(284)+1*s(289)+1*s(291)+1*s(292)+1*s(297)+1*s(299)+1*s(300)+1*s(305)+1*s(307)+1*s(308)+1*s(313)+1*s(315)+1*s(316)+1*s(319)+1*s(324)+1*s(326)+1*s(327)+1 1.14/1.21 Such that:s(258) =< 1 1.14/1.21 s(259) =< 2 1.14/1.21 aux(40) =< B 1.14/1.21 aux(41) =< B+1 1.14/1.21 s(263) =< aux(40) 1.14/1.21 s(265) =< s(263)*aux(41) 1.14/1.21 s(258) =< aux(40) 1.14/1.21 s(266) =< s(258)*aux(40) 1.14/1.21 s(267) =< s(266)*aux(41) 1.14/1.21 s(269) =< aux(40) 1.14/1.21 s(270) =< aux(40) 1.14/1.21 s(269) =< s(270)+1 1.14/1.21 s(271) =< s(270)+1 1.14/1.21 s(272) =< s(270)+2 1.14/1.21 s(273) =< s(263)*s(269) 1.14/1.21 s(274) =< s(263)*s(271) 1.14/1.21 s(270) =< s(271) 1.14/1.21 s(273) =< s(274) 1.14/1.21 s(275) =< s(273)*s(270) 1.14/1.21 s(276) =< s(275)*s(272) 1.14/1.21 s(277) =< aux(40) 1.14/1.21 s(278) =< aux(40) 1.14/1.21 s(277) =< s(278)+1 1.14/1.21 s(279) =< s(278)+1 1.14/1.21 s(280) =< s(278)+2 1.14/1.21 s(281) =< s(263)*s(277) 1.14/1.21 s(282) =< s(263)*s(279) 1.14/1.21 s(278) =< s(279) 1.14/1.21 s(281) =< s(282) 1.14/1.21 s(283) =< s(281)*s(278) 1.14/1.21 s(284) =< s(283)*s(280) 1.14/1.21 s(285) =< aux(40) 1.14/1.21 s(286) =< aux(40) 1.14/1.21 s(285) =< s(286)+1 1.14/1.21 s(287) =< s(286)+1 1.14/1.21 s(288) =< s(286)+2 1.14/1.21 s(289) =< s(263)*s(285) 1.14/1.21 s(290) =< s(263)*s(287) 1.14/1.21 s(286) =< s(287) 1.14/1.21 s(289) =< s(290) 1.14/1.21 s(291) =< s(289)*s(286) 1.14/1.21 s(292) =< s(291)*s(288) 1.14/1.21 s(293) =< aux(40) 1.14/1.21 s(294) =< aux(40) 1.14/1.21 s(293) =< s(294)+1 1.14/1.21 s(295) =< s(294)+1 1.14/1.21 s(296) =< s(294)+2 1.14/1.21 s(297) =< s(263)*s(293) 1.14/1.21 s(298) =< s(263)*s(295) 1.14/1.21 s(294) =< s(295) 1.14/1.21 s(297) =< s(298) 1.14/1.21 s(299) =< s(297)*s(294) 1.14/1.21 s(300) =< s(299)*s(296) 1.14/1.21 s(301) =< aux(40) 1.14/1.21 s(302) =< aux(40) 1.14/1.21 s(301) =< s(302)+1 1.14/1.21 s(303) =< s(302)+1 1.14/1.21 s(304) =< s(302)+2 1.14/1.21 s(305) =< s(263)*s(301) 1.14/1.21 s(306) =< s(263)*s(303) 1.14/1.21 s(302) =< s(303) 1.14/1.21 s(305) =< s(306) 1.14/1.21 s(307) =< s(305)*s(302) 1.14/1.21 s(308) =< s(307)*s(304) 1.14/1.21 s(309) =< aux(40) 1.14/1.21 s(310) =< aux(40) 1.14/1.21 s(309) =< s(310)+1 1.14/1.21 s(311) =< s(310)+1 1.14/1.21 s(312) =< s(310)+2 1.14/1.21 s(313) =< s(263)*s(309) 1.14/1.21 s(314) =< s(263)*s(311) 1.14/1.21 s(310) =< s(311) 1.14/1.21 s(313) =< s(314) 1.14/1.21 s(315) =< s(313)*s(310) 1.14/1.21 s(316) =< s(315)*s(312) 1.14/1.21 s(319) =< aux(41) 1.14/1.21 s(320) =< aux(41) 1.14/1.21 s(321) =< aux(41) 1.14/1.21 s(320) =< s(321)+1 1.14/1.21 s(322) =< s(321)+1 1.14/1.21 s(323) =< s(321)+2 1.14/1.21 s(324) =< s(263)*s(320) 1.14/1.21 s(325) =< s(263)*s(322) 1.14/1.21 s(321) =< s(322) 1.14/1.21 s(324) =< s(325) 1.14/1.21 s(326) =< s(324)*s(321) 1.14/1.21 s(327) =< s(326)*s(323) 1.14/1.21 1.14/1.21 with precondition: [B>=2] 1.14/1.21 1.14/1.21 * Chain [50]: 7*s(331)+1*s(333)+2*s(334)+3*s(337)+3*s(338)+2*s(339)+2*s(340)+1*s(345)+1*s(347)+1*s(348)+1*s(353)+1*s(355)+1*s(356)+0 1.14/1.21 Such that:s(330) =< B+1 1.14/1.21 aux(42) =< B 1.14/1.21 s(331) =< aux(42) 1.14/1.21 s(333) =< s(331)*s(330) 1.14/1.21 s(334) =< aux(42) 1.14/1.21 s(335) =< aux(42) 1.14/1.21 s(334) =< s(330) 1.14/1.21 s(335) =< s(330) 1.14/1.21 s(336) =< s(335) 1.14/1.21 s(336) =< aux(42) 1.14/1.21 s(337) =< s(331)*s(336) 1.14/1.21 s(338) =< s(337)*s(330) 1.14/1.21 s(339) =< s(335) 1.14/1.21 s(340) =< s(339)*s(330) 1.14/1.21 s(341) =< aux(42) 1.14/1.21 s(342) =< aux(42) 1.14/1.21 s(341) =< s(342)+1 1.14/1.21 s(343) =< s(342)+1 1.14/1.21 s(344) =< s(342)+2 1.14/1.21 s(345) =< s(331)*s(341) 1.14/1.21 s(346) =< s(331)*s(343) 1.14/1.21 s(342) =< s(343) 1.14/1.21 s(345) =< s(346) 1.14/1.21 s(347) =< s(345)*s(342) 1.14/1.21 s(348) =< s(347)*s(344) 1.14/1.21 s(349) =< aux(42) 1.14/1.21 s(350) =< aux(42) 1.14/1.21 s(349) =< s(350)+1 1.14/1.21 s(351) =< s(350)+1 1.14/1.21 s(352) =< s(350)+2 1.14/1.21 s(353) =< s(331)*s(349) 1.14/1.21 s(354) =< s(331)*s(351) 1.14/1.21 s(350) =< s(351) 1.14/1.21 s(353) =< s(354) 1.14/1.21 s(355) =< s(353)*s(350) 1.14/1.21 s(356) =< s(355)*s(352) 1.14/1.21 1.14/1.21 with precondition: [B>=3] 1.14/1.21 1.14/1.21 * Chain [49]: 7*s(360)+2*s(365)+1*s(366)+1*s(367)+1*s(372)+1*s(374)+1*s(375)+1*s(381)+1*s(383)+1*s(384)+0 1.14/1.21 Such that:s(359) =< B+1 1.14/1.21 aux(43) =< B 1.14/1.21 s(360) =< aux(43) 1.14/1.21 s(365) =< s(360)*s(359) 1.14/1.21 s(366) =< s(360)*aux(43) 1.14/1.21 s(367) =< s(366)*s(359) 1.14/1.21 s(368) =< aux(43) 1.14/1.21 s(369) =< aux(43) 1.14/1.21 s(368) =< s(369)+1 1.14/1.21 s(370) =< s(369)+1 1.14/1.21 s(371) =< s(369)+2 1.14/1.21 s(372) =< s(360)*s(368) 1.14/1.21 s(373) =< s(360)*s(370) 1.14/1.21 s(369) =< s(370) 1.14/1.21 s(372) =< s(373) 1.14/1.21 s(374) =< s(372)*s(369) 1.14/1.21 s(375) =< s(374)*s(371) 1.14/1.21 s(377) =< aux(43) 1.14/1.21 s(378) =< aux(43) 1.14/1.21 s(377) =< s(378)+1 1.14/1.21 s(379) =< s(378)+1 1.14/1.21 s(380) =< s(378)+2 1.14/1.21 s(381) =< s(360)*s(377) 1.14/1.21 s(382) =< s(360)*s(379) 1.14/1.21 s(378) =< s(379) 1.14/1.21 s(381) =< s(382) 1.14/1.21 s(383) =< s(381)*s(378) 1.14/1.21 s(384) =< s(383)*s(380) 1.14/1.21 1.14/1.21 with precondition: [B>=4] 1.14/1.21 1.14/1.21 1.14/1.21 #### Cost of chains of evalfstart(A,B,C,D,E,F): 1.14/1.21 * Chain [62]: 0 1.14/1.21 with precondition: [] 1.14/1.21 1.14/1.21 * Chain [61]: 5 1.14/1.21 with precondition: [B=1] 1.14/1.21 1.14/1.21 * Chain [60]: 0 1.14/1.21 with precondition: [0>=B] 1.14/1.21 1.14/1.21 * Chain [59]: 0 1.14/1.21 with precondition: [B>=1] 1.14/1.21 1.14/1.21 * Chain [58]: 1*s(385)+1*s(386)+11*s(389)+1*s(390)+1*s(391)+1*s(392)+1*s(397)+1*s(399)+1*s(400)+1*s(405)+1*s(407)+1*s(408)+1*s(413)+1*s(415)+1*s(416)+1*s(421)+1*s(423)+1*s(424)+1*s(429)+1*s(431)+1*s(432)+1*s(437)+1*s(439)+1*s(440)+1*s(441)+1*s(446)+1*s(448)+1*s(449)+1 1.14/1.21 Such that:s(385) =< 1 1.14/1.21 s(386) =< 2 1.14/1.21 s(387) =< B 1.14/1.21 s(388) =< B+1 1.14/1.21 s(389) =< s(387) 1.14/1.21 s(390) =< s(389)*s(388) 1.14/1.21 s(385) =< s(387) 1.14/1.21 s(391) =< s(385)*s(387) 1.14/1.21 s(392) =< s(391)*s(388) 1.14/1.21 s(393) =< s(387) 1.14/1.21 s(394) =< s(387) 1.14/1.21 s(393) =< s(394)+1 1.14/1.21 s(395) =< s(394)+1 1.14/1.21 s(396) =< s(394)+2 1.14/1.21 s(397) =< s(389)*s(393) 1.14/1.21 s(398) =< s(389)*s(395) 1.14/1.21 s(394) =< s(395) 1.14/1.21 s(397) =< s(398) 1.14/1.21 s(399) =< s(397)*s(394) 1.14/1.21 s(400) =< s(399)*s(396) 1.14/1.21 s(401) =< s(387) 1.14/1.21 s(402) =< s(387) 1.14/1.21 s(401) =< s(402)+1 1.14/1.21 s(403) =< s(402)+1 1.14/1.21 s(404) =< s(402)+2 1.14/1.21 s(405) =< s(389)*s(401) 1.14/1.21 s(406) =< s(389)*s(403) 1.14/1.21 s(402) =< s(403) 1.14/1.21 s(405) =< s(406) 1.14/1.21 s(407) =< s(405)*s(402) 1.14/1.21 s(408) =< s(407)*s(404) 1.14/1.21 s(409) =< s(387) 1.14/1.21 s(410) =< s(387) 1.14/1.21 s(409) =< s(410)+1 1.14/1.21 s(411) =< s(410)+1 1.14/1.21 s(412) =< s(410)+2 1.14/1.21 s(413) =< s(389)*s(409) 1.14/1.21 s(414) =< s(389)*s(411) 1.14/1.21 s(410) =< s(411) 1.14/1.21 s(413) =< s(414) 1.14/1.21 s(415) =< s(413)*s(410) 1.14/1.21 s(416) =< s(415)*s(412) 1.14/1.21 s(417) =< s(387) 1.14/1.21 s(418) =< s(387) 1.14/1.21 s(417) =< s(418)+1 1.14/1.21 s(419) =< s(418)+1 1.14/1.21 s(420) =< s(418)+2 1.14/1.21 s(421) =< s(389)*s(417) 1.14/1.21 s(422) =< s(389)*s(419) 1.14/1.21 s(418) =< s(419) 1.14/1.21 s(421) =< s(422) 1.14/1.21 s(423) =< s(421)*s(418) 1.14/1.21 s(424) =< s(423)*s(420) 1.14/1.21 s(425) =< s(387) 1.14/1.21 s(426) =< s(387) 1.14/1.21 s(425) =< s(426)+1 1.14/1.21 s(427) =< s(426)+1 1.14/1.21 s(428) =< s(426)+2 1.14/1.21 s(429) =< s(389)*s(425) 1.14/1.21 s(430) =< s(389)*s(427) 1.14/1.21 s(426) =< s(427) 1.14/1.21 s(429) =< s(430) 1.14/1.21 s(431) =< s(429)*s(426) 1.14/1.21 s(432) =< s(431)*s(428) 1.14/1.21 s(433) =< s(387) 1.14/1.21 s(434) =< s(387) 1.14/1.21 s(433) =< s(434)+1 1.14/1.21 s(435) =< s(434)+1 1.14/1.21 s(436) =< s(434)+2 1.14/1.21 s(437) =< s(389)*s(433) 1.14/1.21 s(438) =< s(389)*s(435) 1.14/1.21 s(434) =< s(435) 1.14/1.21 s(437) =< s(438) 1.14/1.21 s(439) =< s(437)*s(434) 1.14/1.21 s(440) =< s(439)*s(436) 1.14/1.21 s(441) =< s(388) 1.14/1.21 s(442) =< s(388) 1.14/1.21 s(443) =< s(388) 1.14/1.21 s(442) =< s(443)+1 1.14/1.21 s(444) =< s(443)+1 1.14/1.21 s(445) =< s(443)+2 1.14/1.21 s(446) =< s(389)*s(442) 1.14/1.21 s(447) =< s(389)*s(444) 1.14/1.21 s(443) =< s(444) 1.14/1.21 s(446) =< s(447) 1.14/1.21 s(448) =< s(446)*s(443) 1.14/1.21 s(449) =< s(448)*s(445) 1.14/1.21 1.14/1.21 with precondition: [B>=2] 1.14/1.21 1.14/1.21 * Chain [57]: 7*s(452)+1*s(453)+2*s(454)+3*s(457)+3*s(458)+2*s(459)+2*s(460)+1*s(465)+1*s(467)+1*s(468)+1*s(473)+1*s(475)+1*s(476)+0 1.14/1.21 Such that:s(451) =< B 1.14/1.21 s(450) =< B+1 1.14/1.21 s(452) =< s(451) 1.14/1.21 s(453) =< s(452)*s(450) 1.14/1.21 s(454) =< s(451) 1.14/1.21 s(455) =< s(451) 1.14/1.21 s(454) =< s(450) 1.14/1.21 s(455) =< s(450) 1.14/1.21 s(456) =< s(455) 1.14/1.21 s(456) =< s(451) 1.14/1.21 s(457) =< s(452)*s(456) 1.14/1.21 s(458) =< s(457)*s(450) 1.14/1.21 s(459) =< s(455) 1.14/1.21 s(460) =< s(459)*s(450) 1.14/1.21 s(461) =< s(451) 1.14/1.21 s(462) =< s(451) 1.14/1.21 s(461) =< s(462)+1 1.14/1.21 s(463) =< s(462)+1 1.14/1.21 s(464) =< s(462)+2 1.14/1.21 s(465) =< s(452)*s(461) 1.14/1.21 s(466) =< s(452)*s(463) 1.14/1.21 s(462) =< s(463) 1.14/1.21 s(465) =< s(466) 1.14/1.21 s(467) =< s(465)*s(462) 1.14/1.21 s(468) =< s(467)*s(464) 1.14/1.21 s(469) =< s(451) 1.14/1.21 s(470) =< s(451) 1.14/1.21 s(469) =< s(470)+1 1.14/1.21 s(471) =< s(470)+1 1.14/1.21 s(472) =< s(470)+2 1.14/1.21 s(473) =< s(452)*s(469) 1.14/1.21 s(474) =< s(452)*s(471) 1.14/1.21 s(470) =< s(471) 1.14/1.21 s(473) =< s(474) 1.14/1.21 s(475) =< s(473)*s(470) 1.14/1.21 s(476) =< s(475)*s(472) 1.14/1.21 1.14/1.21 with precondition: [B>=3] 1.14/1.21 1.14/1.21 * Chain [56]: 7*s(479)+2*s(480)+1*s(481)+1*s(482)+1*s(487)+1*s(489)+1*s(490)+1*s(495)+1*s(497)+1*s(498)+0 1.14/1.21 Such that:s(478) =< B 1.14/1.21 s(477) =< B+1 1.14/1.21 s(479) =< s(478) 1.14/1.21 s(480) =< s(479)*s(477) 1.14/1.21 s(481) =< s(479)*s(478) 1.14/1.21 s(482) =< s(481)*s(477) 1.14/1.21 s(483) =< s(478) 1.14/1.21 s(484) =< s(478) 1.14/1.21 s(483) =< s(484)+1 1.14/1.21 s(485) =< s(484)+1 1.14/1.21 s(486) =< s(484)+2 1.14/1.21 s(487) =< s(479)*s(483) 1.14/1.21 s(488) =< s(479)*s(485) 1.14/1.21 s(484) =< s(485) 1.14/1.21 s(487) =< s(488) 1.14/1.21 s(489) =< s(487)*s(484) 1.14/1.21 s(490) =< s(489)*s(486) 1.14/1.21 s(491) =< s(478) 1.14/1.21 s(492) =< s(478) 1.14/1.21 s(491) =< s(492)+1 1.14/1.21 s(493) =< s(492)+1 1.14/1.21 s(494) =< s(492)+2 1.14/1.21 s(495) =< s(479)*s(491) 1.14/1.21 s(496) =< s(479)*s(493) 1.14/1.21 s(492) =< s(493) 1.14/1.21 s(495) =< s(496) 1.14/1.21 s(497) =< s(495)*s(492) 1.14/1.21 s(498) =< s(497)*s(494) 1.14/1.21 1.14/1.21 with precondition: [B>=4] 1.14/1.21 1.14/1.21 1.14/1.21 Closed-form bounds of evalfstart(A,B,C,D,E,F): 1.14/1.21 ------------------------------------- 1.14/1.21 * Chain [62] with precondition: [] 1.14/1.21 - Upper bound: 0 1.14/1.21 - Complexity: constant 1.14/1.21 * Chain [61] with precondition: [B=1] 1.14/1.21 - Upper bound: 5 1.14/1.21 - Complexity: constant 1.14/1.21 * Chain [60] with precondition: [0>=B] 1.14/1.21 - Upper bound: 0 1.14/1.21 - Complexity: constant 1.14/1.21 * Chain [59] with precondition: [B>=1] 1.14/1.21 - Upper bound: 0 1.14/1.21 - Complexity: constant 1.14/1.21 * Chain [58] with precondition: [B>=2] 1.14/1.21 - Upper bound: 12*B+4+6*B*B+18*B*B*B+6*B*B*B*B+(B+1)*(3*B)+(B+1)*((B+1)*(3*B))+(B+1)*((B+1)*((B+1)*B))+(B+1) 1.14/1.21 - Complexity: n^4 1.14/1.21 * Chain [57] with precondition: [B>=3] 1.14/1.21 - Upper bound: 5*B*B+11*B+6*B*B*B+2*B*B*B*B+(B+1)*(3*B*B)+(B+1)*(3*B) 1.14/1.21 - Complexity: n^4 1.14/1.21 * Chain [56] with precondition: [B>=4] 1.14/1.21 - Upper bound: 3*B*B+7*B+6*B*B*B+2*B*B*B*B+(B+1)*(B*B)+(B+1)*(2*B) 1.14/1.21 - Complexity: n^4 1.14/1.21 1.14/1.21 ### Maximum cost of evalfstart(A,B,C,D,E,F): max([5,nat(B)*3*nat(B)+nat(B)*7+nat(B)*6*nat(B)*nat(B)+nat(B)*2*nat(B)*nat(B)*nat(B)+nat(B)*2*nat(B+1)+max([nat(B)*nat(B)*nat(B+1),nat(B)*2*nat(B)+nat(B)*4+nat(B+1)*nat(B)+max([nat(B)*3*nat(B)*nat(B+1),nat(B)+4+nat(B)*nat(B)+nat(B)*12*nat(B)*nat(B)+nat(B)*4*nat(B)*nat(B)*nat(B)+nat(B)*3*nat(B+1)*nat(B+1)+nat(B+1)*nat(B)*nat(B+1)*nat(B+1)+nat(B+1)])])]) 1.14/1.21 Asymptotic class: n^4 1.14/1.21 * Total analysis performed in 1070 ms. 1.14/1.21 1.22/1.31 EOF