3.12/3.15 WORST_CASE(?,O(n^1)) 3.12/3.15 3.12/3.15 Preprocessing Cost Relations 3.12/3.15 ===================================== 3.12/3.15 3.12/3.15 #### Computed strongly connected components 3.12/3.15 0. recursive : [lbl101/13] 3.12/3.15 1. recursive : [lbl101_loop_cont/14,lbl91/13] 3.12/3.15 2. non_recursive : [exit_location/1] 3.12/3.15 3. non_recursive : [stop/7] 3.12/3.15 4. non_recursive : [lbl91_loop_cont/8] 3.12/3.15 5. non_recursive : [start/7] 3.12/3.15 6. non_recursive : [start0/7] 3.12/3.15 3.12/3.15 #### Obtained direct recursion through partial evaluation 3.12/3.15 0. SCC is partially evaluated into lbl101/13 3.12/3.15 1. SCC is partially evaluated into lbl91/13 3.12/3.15 2. SCC is completely evaluated into other SCCs 3.12/3.15 3. SCC is completely evaluated into other SCCs 3.12/3.15 4. SCC is partially evaluated into lbl91_loop_cont/8 3.12/3.15 5. SCC is partially evaluated into start/7 3.12/3.15 6. SCC is partially evaluated into start0/7 3.12/3.15 3.12/3.15 Control-Flow Refinement of Cost Relations 3.12/3.15 ===================================== 3.12/3.15 3.12/3.15 ### Specialization of cost equations lbl101/13 3.12/3.15 * CE 11 is refined into CE [20] 3.12/3.15 * CE 9 is refined into CE [21] 3.12/3.15 * CE 8 is refined into CE [22] 3.12/3.15 * CE 10 is refined into CE [23] 3.12/3.15 3.12/3.15 3.12/3.15 ### Cost equations --> "Loop" of lbl101/13 3.12/3.15 * CEs [23] --> Loop 17 3.12/3.15 * CEs [20] --> Loop 18 3.12/3.15 * CEs [21] --> Loop 19 3.12/3.15 * CEs [22] --> Loop 20 3.12/3.15 3.12/3.15 ### Ranking functions of CR lbl101(A,B,C,D,E,F,G,H,I,J,K,L,M) 3.12/3.15 * RF of phase [17]: [-B+D+1,-B+E+1] 3.12/3.15 3.12/3.15 #### Partial ranking functions of CR lbl101(A,B,C,D,E,F,G,H,I,J,K,L,M) 3.12/3.15 * Partial RF of phase [17]: 3.12/3.15 - RF of loop [17:1]: 3.12/3.15 -B+D+1 3.12/3.15 -B+E+1 3.12/3.15 3.12/3.15 3.12/3.15 ### Specialization of cost equations lbl91/13 3.12/3.15 * CE 14 is refined into CE [24,25] 3.12/3.15 * CE 19 is refined into CE [26] 3.12/3.15 * CE 16 is refined into CE [27,28] 3.12/3.15 * CE 17 is refined into CE [29] 3.12/3.15 * CE 15 is refined into CE [30,31] 3.12/3.15 * CE 18 is refined into CE [32] 3.12/3.15 3.12/3.15 3.12/3.15 ### Cost equations --> "Loop" of lbl91/13 3.12/3.15 * CEs [31] --> Loop 21 3.12/3.15 * CEs [30] --> Loop 22 3.12/3.15 * CEs [32] --> Loop 23 3.12/3.15 * CEs [25] --> Loop 24 3.12/3.15 * CEs [24] --> Loop 25 3.12/3.15 * CEs [26] --> Loop 26 3.12/3.15 * CEs [28] --> Loop 27 3.12/3.15 * CEs [27] --> Loop 28 3.12/3.15 * CEs [29] --> Loop 29 3.12/3.15 3.12/3.15 ### Ranking functions of CR lbl91(A,B,C,D,E,F,G,H,I,J,K,L,M) 3.12/3.15 * RF of phase [21,22,23]: [-B+D+1,-C+D+1] 3.12/3.15 3.12/3.15 #### Partial ranking functions of CR lbl91(A,B,C,D,E,F,G,H,I,J,K,L,M) 3.12/3.15 * Partial RF of phase [21,22,23]: 3.12/3.15 - RF of loop [21:1]: 3.12/3.15 -2*A-C+D-1 3.12/3.15 -3/2*A-B/2+E/2-1 3.12/3.15 -2/3*A-B/3+D/3-1/3 3.12/3.15 -B/2+E/2-1 3.12/3.15 -B/2+E/2-3/2*F-1 3.12/3.15 -B/3+D/3-1/3 3.12/3.15 -B/3+D/3-2/3*F-1/3 3.12/3.15 -C+D-1 3.12/3.15 -C+D-2*F-1 3.12/3.15 - RF of loop [22:1]: 3.12/3.15 -2*A-B+E-1 3.12/3.15 -A-C+D 3.12/3.15 -A/2-B/2+D/2 3.12/3.15 -B+E-1 3.12/3.15 -B+E-2*F-1 3.12/3.15 -B/2+D/2 3.12/3.15 -B/2+D/2-F/2 3.12/3.15 -C+D 3.12/3.15 -C+D-F 3.12/3.15 - RF of loop [23:1]: 3.12/3.15 -B+D+1 3.12/3.15 -C+D+1 3.12/3.15 3.12/3.15 3.12/3.15 ### Specialization of cost equations lbl91_loop_cont/8 3.12/3.15 * CE 13 is refined into CE [33] 3.12/3.15 * CE 12 is refined into CE [34] 3.12/3.15 3.12/3.15 3.12/3.15 ### Cost equations --> "Loop" of lbl91_loop_cont/8 3.12/3.15 * CEs [33] --> Loop 30 3.12/3.15 * CEs [34] --> Loop 31 3.12/3.15 3.12/3.15 ### Ranking functions of CR lbl91_loop_cont(A,B,C,D,E,F,G,H) 3.12/3.15 3.12/3.15 #### Partial ranking functions of CR lbl91_loop_cont(A,B,C,D,E,F,G,H) 3.12/3.15 3.12/3.15 3.12/3.15 ### Specialization of cost equations start/7 3.12/3.15 * CE 6 is refined into CE [35] 3.12/3.15 * CE 2 is refined into CE [36,37] 3.12/3.15 * CE 3 is refined into CE [38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57] 3.12/3.15 * CE 4 is refined into CE [58,59] 3.12/3.15 * CE 7 is refined into CE [60,61,62,63,64,65,66,67,68,69] 3.12/3.15 * CE 5 is refined into CE [70] 3.12/3.15 3.12/3.15 3.12/3.15 ### Cost equations --> "Loop" of start/7 3.12/3.15 * CEs [38,61] --> Loop 32 3.12/3.15 * CEs [39] --> Loop 33 3.12/3.15 * CEs [58,60] --> Loop 34 3.12/3.15 * CEs [37,44,59,63] --> Loop 35 3.12/3.15 * CEs [41,48,54,65] --> Loop 36 3.12/3.15 * CEs [40,43,47,51,55,64] --> Loop 37 3.12/3.15 * CEs [42,46,50,53,57] --> Loop 38 3.12/3.15 * CEs [52,56] --> Loop 39 3.12/3.15 * CEs [35] --> Loop 40 3.12/3.15 * CEs [36,66] --> Loop 41 3.12/3.15 * CEs [70] --> Loop 42 3.12/3.15 * CEs [67] --> Loop 43 3.12/3.15 * CEs [45,62,69] --> Loop 44 3.12/3.15 * CEs [49,68] --> Loop 45 3.12/3.15 3.12/3.15 ### Ranking functions of CR start(A,B,C,D,E,F,G) 3.12/3.15 3.12/3.15 #### Partial ranking functions of CR start(A,B,C,D,E,F,G) 3.12/3.15 3.12/3.15 3.12/3.15 ### Specialization of cost equations start0/7 3.12/3.15 * CE 1 is refined into CE [71,72,73,74,75,76,77,78,79,80,81,82,83,84] 3.12/3.15 3.12/3.15 3.12/3.15 ### Cost equations --> "Loop" of start0/7 3.12/3.15 * CEs [81] --> Loop 46 3.12/3.15 * CEs [80] --> Loop 47 3.12/3.15 * CEs [79] --> Loop 48 3.12/3.15 * CEs [78,84] --> Loop 49 3.12/3.15 * CEs [77,83] --> Loop 50 3.12/3.15 * CEs [76,82] --> Loop 51 3.12/3.15 * CEs [75] --> Loop 52 3.12/3.15 * CEs [74] --> Loop 53 3.12/3.15 * CEs [73] --> Loop 54 3.12/3.15 * CEs [72] --> Loop 55 3.12/3.15 * CEs [71] --> Loop 56 3.12/3.15 3.12/3.15 ### Ranking functions of CR start0(A,B,C,D,E,F,G) 3.12/3.15 3.12/3.15 #### Partial ranking functions of CR start0(A,B,C,D,E,F,G) 3.12/3.15 3.12/3.15 3.12/3.15 Computing Bounds 3.12/3.15 ===================================== 3.12/3.15 3.12/3.15 #### Cost of chains of lbl101(A,B,C,D,E,F,G,H,I,J,K,L,M): 3.12/3.15 * Chain [[17],20]: 1*it(17)+0 3.12/3.15 Such that:it(17) =< -B+K+1 3.12/3.15 3.12/3.15 with precondition: [G=2,A=F,A=H,C=J,D=K,E=L,A=M,E>=D,I>=D+1,I>=A+B+1,B>=A+C+1,A+D+1>=I] 3.12/3.15 3.12/3.15 * Chain [[17],19]: 1*it(17)+0 3.12/3.15 Such that:it(17) =< -B+I 3.12/3.15 3.12/3.15 with precondition: [G=3,A=F,A=H,C=J,E=L,A=M,A+K+1=D,A>=0,E>=D,D>=I,I>=A+B+1,B>=A+C+1] 3.12/3.15 3.12/3.15 * Chain [[17],18]: 1*it(17)+0 3.12/3.15 Such that:it(17) =< -B+D+1 3.12/3.15 3.12/3.15 with precondition: [G=4,A=F,A>=0,D>=B,E>=D,B>=A+C+1] 3.12/3.15 3.12/3.15 * Chain [20]: 0 3.12/3.15 with precondition: [G=2,F=A,F=H,B=I,C=J,D=K,E=L,F=M,B>=D+1,E>=D,D+F+1>=B,B>=C+F+1] 3.12/3.15 3.12/3.15 * Chain [19]: 0 3.12/3.15 with precondition: [G=3,F=A,F=H,B=I,C=J,E=L,F=M,F+K+1=D,F>=0,D>=B,E>=D,B>=C+F+1] 3.12/3.15 3.12/3.15 * Chain [18]: 0 3.12/3.15 with precondition: [G=4,F=A,F>=0,E>=D,D+F+1>=B,B>=C+F+1] 3.12/3.15 3.12/3.15 3.12/3.15 #### Cost of chains of lbl91(A,B,C,D,E,F,G,H,I,J,K,L,M): 3.12/3.15 * Chain [[21,22,23],29]: 1*it(21)+1*it(22)+1*it(23)+1*s(3)+0 3.12/3.15 Such that:it(22) =< -2*A-B+E 3.12/3.15 it(21) =< -2*A-C+D 3.12/3.15 it(22) =< -A-C+D 3.12/3.15 it(21) =< -3/2*A-B/2+E/2 3.12/3.15 it(21) =< -2/3*A-B/3+D/3 3.12/3.15 it(22) =< -A/2-B/2+D/2 3.12/3.15 aux(3) =< -B+D 3.12/3.15 aux(4) =< -B+D+1 3.12/3.15 aux(5) =< -B+D-F 3.12/3.15 it(22) =< -B+E-2*F 3.12/3.15 it(22) =< -B+I 3.12/3.15 it(22) =< -B/2+D/2 3.12/3.15 it(22) =< -B/2+D/2-F/2 3.12/3.15 it(21) =< -B/2+E/2-3/2*F 3.12/3.15 it(21) =< -B/2+I/2 3.12/3.15 it(21) =< -B/3+D/3 3.12/3.15 it(21) =< -B/3+D/3-2/3*F 3.12/3.15 it(21) =< -C+D-2*F 3.12/3.15 it(22) =< -C+D-F 3.12/3.15 aux(8) =< D-J 3.12/3.15 aux(9) =< D-J+1 3.12/3.15 aux(13) =< -B+D+I-K 3.12/3.15 aux(14) =< D-K 3.12/3.15 it(21) =< aux(14) 3.12/3.15 it(22) =< aux(14) 3.12/3.15 it(23) =< aux(14) 3.12/3.15 it(22) =< aux(3) 3.12/3.15 s(3) =< aux(3) 3.12/3.15 it(21) =< aux(4) 3.12/3.15 it(22) =< aux(4) 3.12/3.15 it(23) =< aux(4) 3.12/3.15 it(22) =< aux(5) 3.12/3.15 s(3) =< aux(5) 3.12/3.15 it(22) =< aux(13) 3.12/3.15 it(23) =< aux(13) 3.12/3.15 s(3) =< aux(13) 3.12/3.15 it(21) =< aux(13) 3.12/3.15 it(21) =< aux(8) 3.12/3.15 it(22) =< aux(8) 3.12/3.15 it(21) =< aux(9) 3.12/3.15 it(22) =< aux(9) 3.12/3.15 it(23) =< aux(9) 3.12/3.15 3.12/3.15 with precondition: [G=2,A=F,A=H,C=J,E=L,A=M,I>=B,B>=C,I>=K+1,E>=A+D+1,D>=A+K+1,A+K+1>=I] 3.12/3.15 3.12/3.15 * Chain [[21,22,23],28]: 1*it(21)+1*it(22)+1*it(23)+1*s(3)+0 3.12/3.15 Such that:it(21) =< -2*A-C+D 3.12/3.15 aux(5) =< -A-B+D 3.12/3.15 it(22) =< -A-B+I 3.12/3.15 it(21) =< -3/2*A-B/2+E/2 3.12/3.15 it(21) =< -2/3*A-B/3+D/3 3.12/3.15 it(22) =< -A/2-B/2+D/2 3.12/3.15 it(21) =< -A/2-B/2+I/2 3.12/3.15 it(21) =< -A/3-B/3+D/3+I/3-K/3 3.12/3.15 aux(3) =< -B+D 3.12/3.15 aux(4) =< -B+D+1 3.12/3.15 it(21) =< -B/2+E/2-3/2*F 3.12/3.15 it(21) =< -B/3+D/3-2/3*F 3.12/3.15 it(21) =< -C+D-2*F 3.12/3.15 aux(8) =< D-J 3.12/3.15 aux(9) =< D-J+1 3.12/3.15 aux(15) =< -A-B+D+I-K 3.12/3.15 aux(16) =< D-K 3.12/3.15 it(21) =< aux(16) 3.12/3.15 it(22) =< aux(16) 3.12/3.15 it(23) =< aux(16) 3.12/3.15 it(22) =< aux(3) 3.12/3.15 s(3) =< aux(3) 3.12/3.15 it(21) =< aux(4) 3.12/3.15 it(22) =< aux(4) 3.12/3.15 it(23) =< aux(4) 3.12/3.15 it(22) =< aux(5) 3.12/3.15 s(3) =< aux(5) 3.12/3.15 it(22) =< aux(15) 3.12/3.15 it(23) =< aux(15) 3.12/3.15 s(3) =< aux(15) 3.12/3.15 it(21) =< aux(15) 3.12/3.15 it(21) =< aux(8) 3.12/3.15 it(22) =< aux(8) 3.12/3.15 it(21) =< aux(9) 3.12/3.15 it(22) =< aux(9) 3.12/3.15 it(23) =< aux(9) 3.12/3.15 3.12/3.15 with precondition: [G=2,A=F,A=H,C=J,E=L,A=M,B>=C,I>=K+1,I>=A+B+1,E>=A+D+1,D>=A+K+1,A+K+1>=I] 3.12/3.15 3.12/3.15 * Chain [[21,22,23],27]: 1*it(21)+1*it(22)+1*it(23)+1*s(3)+1*s(4)+0 3.12/3.15 Such that:aux(3) =< -B+D 3.12/3.15 aux(4) =< -B+D+1 3.12/3.15 aux(8) =< D-J 3.12/3.15 aux(9) =< D-J+1 3.12/3.15 aux(17) =< -2*A-B+D+I-K 3.12/3.15 aux(18) =< -A-B+D 3.12/3.15 aux(19) =< -A-B+K 3.12/3.15 aux(20) =< D-K 3.12/3.15 aux(6) =< aux(17) 3.12/3.15 aux(6) =< aux(18) 3.12/3.15 it(21) =< aux(18) 3.12/3.15 it(22) =< aux(18) 3.12/3.15 s(4) =< aux(18) 3.12/3.15 it(21) =< aux(19) 3.12/3.15 it(22) =< aux(19) 3.12/3.15 it(21) =< aux(20) 3.12/3.15 it(22) =< aux(20) 3.12/3.15 it(23) =< aux(20) 3.12/3.15 it(22) =< aux(3) 3.12/3.15 s(3) =< aux(3) 3.12/3.15 it(21) =< aux(4) 3.12/3.15 it(22) =< aux(4) 3.12/3.15 it(23) =< aux(4) 3.12/3.15 s(3) =< aux(18) 3.12/3.15 it(22) =< aux(6) 3.12/3.15 it(23) =< aux(6) 3.12/3.15 s(3) =< aux(6) 3.12/3.15 it(21) =< aux(6) 3.12/3.15 it(21) =< aux(8) 3.12/3.15 it(22) =< aux(8) 3.12/3.15 it(21) =< aux(9) 3.12/3.15 it(22) =< aux(9) 3.12/3.15 it(23) =< aux(9) 3.12/3.15 3.12/3.15 with precondition: [G=2,A=F,A=H,C=J,E=L,A=M,B>=C,I>=K+1,I>=2*A+B+2,E>=A+D+1,D>=A+K+1,A+K+1>=I] 3.12/3.15 3.12/3.15 * Chain [[21,22,23],26]: 1*it(21)+1*it(22)+1*it(23)+1*s(3)+0 3.12/3.15 Such that:it(22) =< -2*A-B+E 3.12/3.15 it(21) =< -2*A-C+D 3.12/3.15 it(22) =< -A-C+D 3.12/3.15 it(21) =< -3/2*A-B/2+E/2 3.12/3.15 it(21) =< -2/3*A-B/3+D/3 3.12/3.15 it(22) =< -A/2-B/2+D/2 3.12/3.15 aux(3) =< -B+D 3.12/3.15 aux(4) =< -B+D+1 3.12/3.15 aux(5) =< -B+D-F 3.12/3.15 it(22) =< -B+E-2*F 3.12/3.15 it(22) =< -B/2+D/2-F/2 3.12/3.15 it(21) =< -B/2+E/2-3/2*F 3.12/3.15 it(21) =< -B/3+D/3-2/3*F 3.12/3.15 aux(8) =< -C+D 3.12/3.15 aux(9) =< -C+D+1 3.12/3.15 it(21) =< -C+D-2*F 3.12/3.15 it(22) =< -C+D-F 3.12/3.15 aux(21) =< A-B+D+1 3.12/3.15 it(21) =< aux(21) 3.12/3.15 it(22) =< aux(21) 3.12/3.15 it(23) =< aux(21) 3.12/3.15 it(22) =< aux(3) 3.12/3.15 s(3) =< aux(3) 3.12/3.15 it(21) =< aux(4) 3.12/3.15 it(22) =< aux(4) 3.12/3.15 it(23) =< aux(4) 3.12/3.15 it(22) =< aux(5) 3.12/3.15 s(3) =< aux(5) 3.12/3.15 s(3) =< aux(21) 3.12/3.15 it(21) =< aux(8) 3.12/3.15 it(22) =< aux(8) 3.12/3.15 it(21) =< aux(9) 3.12/3.15 it(22) =< aux(9) 3.12/3.15 it(23) =< aux(9) 3.12/3.15 3.12/3.15 with precondition: [G=4,A=F,A>=0,D>=B,B>=C,E>=A+D+1] 3.12/3.15 3.12/3.15 * Chain [[21,22,23],25]: 1*it(21)+1*it(22)+1*it(23)+1*s(3)+0 3.12/3.15 Such that:it(21) =< -2*A-C+D 3.12/3.15 it(21) =< -3/2*A-B/2+E/2 3.12/3.15 it(21) =< -2/3*A-B/3+D/3 3.12/3.15 aux(4) =< -B+D+1 3.12/3.15 aux(5) =< -B+D-F 3.12/3.15 it(21) =< -B/2+E/2-3/2*F 3.12/3.15 it(21) =< -B/3+D/3-2/3*F 3.12/3.15 aux(8) =< -C+D 3.12/3.15 aux(9) =< -C+D+1 3.12/3.15 it(21) =< -C+D-2*F 3.12/3.15 aux(22) =< -B+D 3.12/3.15 it(21) =< aux(22) 3.12/3.15 it(22) =< aux(22) 3.12/3.15 it(23) =< aux(22) 3.12/3.15 s(3) =< aux(22) 3.12/3.16 it(21) =< aux(4) 3.12/3.16 it(22) =< aux(4) 3.12/3.16 it(23) =< aux(4) 3.12/3.16 it(22) =< aux(5) 3.12/3.16 s(3) =< aux(5) 3.12/3.16 it(21) =< aux(8) 3.12/3.16 it(22) =< aux(8) 3.12/3.16 it(21) =< aux(9) 3.12/3.16 it(22) =< aux(9) 3.12/3.16 it(23) =< aux(9) 3.12/3.16 3.12/3.16 with precondition: [G=4,A=F,A>=0,B>=C,D>=A+B+1,E>=A+D+1] 3.12/3.16 3.12/3.16 * Chain [[21,22,23],24]: 1*it(21)+1*it(22)+1*it(23)+1*s(3)+1*s(5)+0 3.12/3.16 Such that:aux(3) =< -B+D 3.12/3.16 aux(4) =< -B+D+1 3.12/3.16 aux(8) =< -C+D 3.12/3.16 aux(9) =< -C+D+1 3.12/3.16 aux(23) =< -B+D-F 3.12/3.16 it(21) =< aux(23) 3.12/3.16 it(22) =< aux(23) 3.12/3.16 s(5) =< aux(23) 3.12/3.16 it(23) =< aux(23) 3.12/3.16 it(22) =< aux(3) 3.12/3.16 s(3) =< aux(3) 3.12/3.16 it(21) =< aux(4) 3.12/3.16 it(22) =< aux(4) 3.12/3.16 it(23) =< aux(4) 3.12/3.16 s(3) =< aux(23) 3.12/3.16 it(21) =< aux(8) 3.12/3.16 it(22) =< aux(8) 3.12/3.16 it(21) =< aux(9) 3.12/3.16 it(22) =< aux(9) 3.12/3.16 it(23) =< aux(9) 3.12/3.16 3.12/3.16 with precondition: [G=4,A=F,A>=0,B>=C,D>=2*A+B+2,E>=A+D+1] 3.12/3.16 3.12/3.16 * Chain [29]: 0 3.12/3.16 with precondition: [G=2,A=F,A=H,B=I,C=J,D=K,E=L,A=M,B>=C,B>=D+1,E>=A+D+1,A+D+1>=B] 3.12/3.16 3.12/3.16 * Chain [28]: 0 3.12/3.16 with precondition: [G=2,A=F,A=H,C=J,D=K,E=L,A=M,A+B+1=I,I>=D+1,I>=A+C+1,E>=A+D+1,A+D+1>=I] 3.12/3.16 3.12/3.16 * Chain [27]: 1*s(4)+0 3.12/3.16 Such that:s(4) =< -B+D-F 3.12/3.16 3.12/3.16 with precondition: [G=2,A=F,A=H,C=J,D=K,E=L,A=M,B>=C,I>=D+1,I>=2*A+B+2,E>=A+D+1,A+D+1>=I] 3.12/3.16 3.12/3.16 * Chain [26]: 0 3.12/3.16 with precondition: [G=4] 3.12/3.16 3.12/3.16 * Chain [25]: 0 3.12/3.16 with precondition: [G=4,A=F,A>=0,D>=B,B>=C,E>=A+D+1] 3.12/3.16 3.12/3.16 * Chain [24]: 1*s(5)+0 3.12/3.16 Such that:s(5) =< -B+D-F 3.12/3.16 3.12/3.16 with precondition: [G=4,A=F,A>=0,B>=C,D>=A+B+1,E>=A+D+1] 3.12/3.16 3.12/3.16 3.12/3.16 #### Cost of chains of lbl91_loop_cont(A,B,C,D,E,F,G,H): 3.12/3.16 * Chain [31]: 0 3.12/3.16 with precondition: [A=2] 3.12/3.16 3.12/3.16 * Chain [30]: 0 3.12/3.16 with precondition: [A=4] 3.12/3.16 3.12/3.16 3.12/3.16 #### Cost of chains of start(A,B,C,D,E,F,G): 3.12/3.16 * Chain [45]: 1*s(26)+4*s(32)+1*s(34)+1 3.12/3.16 Such that:s(26) =< -2*A-B+D 3.12/3.16 s(31) =< -2*A-B+E 3.12/3.16 aux(25) =< -A-B+E 3.12/3.16 s(32) =< s(31) 3.12/3.16 s(34) =< s(31) 3.12/3.16 s(32) =< aux(25) 3.12/3.16 3.12/3.16 with precondition: [F=A,C=B,D=E,F>=0,D>=3*F+C+3] 3.12/3.16 3.12/3.16 * Chain [44]: 1*s(37)+1*s(38)+1*s(45)+1*s(46)+2*s(47)+1*s(48)+2*s(55)+1*s(56)+1 3.12/3.16 Such that:s(37) =< -3*A-C+D 3.12/3.16 aux(27) =< -2*A-B+D 3.12/3.16 s(38) =< -2*A-B/2+D/2 3.12/3.16 s(38) =< -2*A-C/2+D/2 3.12/3.16 aux(28) =< -A-B+D 3.12/3.16 aux(30) =< -A-B+E 3.12/3.16 s(48) =< -A-B/3+D/3 3.12/3.16 s(38) =< -4/3*A-B/3+D/3 3.12/3.16 s(38) =< -B/2+D/2-2*F 3.12/3.16 s(37) =< -B/2+D/2-3/2*F 3.12/3.16 s(48) =< -B/2+E/2-3/2*F 3.12/3.16 s(48) =< -B/3+D/3-F 3.12/3.16 s(38) =< -B/3+D/3-4/3*F 3.12/3.16 aux(31) =< -3*A-B+D 3.12/3.16 aux(32) =< -2*A-B+E 3.12/3.16 aux(33) =< -3/2*A-B/2+D/2 3.12/3.16 aux(34) =< -B+D-3*F 3.12/3.16 s(48) =< aux(31) 3.12/3.16 s(47) =< aux(32) 3.12/3.16 s(37) =< aux(33) 3.12/3.16 s(48) =< aux(33) 3.12/3.16 s(48) =< aux(34) 3.12/3.16 s(48) =< aux(30) 3.12/3.16 s(55) =< aux(30) 3.12/3.16 s(56) =< aux(30) 3.12/3.16 s(55) =< aux(32) 3.12/3.16 s(37) =< aux(31) 3.12/3.16 s(38) =< aux(31) 3.12/3.16 s(42) =< aux(31) 3.12/3.16 s(37) =< aux(27) 3.12/3.16 s(37) =< aux(34) 3.12/3.16 s(38) =< aux(34) 3.12/3.16 s(42) =< aux(34) 3.12/3.16 s(38) =< aux(28) 3.12/3.16 s(37) =< aux(28) 3.12/3.16 s(45) =< aux(28) 3.12/3.16 s(46) =< aux(27) 3.12/3.16 s(38) =< aux(27) 3.12/3.16 s(45) =< aux(27) 3.12/3.16 s(37) =< s(42) 3.12/3.16 s(46) =< s(42) 3.12/3.16 s(46) =< aux(28) 3.12/3.16 3.12/3.16 with precondition: [F=A,C=B,D=E,F>=0,D>=2*F+C+2] 3.12/3.16 3.12/3.16 * Chain [43]: 1*s(58)+1*s(59)+1*s(66)+1*s(67)+0 3.12/3.16 Such that:s(59) =< -3*A-B+D 3.12/3.16 s(58) =< -2*A-C+E 3.12/3.16 s(58) =< -A-B/2+D/2 3.12/3.16 s(59) =< -A-B/3+D/3 3.12/3.16 s(59) =< -3/2*A-C/2+E/2 3.12/3.16 s(60) =< -B+D 3.12/3.16 s(59) =< -B+D-3*F 3.12/3.16 s(58) =< -B/2+D/2-F 3.12/3.16 s(59) =< -B/2+D/2-3/2*F 3.12/3.16 s(59) =< -B/3+D/3-F 3.12/3.16 aux(35) =< -2*A-B+D 3.12/3.16 aux(36) =< -A-B+D 3.12/3.16 aux(37) =< -B+D-2*F 3.12/3.16 s(58) =< aux(35) 3.12/3.16 s(63) =< aux(35) 3.12/3.16 s(58) =< aux(37) 3.12/3.16 s(63) =< aux(37) 3.12/3.16 s(59) =< s(60) 3.12/3.16 s(58) =< s(60) 3.12/3.16 s(66) =< s(60) 3.12/3.16 s(58) =< aux(36) 3.12/3.16 s(67) =< aux(36) 3.12/3.16 s(59) =< aux(36) 3.12/3.16 s(66) =< aux(36) 3.12/3.16 s(58) =< s(63) 3.12/3.16 s(67) =< s(63) 3.12/3.16 s(67) =< s(60) 3.12/3.16 3.12/3.16 with precondition: [F=A,C=B,D=E,F>=0,D>=C+F+1] 3.12/3.16 3.12/3.16 * Chain [42]: 0 3.12/3.16 with precondition: [F=A,C=B,E=D,0>=F+1] 3.12/3.16 3.12/3.16 * Chain [41]: 0 3.12/3.16 with precondition: [F=A,C=B,E=D,F>=0,E>=C] 3.12/3.16 3.12/3.16 * Chain [40]: 0 3.12/3.16 with precondition: [F=A,C=B,E=D,F>=0,C>=E+1] 3.12/3.16 3.12/3.16 * Chain [39]: 1*s(68)+6*s(78)+2*s(80)+2*s(82)+1*s(83)+1 3.12/3.16 Such that:aux(45) =< -4*A-B+E 3.12/3.16 aux(46) =< -3*A-B+E 3.12/3.16 aux(47) =< -2*A-B+E 3.12/3.16 aux(48) =< -A-B+E 3.12/3.16 s(73) =< aux(45) 3.12/3.16 s(68) =< aux(45) 3.12/3.16 s(68) =< aux(46) 3.12/3.16 s(69) =< aux(46) 3.12/3.16 s(73) =< aux(46) 3.12/3.16 s(69) =< aux(47) 3.12/3.16 s(78) =< s(73) 3.12/3.16 s(80) =< s(73) 3.12/3.16 s(78) =< s(69) 3.12/3.16 s(82) =< s(69) 3.12/3.16 s(82) =< s(73) 3.12/3.16 s(78) =< aux(48) 3.12/3.16 s(83) =< aux(46) 3.12/3.16 s(83) =< aux(47) 3.12/3.16 3.12/3.16 with precondition: [F=A,C=B,E=D,F>=0,E>=5*F+C+5] 3.12/3.16 3.12/3.16 * Chain [38]: 2*s(103)+3*s(105)+4*s(106)+3*s(107)+1*s(119)+1*s(120)+1*s(121)+1*s(123)+1*s(130)+2*s(131)+1*s(133)+1*s(139)+1*s(140)+1*s(141)+1 3.12/3.16 Such that:s(133) =< -5/2*A-B/2+D/2 3.12/3.16 s(121) =< -5/2*A-B/2+E/2 3.12/3.16 s(133) =< -5/3*A-B/3+D/3 3.12/3.16 s(121) =< -5/3*A-B/3+E/3 3.12/3.16 aux(61) =< -4*A-B+E 3.12/3.16 aux(62) =< -3*A-B+E 3.12/3.16 aux(63) =< -2*A-B+E 3.12/3.16 aux(64) =< -A-B+E 3.12/3.16 aux(65) =< -B/2+E/2-5/2*F 3.12/3.16 aux(66) =< -B/3+E/3-5/3*F 3.12/3.16 s(100) =< aux(61) 3.12/3.16 s(119) =< aux(61) 3.12/3.16 s(121) =< aux(65) 3.12/3.16 s(133) =< aux(65) 3.12/3.16 s(121) =< aux(66) 3.12/3.16 s(133) =< aux(66) 3.12/3.16 s(100) =< aux(62) 3.12/3.16 s(103) =< aux(62) 3.12/3.16 s(105) =< aux(62) 3.12/3.16 s(103) =< s(100) 3.12/3.16 s(106) =< aux(62) 3.12/3.16 s(103) =< aux(63) 3.12/3.16 s(107) =< aux(63) 3.12/3.16 s(106) =< aux(63) 3.12/3.16 s(107) =< aux(62) 3.12/3.16 s(103) =< aux(64) 3.12/3.16 s(106) =< aux(64) 3.12/3.16 s(119) =< aux(62) 3.12/3.16 s(121) =< aux(62) 3.12/3.16 s(123) =< aux(62) 3.12/3.16 s(124) =< aux(62) 3.12/3.16 s(120) =< aux(63) 3.12/3.16 s(121) =< aux(63) 3.12/3.16 s(123) =< aux(63) 3.12/3.16 s(124) =< aux(63) 3.12/3.16 s(130) =< aux(63) 3.12/3.16 s(123) =< s(124) 3.12/3.16 s(131) =< s(124) 3.12/3.16 s(121) =< s(124) 3.12/3.16 s(130) =< s(124) 3.12/3.16 s(123) =< s(100) 3.12/3.16 s(131) =< s(100) 3.12/3.16 s(121) =< aux(64) 3.12/3.16 s(123) =< aux(64) 3.12/3.16 s(130) =< aux(64) 3.12/3.16 s(133) =< aux(62) 3.12/3.16 s(139) =< s(100) 3.12/3.16 s(133) =< s(124) 3.12/3.16 s(140) =< s(124) 3.12/3.16 s(141) =< s(124) 3.12/3.16 s(140) =< s(100) 3.12/3.16 s(133) =< aux(64) 3.12/3.16 s(140) =< aux(64) 3.12/3.16 s(141) =< aux(64) 3.12/3.16 3.12/3.16 with precondition: [F=A,C=B,E=D,F>=0,E>=4*F+C+4] 3.12/3.16 3.12/3.16 * Chain [37]: 2*s(143)+1*s(144)+1*s(146)+4*s(153)+2*s(154)+1*s(155)+1*s(162)+1*s(165)+1*s(166)+1*s(167)+2*s(175)+1*s(176)+1*s(177)+1*s(178)+1*s(179)+1*s(187)+2*s(197)+1*s(199)+1 3.12/3.16 Such that:s(179) =< -5/2*A-B/2+D/2 3.12/3.16 s(167) =< -5/2*A-B/2+E/2 3.12/3.16 s(179) =< -5/3*A-B/3+D/3 3.12/3.16 s(155) =< -4/3*A-B/3+D/3 3.12/3.16 s(144) =< -4/3*A-B/3+E/3 3.12/3.16 s(146) =< -3/2*A-B/2+E/2 3.12/3.16 s(144) =< -2/3*A-B/3+E/3 3.12/3.16 aux(80) =< -4*A-B+D 3.12/3.16 aux(81) =< -4*A-B+E 3.12/3.16 aux(82) =< -3*A-B+E 3.12/3.16 aux(83) =< -2*A-B+E 3.12/3.16 aux(84) =< -2*A-B/2+D/2 3.12/3.16 aux(85) =< -2*A-B/2+E/2 3.12/3.16 aux(86) =< -A-B+E 3.12/3.16 aux(87) =< -5/3*A-B/3+E/3 3.12/3.16 aux(88) =< -B+D-4*F 3.12/3.16 aux(89) =< -B+D-3*F 3.12/3.16 aux(90) =< -B+D-2*F 3.12/3.16 aux(91) =< -B+D-F 3.12/3.16 aux(92) =< -B+E-4*F 3.12/3.16 aux(93) =< -B/2+D/2-2*F 3.12/3.16 aux(94) =< -B/2+E/2-5/2*F 3.12/3.16 aux(95) =< -B/3+D/3-5/3*F 3.12/3.16 aux(96) =< -B/3+D/3-4/3*F 3.12/3.16 s(170) =< aux(80) 3.12/3.16 s(178) =< aux(80) 3.12/3.16 s(166) =< aux(81) 3.12/3.16 s(183) =< aux(81) 3.12/3.16 s(143) =< aux(82) 3.12/3.16 s(194) =< aux(82) 3.12/3.16 s(155) =< aux(84) 3.12/3.16 s(166) =< aux(84) 3.12/3.16 s(178) =< aux(84) 3.12/3.16 s(144) =< aux(85) 3.12/3.16 s(178) =< aux(85) 3.12/3.16 s(167) =< aux(87) 3.12/3.16 s(179) =< aux(87) 3.12/3.16 s(170) =< aux(88) 3.12/3.16 s(183) =< aux(88) 3.12/3.16 s(166) =< aux(92) 3.12/3.16 s(178) =< aux(92) 3.12/3.16 s(144) =< aux(93) 3.12/3.16 s(155) =< aux(93) 3.12/3.16 s(166) =< aux(93) 3.12/3.16 s(178) =< aux(93) 3.12/3.16 s(167) =< aux(94) 3.12/3.16 s(179) =< aux(94) 3.12/3.16 s(167) =< aux(95) 3.12/3.16 s(179) =< aux(95) 3.12/3.16 s(144) =< aux(96) 3.12/3.16 s(155) =< aux(96) 3.12/3.16 s(168) =< aux(89) 3.12/3.16 s(166) =< aux(90) 3.12/3.16 s(167) =< aux(90) 3.12/3.16 s(168) =< aux(90) 3.12/3.16 s(173) =< aux(90) 3.12/3.16 s(165) =< aux(91) 3.12/3.16 s(166) =< aux(91) 3.12/3.16 s(167) =< aux(91) 3.12/3.16 s(173) =< aux(91) 3.12/3.16 s(175) =< aux(91) 3.12/3.16 s(166) =< s(168) 3.12/3.16 s(176) =< s(168) 3.12/3.16 s(167) =< s(168) 3.12/3.16 s(175) =< s(168) 3.12/3.16 s(166) =< s(170) 3.12/3.16 s(176) =< s(170) 3.12/3.16 s(166) =< s(173) 3.12/3.16 s(175) =< s(173) 3.12/3.16 s(176) =< s(173) 3.12/3.16 s(167) =< s(173) 3.12/3.16 s(179) =< aux(89) 3.12/3.16 s(177) =< aux(90) 3.12/3.16 s(178) =< aux(90) 3.12/3.16 s(179) =< s(173) 3.12/3.16 s(178) =< s(173) 3.12/3.16 s(178) =< s(168) 3.12/3.16 s(187) =< s(168) 3.12/3.16 s(179) =< s(168) 3.12/3.16 s(178) =< s(183) 3.12/3.16 s(187) =< s(183) 3.12/3.16 s(187) =< s(173) 3.12/3.16 s(179) =< aux(91) 3.12/3.16 s(178) =< aux(91) 3.12/3.16 s(144) =< aux(83) 3.12/3.16 s(146) =< aux(83) 3.12/3.16 s(153) =< aux(83) 3.12/3.16 s(154) =< aux(83) 3.12/3.16 s(146) =< aux(82) 3.12/3.16 s(154) =< aux(82) 3.12/3.16 s(144) =< aux(86) 3.12/3.16 s(146) =< aux(86) 3.12/3.16 s(153) =< aux(86) 3.12/3.16 s(194) =< aux(83) 3.12/3.16 s(197) =< aux(83) 3.12/3.16 s(199) =< aux(83) 3.12/3.16 s(197) =< s(194) 3.12/3.16 s(197) =< aux(86) 3.12/3.16 s(155) =< aux(82) 3.12/3.16 s(155) =< aux(83) 3.12/3.16 s(162) =< aux(83) 3.12/3.16 s(162) =< aux(82) 3.12/3.16 s(155) =< aux(86) 3.12/3.16 s(162) =< aux(86) 3.12/3.16 3.12/3.16 with precondition: [F=A,C=B,E=D,F>=0,E>=3*F+C+3] 3.12/3.16 3.12/3.16 * Chain [36]: 1*s(202)+1*s(203)+1*s(211)+1*s(212)+3*s(213)+1*s(215)+1*s(217)+1*s(225)+1 3.12/3.16 Such that:s(206) =< -3*A-C+D 3.12/3.16 aux(98) =< -2*A-B+D 3.12/3.16 s(216) =< -2*A-B+E 3.12/3.16 s(203) =< -2*A-B/2+E/2 3.12/3.16 aux(99) =< -A-B+D 3.12/3.16 s(202) =< -A-B/2+D/2 3.12/3.16 s(217) =< -A-B/2+E/2 3.12/3.16 s(215) =< -A-B/3+E/3 3.12/3.16 s(203) =< -4/3*A-B/3+E/3 3.12/3.16 s(215) =< -3/2*A-B/2+E/2 3.12/3.16 s(202) =< -3/2*A-C/2+D/2 3.12/3.16 s(203) =< -2/3*A-B/3+D/3 3.12/3.16 s(215) =< -A/3-B/3+E/3 3.12/3.16 s(206) =< -B+E-3*F 3.12/3.16 s(203) =< -B/2+D/2-2*F 3.12/3.16 s(215) =< -B/3+D/3-F 3.12/3.16 s(203) =< -B/3+D/3-4/3*F 3.12/3.16 aux(102) =< -3*A-B+E 3.12/3.16 aux(103) =< -A-B+E 3.12/3.16 aux(104) =< -B+D-3*F 3.12/3.16 aux(105) =< -B/2+E/2-3/2*F 3.12/3.16 s(215) =< aux(102) 3.12/3.16 s(213) =< aux(103) 3.12/3.16 s(215) =< aux(104) 3.12/3.16 s(202) =< aux(105) 3.12/3.16 s(215) =< aux(105) 3.12/3.16 s(215) =< aux(103) 3.12/3.16 s(217) =< aux(103) 3.12/3.16 s(225) =< aux(103) 3.12/3.16 s(217) =< s(216) 3.12/3.16 s(225) =< s(216) 3.12/3.16 s(202) =< aux(102) 3.12/3.16 s(203) =< aux(102) 3.12/3.16 s(202) =< aux(99) 3.12/3.16 s(203) =< aux(99) 3.12/3.16 s(202) =< aux(104) 3.12/3.16 s(203) =< aux(104) 3.12/3.16 s(211) =< aux(99) 3.12/3.16 s(202) =< aux(98) 3.12/3.16 s(212) =< aux(98) 3.12/3.16 s(203) =< aux(98) 3.12/3.16 s(211) =< aux(98) 3.12/3.16 s(202) =< s(206) 3.12/3.16 s(212) =< s(206) 3.12/3.16 s(212) =< aux(99) 3.12/3.16 3.12/3.16 with precondition: [F=A,C=B,E=D,F>=0,E>=2*F+C+2] 3.12/3.16 3.12/3.16 * Chain [35]: 2*s(226)+1*s(228)+1*s(229)+1*s(237)+1*s(238)+1 3.12/3.16 Such that:s(229) =< -3*A-B+E 3.12/3.16 s(228) =< -2*A-B+E 3.12/3.16 aux(106) =< -2*A-C+D 3.12/3.16 aux(107) =< -A-B+D 3.12/3.16 s(229) =< -A-B/3+E/3 3.12/3.16 s(228) =< -A-C/2+D/2 3.12/3.16 s(229) =< -3/2*A-B/2+E/2 3.12/3.16 s(228) =< -A/2-B/2+D/2 3.12/3.16 s(229) =< -A/3-B/3+D/3 3.12/3.16 aux(108) =< -B+D 3.12/3.16 s(229) =< -B+D-3*F 3.12/3.16 aux(109) =< -B+E-2*F 3.12/3.16 s(228) =< -B/2+E/2-F 3.12/3.16 s(229) =< -B/2+E/2-3/2*F 3.12/3.16 s(229) =< -B/3+D/3-F 3.12/3.16 aux(110) =< -A-B+E 3.12/3.16 s(226) =< aux(110) 3.12/3.16 s(228) =< aux(106) 3.12/3.16 s(232) =< aux(106) 3.12/3.16 s(228) =< aux(108) 3.12/3.16 s(229) =< aux(108) 3.12/3.16 s(228) =< aux(109) 3.12/3.16 s(232) =< aux(109) 3.12/3.16 s(237) =< aux(108) 3.12/3.16 s(228) =< aux(107) 3.12/3.16 s(238) =< aux(107) 3.12/3.16 s(229) =< aux(107) 3.12/3.16 s(237) =< aux(107) 3.12/3.16 s(228) =< s(232) 3.12/3.16 s(238) =< s(232) 3.12/3.16 s(238) =< aux(108) 3.12/3.16 3.12/3.16 with precondition: [F=A,C=B,E=D,F>=0,E>=C+F+1] 3.12/3.16 3.12/3.16 * Chain [34]: 0 3.12/3.16 with precondition: [F=A,C=B,E=D,E>=C,C+F>=E] 3.12/3.16 3.12/3.16 * Chain [33]: 1 3.12/3.16 with precondition: [F=A,C=B,E=D,E>=2*F+C+2,C+3*F+2>=E] 3.12/3.16 3.12/3.16 * Chain [32]: 1 3.12/3.16 with precondition: [F=A,C=B,E=D,E>=C+F+1,C+2*F+1>=E] 3.12/3.16 3.12/3.16 3.12/3.16 #### Cost of chains of start0(A,B,C,D,E,F,G): 3.12/3.16 * Chain [56]: 0 3.12/3.16 with precondition: [0>=A+1] 3.12/3.16 3.12/3.16 * Chain [55]: 0 3.12/3.16 with precondition: [A>=0,E>=C] 3.12/3.16 3.12/3.16 * Chain [54]: 0 3.12/3.16 with precondition: [A>=0,C>=E+1] 3.12/3.16 3.12/3.16 * Chain [53]: 1*s(244)+6*s(246)+2*s(247)+2*s(248)+1*s(249)+1 3.12/3.16 Such that:s(239) =< -4*A-C+E 3.12/3.16 s(240) =< -3*A-C+E 3.12/3.16 s(241) =< -2*A-C+E 3.12/3.16 s(242) =< -A-C+E 3.12/3.16 s(243) =< s(239) 3.12/3.16 s(244) =< s(239) 3.12/3.16 s(244) =< s(240) 3.12/3.16 s(245) =< s(240) 3.12/3.16 s(243) =< s(240) 3.12/3.16 s(245) =< s(241) 3.12/3.16 s(246) =< s(243) 3.12/3.16 s(247) =< s(243) 3.12/3.16 s(246) =< s(245) 3.12/3.16 s(248) =< s(245) 3.12/3.16 s(248) =< s(243) 3.12/3.16 s(246) =< s(242) 3.12/3.16 s(249) =< s(240) 3.12/3.16 s(249) =< s(241) 3.12/3.16 3.12/3.16 with precondition: [A>=0,E>=5*A+C+5] 3.12/3.16 3.12/3.16 * Chain [52]: 1*s(250)+1*s(251)+1*s(259)+2*s(260)+3*s(261)+4*s(262)+3*s(263)+1*s(264)+1*s(266)+1*s(267)+2*s(268)+1*s(269)+1*s(270)+1*s(271)+1 3.12/3.16 Such that:s(252) =< -4*A-C+E 3.12/3.16 s(253) =< -3*A-C+E 3.12/3.16 s(254) =< -2*A-C+E 3.12/3.16 s(255) =< -A-C+E 3.12/3.16 aux(111) =< -5/2*A-C/2+E/2 3.12/3.16 aux(112) =< -5/3*A-C/3+E/3 3.12/3.16 aux(113) =< -C/2+E/2 3.12/3.16 aux(114) =< -C/3+E/3 3.12/3.16 s(250) =< aux(111) 3.12/3.16 s(251) =< aux(111) 3.12/3.16 s(256) =< aux(111) 3.12/3.16 s(250) =< aux(112) 3.12/3.16 s(251) =< aux(112) 3.12/3.16 s(257) =< aux(112) 3.12/3.16 s(250) =< aux(113) 3.12/3.16 s(251) =< aux(113) 3.12/3.16 s(256) =< aux(113) 3.12/3.16 s(250) =< aux(114) 3.12/3.16 s(251) =< aux(114) 3.12/3.16 s(257) =< aux(114) 3.12/3.16 s(258) =< s(252) 3.12/3.16 s(259) =< s(252) 3.12/3.16 s(251) =< s(256) 3.12/3.16 s(250) =< s(256) 3.12/3.16 s(251) =< s(257) 3.12/3.16 s(250) =< s(257) 3.12/3.16 s(258) =< s(253) 3.12/3.16 s(260) =< s(253) 3.12/3.16 s(261) =< s(253) 3.12/3.16 s(260) =< s(258) 3.12/3.16 s(262) =< s(253) 3.12/3.16 s(260) =< s(254) 3.12/3.16 s(263) =< s(254) 3.12/3.16 s(262) =< s(254) 3.12/3.16 s(263) =< s(253) 3.12/3.16 s(260) =< s(255) 3.12/3.16 s(262) =< s(255) 3.12/3.16 s(259) =< s(253) 3.12/3.16 s(251) =< s(253) 3.12/3.16 s(264) =< s(253) 3.12/3.16 s(265) =< s(253) 3.12/3.16 s(266) =< s(254) 3.12/3.16 s(251) =< s(254) 3.12/3.16 s(264) =< s(254) 3.12/3.16 s(265) =< s(254) 3.12/3.16 s(267) =< s(254) 3.12/3.16 s(264) =< s(265) 3.12/3.16 s(268) =< s(265) 3.12/3.16 s(251) =< s(265) 3.12/3.16 s(267) =< s(265) 3.12/3.16 s(264) =< s(258) 3.12/3.16 s(268) =< s(258) 3.12/3.16 s(251) =< s(255) 3.12/3.16 s(264) =< s(255) 3.12/3.16 s(267) =< s(255) 3.12/3.16 s(250) =< s(253) 3.12/3.16 s(269) =< s(258) 3.12/3.16 s(250) =< s(265) 3.12/3.16 s(270) =< s(265) 3.12/3.16 s(271) =< s(265) 3.12/3.16 s(270) =< s(258) 3.12/3.16 s(250) =< s(255) 3.12/3.16 s(270) =< s(255) 3.12/3.16 s(271) =< s(255) 3.12/3.16 3.12/3.16 with precondition: [A>=0,E>=4*A+C+4] 3.12/3.16 3.12/3.16 * Chain [51]: 1*s(272)+1*s(273)+1*s(274)+1*s(275)+1*s(276)+2*s(295)+2*s(298)+1*s(302)+2*s(303)+2*s(304)+4*s(305)+8*s(307)+2*s(308)+2*s(309)+1*s(311)+1 3.12/3.16 Such that:aux(115) =< -4*A-C+E 3.12/3.16 aux(116) =< -3*A-C+E 3.12/3.16 aux(118) =< -2*A-C/2+E/2 3.12/3.16 aux(120) =< -5/2*A-C/2+E/2 3.12/3.16 aux(121) =< -5/3*A-C/3+E/3 3.12/3.16 aux(122) =< -4/3*A-C/3+E/3 3.12/3.16 s(276) =< -3/2*A-C/2+E/2 3.12/3.16 s(275) =< -2/3*A-C/3+E/3 3.12/3.16 aux(123) =< -C+E 3.12/3.16 aux(124) =< -C/2+E/2 3.12/3.16 aux(125) =< -C/3+E/3 3.12/3.16 aux(127) =< -2*A-C+E 3.12/3.16 aux(128) =< -A-C+E 3.12/3.16 s(305) =< aux(127) 3.12/3.16 s(307) =< aux(127) 3.12/3.16 s(307) =< aux(128) 3.12/3.16 s(277) =< aux(115) 3.12/3.16 s(281) =< aux(118) 3.12/3.16 s(272) =< aux(120) 3.12/3.16 s(273) =< aux(120) 3.12/3.16 s(291) =< aux(120) 3.12/3.16 s(272) =< aux(121) 3.12/3.16 s(284) =< aux(121) 3.12/3.16 s(274) =< aux(122) 3.12/3.16 s(275) =< aux(122) 3.12/3.16 s(293) =< aux(122) 3.12/3.16 s(277) =< aux(123) 3.12/3.16 s(272) =< aux(124) 3.12/3.16 s(273) =< aux(124) 3.12/3.16 s(281) =< aux(124) 3.12/3.16 s(291) =< aux(124) 3.12/3.16 s(272) =< aux(125) 3.12/3.16 s(274) =< aux(125) 3.12/3.16 s(275) =< aux(125) 3.12/3.16 s(284) =< aux(125) 3.12/3.16 s(293) =< aux(125) 3.12/3.16 s(295) =< s(277) 3.12/3.16 s(298) =< aux(116) 3.12/3.16 s(299) =< aux(116) 3.12/3.16 s(274) =< s(281) 3.12/3.16 s(295) =< s(281) 3.12/3.16 s(275) =< s(281) 3.12/3.16 s(273) =< s(284) 3.12/3.16 s(272) =< s(284) 3.12/3.16 s(273) =< s(291) 3.12/3.16 s(272) =< s(291) 3.12/3.16 s(275) =< s(293) 3.12/3.16 s(274) =< s(293) 3.12/3.16 s(295) =< aux(127) 3.12/3.16 s(273) =< aux(127) 3.12/3.16 s(299) =< aux(127) 3.12/3.16 s(301) =< aux(127) 3.12/3.16 s(302) =< aux(128) 3.12/3.16 s(295) =< aux(128) 3.12/3.16 s(273) =< aux(128) 3.12/3.16 s(301) =< aux(128) 3.12/3.16 s(303) =< aux(128) 3.12/3.16 s(295) =< s(299) 3.12/3.16 s(304) =< s(299) 3.12/3.16 s(273) =< s(299) 3.12/3.16 s(303) =< s(299) 3.12/3.16 s(304) =< s(277) 3.12/3.16 s(295) =< s(301) 3.12/3.16 s(303) =< s(301) 3.12/3.16 s(304) =< s(301) 3.12/3.16 s(273) =< s(301) 3.12/3.16 s(272) =< aux(116) 3.12/3.16 s(272) =< s(301) 3.12/3.16 s(272) =< s(299) 3.12/3.16 s(272) =< aux(128) 3.12/3.16 s(275) =< aux(127) 3.12/3.16 s(276) =< aux(127) 3.12/3.16 s(308) =< aux(127) 3.12/3.16 s(276) =< aux(116) 3.12/3.16 s(308) =< aux(116) 3.12/3.16 s(275) =< aux(128) 3.12/3.16 s(276) =< aux(128) 3.12/3.16 s(309) =< aux(127) 3.12/3.16 s(309) =< s(299) 3.12/3.16 s(309) =< aux(128) 3.12/3.16 s(274) =< aux(116) 3.12/3.16 s(274) =< aux(127) 3.12/3.16 s(311) =< aux(127) 3.12/3.16 s(311) =< aux(116) 3.12/3.16 s(274) =< aux(128) 3.12/3.16 s(311) =< aux(128) 3.12/3.16 3.12/3.16 with precondition: [A>=0,E>=3*A+C+3] 3.12/3.16 3.12/3.16 * Chain [50]: 1*s(320)+1*s(322)+1*s(323)+1*s(324)+4*s(329)+5*s(330)+2*s(332)+1*s(333)+1*s(335)+1*s(338)+2*s(343)+1 3.12/3.16 Such that:aux(132) =< -A-C/2+E/2 3.12/3.16 s(320) =< -2/3*A-C/3+E/3 3.12/3.16 s(324) =< -A/3-C/3+E/3 3.12/3.16 aux(144) =< -3*A-C+E 3.12/3.16 aux(145) =< -2*A-C+E 3.12/3.16 aux(146) =< -2*A-C/2+E/2 3.12/3.16 aux(147) =< -A-C+E 3.12/3.16 aux(148) =< -A-C/3+E/3 3.12/3.16 aux(149) =< -4/3*A-C/3+E/3 3.12/3.16 aux(150) =< -3/2*A-C/2+E/2 3.12/3.16 aux(151) =< -C+E 3.12/3.16 aux(152) =< -C/2+E/2 3.12/3.16 aux(153) =< -C/3+E/3 3.12/3.16 s(320) =< aux(146) 3.12/3.16 s(335) =< aux(146) 3.12/3.16 s(324) =< aux(148) 3.12/3.16 s(338) =< aux(148) 3.12/3.16 s(320) =< aux(149) 3.12/3.16 s(335) =< aux(149) 3.12/3.16 s(317) =< aux(144) 3.12/3.16 s(322) =< aux(132) 3.12/3.16 s(323) =< aux(132) 3.12/3.16 s(322) =< aux(150) 3.12/3.16 s(324) =< aux(150) 3.12/3.16 s(328) =< aux(150) 3.12/3.16 s(317) =< aux(151) 3.12/3.16 s(320) =< aux(152) 3.12/3.16 s(322) =< aux(152) 3.12/3.16 s(324) =< aux(152) 3.12/3.16 s(328) =< aux(152) 3.12/3.16 s(320) =< aux(153) 3.12/3.16 s(324) =< aux(153) 3.12/3.16 s(324) =< s(317) 3.12/3.16 s(329) =< aux(147) 3.12/3.16 s(322) =< s(328) 3.12/3.16 s(324) =< s(328) 3.12/3.16 s(324) =< aux(147) 3.12/3.16 s(323) =< aux(147) 3.12/3.16 s(330) =< aux(147) 3.12/3.16 s(323) =< aux(145) 3.12/3.16 s(330) =< aux(145) 3.12/3.16 s(322) =< s(317) 3.12/3.16 s(320) =< s(317) 3.12/3.16 s(322) =< aux(147) 3.12/3.16 s(320) =< aux(147) 3.12/3.16 s(322) =< aux(145) 3.12/3.16 s(332) =< aux(145) 3.12/3.16 s(320) =< aux(145) 3.12/3.16 s(332) =< s(317) 3.12/3.16 s(332) =< aux(147) 3.12/3.16 s(333) =< aux(144) 3.12/3.16 s(333) =< aux(150) 3.12/3.16 s(338) =< aux(150) 3.12/3.16 s(333) =< aux(151) 3.12/3.16 s(333) =< aux(152) 3.12/3.16 s(335) =< aux(152) 3.12/3.16 s(338) =< aux(152) 3.12/3.16 s(335) =< aux(153) 3.12/3.16 s(338) =< aux(153) 3.12/3.16 s(338) =< s(317) 3.12/3.16 s(343) =< aux(145) 3.12/3.16 s(333) =< s(328) 3.12/3.16 s(338) =< s(328) 3.12/3.16 s(338) =< aux(147) 3.12/3.16 s(333) =< s(317) 3.12/3.16 s(335) =< s(317) 3.12/3.16 s(333) =< aux(145) 3.12/3.16 s(335) =< aux(147) 3.12/3.16 s(333) =< aux(147) 3.12/3.16 s(335) =< aux(145) 3.12/3.16 3.12/3.16 with precondition: [A>=0,E>=2*A+C+2] 3.12/3.16 3.12/3.16 * Chain [49]: 1*s(349)+1*s(350)+2*s(356)+2*s(358)+2*s(359)+1*s(360)+1*s(361)+1 3.12/3.16 Such that:s(350) =< -A/2-C/2+E/2 3.12/3.16 s(349) =< -A/3-C/3+E/3 3.12/3.16 aux(161) =< -3*A-C+E 3.12/3.16 aux(162) =< -2*A-C+E 3.12/3.16 aux(163) =< -A-C+E 3.12/3.16 aux(164) =< -A-C/2+E/2 3.12/3.16 aux(165) =< -A-C/3+E/3 3.12/3.16 aux(166) =< -3/2*A-C/2+E/2 3.12/3.16 aux(167) =< -C+E 3.12/3.16 aux(168) =< -C/2+E/2 3.12/3.16 aux(169) =< -C/3+E/3 3.12/3.16 s(349) =< aux(161) 3.12/3.16 s(360) =< aux(161) 3.12/3.16 s(350) =< aux(164) 3.12/3.16 s(361) =< aux(164) 3.12/3.16 s(349) =< aux(165) 3.12/3.16 s(360) =< aux(165) 3.12/3.16 s(349) =< aux(166) 3.12/3.16 s(360) =< aux(166) 3.12/3.16 s(349) =< aux(169) 3.12/3.16 s(360) =< aux(169) 3.12/3.16 s(350) =< aux(162) 3.12/3.16 s(351) =< aux(162) 3.12/3.16 s(349) =< aux(167) 3.12/3.16 s(350) =< aux(167) 3.12/3.16 s(351) =< aux(167) 3.12/3.16 s(349) =< aux(168) 3.12/3.16 s(350) =< aux(168) 3.12/3.16 s(356) =< aux(163) 3.12/3.16 s(350) =< s(351) 3.12/3.16 s(358) =< aux(167) 3.12/3.16 s(350) =< aux(163) 3.12/3.16 s(359) =< aux(163) 3.12/3.16 s(349) =< aux(163) 3.12/3.16 s(358) =< aux(163) 3.12/3.16 s(359) =< s(351) 3.12/3.16 s(359) =< aux(167) 3.12/3.16 s(361) =< aux(162) 3.12/3.16 s(360) =< aux(167) 3.12/3.16 s(361) =< aux(167) 3.12/3.16 s(360) =< aux(168) 3.12/3.16 s(361) =< aux(168) 3.12/3.16 s(361) =< s(351) 3.12/3.16 s(361) =< aux(163) 3.12/3.16 s(360) =< aux(163) 3.12/3.16 3.12/3.16 with precondition: [A>=0,E>=A+C+1] 3.12/3.16 3.12/3.16 * Chain [48]: 0 3.12/3.16 with precondition: [E>=C,A+C>=E] 3.12/3.16 3.12/3.16 * Chain [47]: 1 3.12/3.16 with precondition: [E>=2*A+C+2,C+3*A+2>=E] 3.12/3.16 3.12/3.16 * Chain [46]: 1 3.12/3.16 with precondition: [E>=A+C+1,C+2*A+1>=E] 3.12/3.16 3.12/3.16 3.12/3.16 Closed-form bounds of start0(A,B,C,D,E,F,G): 3.12/3.16 ------------------------------------- 3.12/3.16 * Chain [56] with precondition: [0>=A+1] 3.12/3.16 - Upper bound: 0 3.12/3.16 - Complexity: constant 3.12/3.16 * Chain [55] with precondition: [A>=0,E>=C] 3.12/3.16 - Upper bound: 0 3.12/3.16 - Complexity: constant 3.12/3.16 * Chain [54] with precondition: [A>=0,C>=E+1] 3.12/3.16 - Upper bound: 0 3.12/3.16 - Complexity: constant 3.12/3.16 * Chain [53] with precondition: [A>=0,E>=5*A+C+5] 3.12/3.16 - Upper bound: -45*A-12*C+12*E+1 3.12/3.16 - Complexity: n 3.12/3.16 * Chain [52] with precondition: [A>=0,E>=4*A+C+4] 3.12/3.16 - Upper bound: -60*A-21*C+21*E+1+nat(-5/2*A-C/2+E/2)*2 3.12/3.16 - Complexity: n 3.12/3.16 * Chain [51] with precondition: [A>=0,E>=3*A+C+3] 3.12/3.16 - Upper bound: -2/3*A-C/3+E/3+(-3/2*A-C/2+E/2+(-34*A-17*C+17*E+(-12*A-4*C+4*E+(-3*A-3*C+3*E+1+nat(-4*A-C+E)*2))+nat(-5/2*A-C/2+E/2)*2+nat(-4/3*A-C/3+E/3))) 3.12/3.16 - Complexity: n 3.12/3.16 * Chain [50] with precondition: [A>=0,E>=2*A+C+2] 3.12/3.16 - Upper bound: -A/3-C/3+E/3+(-2/3*A-C/3+E/3+(-8*A-4*C+4*E+(-11*A-10*C+10*E+1+nat(-A-C/3+E/3)+nat(-3*A-C+E))+nat(-2*A-C/2+E/2))) 3.12/3.16 - Complexity: n 3.12/3.16 * Chain [49] with precondition: [A>=0,E>=A+C+1] 3.12/3.16 - Upper bound: -A/3-C/3+E/3+(-A/2-C/2+E/2+(-4*A-6*C+6*E+1+nat(-A-C/2+E/2)+nat(-3*A-C+E))) 3.12/3.16 - Complexity: n 3.12/3.16 * Chain [48] with precondition: [E>=C,A+C>=E] 3.12/3.16 - Upper bound: 0 3.12/3.16 - Complexity: constant 3.12/3.16 * Chain [47] with precondition: [E>=2*A+C+2,C+3*A+2>=E] 3.12/3.16 - Upper bound: 1 3.12/3.16 - Complexity: constant 3.12/3.16 * Chain [46] with precondition: [E>=A+C+1,C+2*A+1>=E] 3.12/3.16 - Upper bound: 1 3.12/3.16 - Complexity: constant 3.12/3.16 3.12/3.16 ### Maximum cost of start0(A,B,C,D,E,F,G): nat(-3*A-C+E)+max([nat(-A-C+E)*3+max([nat(-A-C/2+E/2)+nat(-A-C+E)+nat(-A/3-C/3+E/3)+max([nat(-C+E)*2+nat(-A/2-C/2+E/2),nat(-A-C+E)*5+nat(-A-C/2+E/2)+nat(-A-C/3+E/3)+nat(-2*A-C+E)*4+nat(-2*A-C/2+E/2)+nat(-2/3*A-C/3+E/3)]),nat(-3*A-C+E)*3+nat(-4*A-C+E)*2+nat(-2*A-C+E)*17+nat(-5/2*A-C/2+E/2)*2+nat(-4/3*A-C/3+E/3)+nat(-3/2*A-C/2+E/2)+nat(-2/3*A-C/3+E/3)]),nat(-3*A-C+E)*2+nat(-4*A-C+E)*2+max([nat(-4*A-C+E)*7,nat(-2*A-C+E)*5+nat(-3*A-C+E)*11+nat(-5/2*A-C/2+E/2)*2])])+1 3.12/3.16 Asymptotic class: n 3.12/3.16 * Total analysis performed in 2950 ms. 3.12/3.16 3.17/3.26 EOF