1.95/1.97 WORST_CASE(?,O(n^2)) 1.95/1.97 1.95/1.97 Preprocessing Cost Relations 1.95/1.97 ===================================== 1.95/1.97 1.95/1.97 #### Computed strongly connected components 1.95/1.97 0. recursive : [lbl82/9] 1.95/1.97 1. recursive : [lbl111/10,lbl82_loop_cont/11] 1.95/1.97 2. non_recursive : [exit_location/1] 1.95/1.97 3. non_recursive : [stop/9] 1.95/1.97 4. non_recursive : [lbl16/9] 1.95/1.97 5. non_recursive : [lbl111_loop_cont/10] 1.95/1.97 6. non_recursive : [start/9] 1.95/1.97 7. non_recursive : [start0/9] 1.95/1.97 1.95/1.97 #### Obtained direct recursion through partial evaluation 1.95/1.97 0. SCC is partially evaluated into lbl82/9 1.95/1.97 1. SCC is partially evaluated into lbl111/10 1.95/1.97 2. SCC is completely evaluated into other SCCs 1.95/1.97 3. SCC is completely evaluated into other SCCs 1.95/1.97 4. SCC is completely evaluated into other SCCs 1.95/1.97 5. SCC is partially evaluated into lbl111_loop_cont/10 1.95/1.97 6. SCC is partially evaluated into start/9 1.95/1.97 7. SCC is partially evaluated into start0/9 1.95/1.97 1.95/1.97 Control-Flow Refinement of Cost Relations 1.95/1.97 ===================================== 1.95/1.97 1.95/1.97 ### Specialization of cost equations lbl82/9 1.95/1.97 * CE 16 is refined into CE [17] 1.95/1.97 * CE 15 is refined into CE [18] 1.95/1.97 * CE 14 is refined into CE [19] 1.95/1.97 1.95/1.97 1.95/1.97 ### Cost equations --> "Loop" of lbl82/9 1.95/1.97 * CEs [17] --> Loop 17 1.95/1.97 * CEs [18] --> Loop 18 1.95/1.97 * CEs [19] --> Loop 19 1.95/1.97 1.95/1.97 ### Ranking functions of CR lbl82(A,B,D,F,H,I,J,K,L) 1.95/1.97 1.95/1.97 #### Partial ranking functions of CR lbl82(A,B,D,F,H,I,J,K,L) 1.95/1.97 1.95/1.97 1.95/1.97 ### Specialization of cost equations lbl111/10 1.95/1.97 * CE 5 is refined into CE [20] 1.95/1.97 * CE 11 is refined into CE [21] 1.95/1.97 * CE 9 is discarded (unfeasible) 1.95/1.97 * CE 4 is refined into CE [22] 1.95/1.97 * CE 8 is refined into CE [23] 1.95/1.97 * CE 7 is refined into CE [24] 1.95/1.97 * CE 10 is refined into CE [25] 1.95/1.97 * CE 6 is refined into CE [26] 1.95/1.97 1.95/1.97 1.95/1.97 ### Cost equations --> "Loop" of lbl111/10 1.95/1.97 * CEs [24] --> Loop 20 1.95/1.97 * CEs [25] --> Loop 21 1.95/1.97 * CEs [26] --> Loop 22 1.95/1.97 * CEs [20] --> Loop 23 1.95/1.97 * CEs [21] --> Loop 24 1.95/1.97 * CEs [22] --> Loop 25 1.95/1.97 * CEs [23] --> Loop 26 1.95/1.97 1.95/1.97 ### Ranking functions of CR lbl111(A,B,D,F,H,I,J,K,L,M) 1.95/1.97 1.95/1.97 #### Partial ranking functions of CR lbl111(A,B,D,F,H,I,J,K,L,M) 1.95/1.97 * Partial RF of phase [20,21,22]: 1.95/1.97 - RF of loop [20:1]: 1.95/1.97 A/2-D depends on loops [21:1] 1.95/1.97 -D+H/2 depends on loops [21:1] 1.95/1.97 -D/2+F/2 depends on loops [21:1] 1.95/1.97 - RF of loop [20:1,22:1]: 1.95/1.97 F-1 1.95/1.97 - RF of loop [21:1]: 1.95/1.97 D depends on loops [20:1,22:1] 1.95/1.97 D-F+1 depends on loops [20:1,22:1] 1.95/1.97 - RF of loop [22:1]: 1.95/1.97 -D/2+1/2 depends on loops [21:1] 1.95/1.97 1.95/1.97 1.95/1.97 ### Specialization of cost equations lbl111_loop_cont/10 1.95/1.97 * CE 12 is refined into CE [27] 1.95/1.97 * CE 13 is refined into CE [28] 1.95/1.97 1.95/1.97 1.95/1.97 ### Cost equations --> "Loop" of lbl111_loop_cont/10 1.95/1.97 * CEs [27] --> Loop 27 1.95/1.97 * CEs [28] --> Loop 28 1.95/1.97 1.95/1.97 ### Ranking functions of CR lbl111_loop_cont(A,B,C,D,E,F,G,H,I,J) 1.95/1.97 1.95/1.97 #### Partial ranking functions of CR lbl111_loop_cont(A,B,C,D,E,F,G,H,I,J) 1.95/1.97 1.95/1.97 1.95/1.97 ### Specialization of cost equations start/9 1.95/1.97 * CE 3 is refined into CE [29,30,31,32,33] 1.95/1.97 * CE 2 is refined into CE [34] 1.95/1.97 1.95/1.97 1.95/1.97 ### Cost equations --> "Loop" of start/9 1.95/1.97 * CEs [32] --> Loop 29 1.95/1.97 * CEs [30] --> Loop 30 1.95/1.97 * CEs [31,33] --> Loop 31 1.95/1.97 * CEs [34] --> Loop 32 1.95/1.97 * CEs [29] --> Loop 33 1.95/1.97 1.95/1.97 ### Ranking functions of CR start(A,B,C,D,E,F,G,H,I) 1.95/1.97 1.95/1.97 #### Partial ranking functions of CR start(A,B,C,D,E,F,G,H,I) 1.95/1.97 1.95/1.97 1.95/1.97 ### Specialization of cost equations start0/9 1.95/1.97 * CE 1 is refined into CE [35,36,37,38,39] 1.95/1.97 1.95/1.97 1.95/1.97 ### Cost equations --> "Loop" of start0/9 1.95/1.97 * CEs [39] --> Loop 34 1.95/1.97 * CEs [38] --> Loop 35 1.95/1.97 * CEs [37] --> Loop 36 1.95/1.97 * CEs [36] --> Loop 37 1.95/1.97 * CEs [35] --> Loop 38 1.95/1.97 1.95/1.97 ### Ranking functions of CR start0(A,B,C,D,E,F,G,H,I) 1.95/1.97 1.95/1.97 #### Partial ranking functions of CR start0(A,B,C,D,E,F,G,H,I) 1.95/1.97 1.95/1.97 1.95/1.97 Computing Bounds 1.95/1.97 ===================================== 1.95/1.97 1.95/1.97 #### Cost of chains of lbl82(A,B,D,F,H,I,J,K,L): 1.95/1.97 * Chain [19]: 0 1.95/1.97 with precondition: [F=0,I=2,L=0,D=A,D=H,B=J,D=K,D>=2,D>=B+1] 1.95/1.97 1.95/1.97 * Chain [18]: 0 1.95/1.97 with precondition: [I=3,D=A,D=H,B=J,F=L,D=F+K,F>=1,D>=B,D>=F+2] 1.95/1.97 1.95/1.97 * Chain [17]: 0 1.95/1.97 with precondition: [I=4,D=A,D=H,F>=0,D>=B,D>=F+2,D+F>=B+1] 1.95/1.97 1.95/1.97 1.95/1.97 #### Cost of chains of lbl111(A,B,D,F,H,I,J,K,L,M): 1.95/1.97 * Chain [[20,21,22],26]: 2*it(20)+1*it(21)+0 1.95/1.97 Such that:aux(24) =< -2*F+M+1 1.95/1.97 aux(167) =< D 1.95/1.97 aux(168) =< D-F+1 1.95/1.97 aux(169) =< F 1.95/1.97 aux(170) =< J 1.95/1.97 aux(24) =< aux(168) 1.95/1.97 aux(29) =< aux(170) 1.95/1.97 it(20) =< aux(169) 1.95/1.97 aux(75) =< aux(170)+2 1.95/1.97 aux(82) =< aux(170)+1 1.95/1.97 aux(29) =< aux(170) 1.95/1.97 aux(127) =< aux(29)+1 1.95/1.97 aux(75) =< aux(29)+2 1.95/1.97 aux(132) =< it(20)*aux(127) 1.95/1.97 aux(14) =< it(20)*aux(127) 1.95/1.97 aux(17) =< it(20)*aux(75) 1.95/1.97 aux(102) =< it(20)*aux(82) 1.95/1.97 aux(14) =< it(20)*aux(82) 1.95/1.97 aux(16) =< it(20)*aux(170) 1.95/1.97 aux(30) =< it(20)*aux(29) 1.95/1.97 aux(13) =< it(20)*aux(29) 1.95/1.97 aux(13) =< it(20)*aux(170) 1.95/1.97 aux(19) =< aux(30) 1.95/1.97 aux(19) =< aux(16) 1.95/1.97 aux(20) =< aux(132) 1.95/1.97 aux(20) =< aux(102) 1.95/1.97 it(21) =< aux(17)+aux(16)+aux(168) 1.95/1.97 it(21) =< aux(14)+aux(13)+aux(167) 1.95/1.97 it(21) =< aux(17)+aux(16)+aux(24) 1.95/1.97 it(21) =< aux(20)+aux(19)+aux(167) 1.95/1.97 1.95/1.97 with precondition: [I=2,A=H,A=J,A=M,D>=0,F>=1,A>=B,A>=F+1,D+F>=2,A>=D+F] 1.95/1.97 1.95/1.97 * Chain [[20,21,22],25]: 2*it(20)+1*it(21)+0 1.95/1.97 Such that:aux(18) =< D-F+1 1.95/1.97 aux(24) =< 2*D 1.95/1.97 aux(171) =< D 1.95/1.97 aux(172) =< F 1.95/1.97 aux(173) =< H 1.95/1.97 aux(24) =< aux(171) 1.95/1.97 aux(29) =< aux(173) 1.95/1.97 it(20) =< aux(172) 1.95/1.97 aux(75) =< aux(173)+2 1.95/1.97 aux(82) =< aux(173)+1 1.95/1.97 aux(29) =< aux(173) 1.95/1.97 aux(127) =< aux(29)+1 1.95/1.97 aux(75) =< aux(29)+2 1.95/1.97 aux(132) =< it(20)*aux(127) 1.95/1.97 aux(14) =< it(20)*aux(127) 1.95/1.97 aux(17) =< it(20)*aux(75) 1.95/1.97 aux(102) =< it(20)*aux(82) 1.95/1.97 aux(14) =< it(20)*aux(82) 1.95/1.97 aux(16) =< it(20)*aux(173) 1.95/1.97 aux(30) =< it(20)*aux(29) 1.95/1.97 aux(13) =< it(20)*aux(29) 1.95/1.97 aux(13) =< it(20)*aux(173) 1.95/1.97 aux(19) =< aux(30) 1.95/1.97 aux(19) =< aux(16) 1.95/1.97 aux(20) =< aux(132) 1.95/1.97 aux(20) =< aux(102) 1.95/1.97 it(21) =< aux(17)+aux(16)+aux(18) 1.95/1.97 it(21) =< aux(14)+aux(13)+aux(171) 1.95/1.97 it(21) =< aux(17)+aux(16)+aux(24) 1.95/1.97 it(21) =< aux(20)+aux(19)+aux(171) 1.95/1.97 1.95/1.97 with precondition: [I=4,A=H,D>=0,F>=1,A>=B,A>=F+1,D+F>=2,A>=D+F] 1.95/1.97 1.95/1.97 * Chain [[20,21,22],24]: 2*it(20)+1*it(21)+0 1.95/1.97 Such that:aux(18) =< D-F+1 1.95/1.97 aux(24) =< 2*D 1.95/1.97 aux(163) =< -F+H 1.95/1.97 aux(174) =< D 1.95/1.97 aux(175) =< F 1.95/1.97 aux(176) =< H 1.95/1.97 aux(24) =< aux(174) 1.95/1.97 aux(163) =< aux(174) 1.95/1.97 aux(29) =< aux(176) 1.95/1.97 it(20) =< aux(175) 1.95/1.97 aux(75) =< aux(176)+2 1.95/1.97 aux(82) =< aux(176)+1 1.95/1.97 aux(29) =< aux(176) 1.95/1.97 aux(127) =< aux(29)+1 1.95/1.97 aux(75) =< aux(29)+2 1.95/1.97 aux(132) =< it(20)*aux(127) 1.95/1.97 aux(14) =< it(20)*aux(127) 1.95/1.97 aux(17) =< it(20)*aux(75) 1.95/1.97 aux(102) =< it(20)*aux(82) 1.95/1.97 aux(14) =< it(20)*aux(82) 1.95/1.97 aux(16) =< it(20)*aux(176) 1.95/1.97 aux(30) =< it(20)*aux(29) 1.95/1.97 aux(13) =< it(20)*aux(29) 1.95/1.97 aux(13) =< it(20)*aux(176) 1.95/1.97 aux(19) =< aux(30) 1.95/1.97 aux(19) =< aux(16) 1.95/1.97 aux(20) =< aux(132) 1.95/1.97 aux(20) =< aux(102) 1.95/1.97 it(21) =< aux(17)+aux(16)+aux(18) 1.95/1.97 it(21) =< aux(14)+aux(13)+aux(174) 1.95/1.97 it(21) =< aux(17)+aux(16)+aux(24) 1.95/1.97 it(21) =< aux(20)+aux(19)+aux(163) 1.95/1.97 1.95/1.97 with precondition: [I=4,A=H,D>=0,F>=1,A>=B,A>=F+1,D+F>=2,A>=D+F] 1.95/1.97 1.95/1.97 * Chain [[20,21,22],23]: 2*it(20)+1*it(21)+0 1.95/1.97 Such that:aux(18) =< D-F+1 1.95/1.97 aux(24) =< 2*D 1.95/1.97 aux(163) =< -F+H 1.95/1.97 aux(177) =< D 1.95/1.97 aux(178) =< F 1.95/1.97 aux(179) =< H 1.95/1.97 aux(24) =< aux(177) 1.95/1.97 aux(163) =< aux(177) 1.95/1.97 aux(29) =< aux(179) 1.95/1.97 it(20) =< aux(178) 1.95/1.97 aux(75) =< aux(179)+2 1.95/1.97 aux(82) =< aux(179)+1 1.95/1.97 aux(29) =< aux(179) 1.95/1.97 aux(127) =< aux(29)+1 1.95/1.97 aux(75) =< aux(29)+2 1.95/1.97 aux(132) =< it(20)*aux(127) 1.95/1.97 aux(14) =< it(20)*aux(127) 1.95/1.97 aux(17) =< it(20)*aux(75) 1.95/1.97 aux(102) =< it(20)*aux(82) 1.95/1.97 aux(14) =< it(20)*aux(82) 1.95/1.97 aux(16) =< it(20)*aux(179) 1.95/1.97 aux(30) =< it(20)*aux(29) 1.95/1.97 aux(13) =< it(20)*aux(29) 1.95/1.97 aux(13) =< it(20)*aux(179) 1.95/1.97 aux(19) =< aux(30) 1.95/1.97 aux(19) =< aux(16) 1.95/1.97 aux(20) =< aux(132) 1.95/1.97 aux(20) =< aux(102) 1.95/1.97 it(21) =< aux(17)+aux(16)+aux(18) 1.95/1.97 it(21) =< aux(14)+aux(13)+aux(177) 1.95/1.97 it(21) =< aux(17)+aux(16)+aux(24) 1.95/1.97 it(21) =< aux(20)+aux(19)+aux(163) 1.95/1.97 1.95/1.97 with precondition: [I=4,A=H,A>=5,D>=0,F>=2,A>=B,A>=F+1,D+3*F>=9,A>=D+F] 1.95/1.97 1.95/1.97 * Chain [24]: 0 1.95/1.97 with precondition: [I=4,H=A,F>=1,H>=B,H>=F+1,H>=D+F] 1.95/1.97 1.95/1.97 * Chain [23]: 0 1.95/1.97 with precondition: [I=4,H=A,D>=1,H>=B,F>=D+1,H>=D+F] 1.95/1.97 1.95/1.97 1.95/1.97 #### Cost of chains of lbl111_loop_cont(A,B,C,D,E,F,G,H,I,J): 1.95/1.97 * Chain [28]: 0 1.95/1.97 with precondition: [A=2,G=0,B=E,B=I,B>=2,H>=2,B>=C+1] 1.95/1.97 1.95/1.97 * Chain [27]: 0 1.95/1.97 with precondition: [A=4,H>=2] 1.95/1.97 1.95/1.97 1.95/1.97 #### Cost of chains of start(A,B,C,D,E,F,G,H,I): 1.95/1.97 * Chain [33]: 2*s(48)+1*s(61)+0 1.95/1.97 Such that:s(43) =< 1 1.95/1.97 aux(185) =< -D+3 1.95/1.97 aux(186) =< -E+3 1.95/1.97 aux(187) =< H 1.95/1.97 s(42) =< aux(185) 1.95/1.97 s(44) =< aux(185) 1.95/1.97 s(42) =< aux(186) 1.95/1.97 s(44) =< aux(186) 1.95/1.97 s(42) =< s(44) 1.95/1.97 s(47) =< aux(187) 1.95/1.97 s(48) =< aux(187) 1.95/1.97 s(49) =< aux(187)+2 1.95/1.97 s(50) =< aux(187)+1 1.95/1.97 s(47) =< aux(187) 1.95/1.97 s(51) =< s(47)+1 1.95/1.97 s(49) =< s(47)+2 1.95/1.97 s(52) =< s(48)*s(51) 1.95/1.97 s(53) =< s(48)*s(51) 1.95/1.97 s(54) =< s(48)*s(49) 1.95/1.97 s(55) =< s(48)*s(50) 1.95/1.97 s(53) =< s(48)*s(50) 1.95/1.97 s(56) =< s(48)*aux(187) 1.95/1.97 s(57) =< s(48)*s(47) 1.95/1.97 s(58) =< s(48)*s(47) 1.95/1.97 s(58) =< s(48)*aux(187) 1.95/1.97 s(59) =< s(57) 1.95/1.97 s(59) =< s(56) 1.95/1.97 s(60) =< s(52) 1.95/1.97 s(60) =< s(55) 1.95/1.97 s(61) =< s(54)+s(56)+s(44) 1.95/1.97 s(61) =< s(53)+s(58)+s(43) 1.95/1.97 s(61) =< s(54)+s(56)+s(42) 1.95/1.97 s(61) =< s(60)+s(59)+s(43) 1.95/1.97 1.95/1.97 with precondition: [F=0,G=0,D=A,C=B,D=E,D=H,D>=2,D>=C+1] 1.95/1.97 1.95/1.97 * Chain [32]: 0 1.95/1.97 with precondition: [H=A,C=B,E=D,G=F,1>=H] 1.95/1.97 1.95/1.97 * Chain [31]: 4*s(70)+2*s(83)+0 1.95/1.97 Such that:aux(188) =< 1 1.95/1.97 s(65) =< 2 1.95/1.97 s(64) =< -A+3 1.95/1.97 s(64) =< -H+3 1.95/1.97 aux(189) =< H 1.95/1.97 s(68) =< s(65) 1.95/1.97 s(68) =< aux(188) 1.95/1.97 s(69) =< aux(189) 1.95/1.97 s(70) =< aux(189) 1.95/1.97 s(71) =< aux(189)+2 1.95/1.97 s(72) =< aux(189)+1 1.95/1.97 s(69) =< aux(189) 1.95/1.97 s(73) =< s(69)+1 1.95/1.97 s(71) =< s(69)+2 1.95/1.97 s(74) =< s(70)*s(73) 1.95/1.97 s(75) =< s(70)*s(73) 1.95/1.97 s(76) =< s(70)*s(71) 1.95/1.97 s(77) =< s(70)*s(72) 1.95/1.97 s(75) =< s(70)*s(72) 1.95/1.97 s(78) =< s(70)*aux(189) 1.95/1.97 s(79) =< s(70)*s(69) 1.95/1.97 s(80) =< s(70)*s(69) 1.95/1.97 s(80) =< s(70)*aux(189) 1.95/1.97 s(81) =< s(79) 1.95/1.97 s(81) =< s(78) 1.95/1.97 s(82) =< s(74) 1.95/1.97 s(82) =< s(77) 1.95/1.97 s(83) =< s(76)+s(78)+s(64) 1.95/1.97 s(83) =< s(75)+s(80)+aux(188) 1.95/1.97 s(83) =< s(76)+s(78)+s(68) 1.95/1.97 s(83) =< s(82)+s(81)+aux(188) 1.95/1.97 1.95/1.97 with precondition: [H=A,C=B,E=D,G=F,H>=2] 1.95/1.97 1.95/1.97 * Chain [30]: 0 1.95/1.97 with precondition: [H=A,C=B,E=D,G=F,H>=3] 1.95/1.97 1.95/1.97 * Chain [29]: 2*s(92)+1*s(105)+0 1.95/1.97 Such that:s(86) =< 2 1.95/1.97 s(85) =< -A+3 1.95/1.97 s(85) =< -H+3 1.95/1.97 aux(190) =< 1 1.95/1.97 aux(191) =< H 1.95/1.97 s(86) =< aux(190) 1.95/1.97 s(91) =< aux(191) 1.95/1.97 s(92) =< aux(191) 1.95/1.97 s(93) =< aux(191)+2 1.95/1.97 s(94) =< aux(191)+1 1.95/1.97 s(91) =< aux(191) 1.95/1.97 s(95) =< s(91)+1 1.95/1.97 s(93) =< s(91)+2 1.95/1.97 s(96) =< s(92)*s(95) 1.95/1.97 s(97) =< s(92)*s(95) 1.95/1.97 s(98) =< s(92)*s(93) 1.95/1.97 s(99) =< s(92)*s(94) 1.95/1.97 s(97) =< s(92)*s(94) 1.95/1.97 s(100) =< s(92)*aux(191) 1.95/1.97 s(101) =< s(92)*s(91) 1.95/1.97 s(102) =< s(92)*s(91) 1.95/1.97 s(102) =< s(92)*aux(191) 1.95/1.97 s(103) =< s(101) 1.95/1.97 s(103) =< s(100) 1.95/1.97 s(104) =< s(96) 1.95/1.97 s(104) =< s(99) 1.95/1.97 s(105) =< s(98)+s(100)+s(85) 1.95/1.97 s(105) =< s(97)+s(102)+aux(190) 1.95/1.97 s(105) =< s(98)+s(100)+s(86) 1.95/1.97 s(105) =< s(104)+s(103)+aux(190) 1.95/1.97 1.95/1.97 with precondition: [H=A,C=B,E=D,G=F,H>=5] 1.95/1.97 1.95/1.97 1.95/1.97 #### Cost of chains of start0(A,B,C,D,E,F,G,H,I): 1.95/1.97 * Chain [38]: 2*s(113)+1*s(126)+0 1.95/1.97 Such that:s(106) =< 1 1.95/1.97 s(109) =< E 1.95/1.97 aux(192) =< -A+3 1.95/1.97 aux(193) =< -E+3 1.95/1.97 s(107) =< aux(192) 1.95/1.97 s(107) =< aux(193) 1.95/1.97 s(112) =< s(109) 1.95/1.97 s(113) =< s(109) 1.95/1.97 s(114) =< s(109)+2 1.95/1.97 s(115) =< s(109)+1 1.95/1.97 s(112) =< s(109) 1.95/1.97 s(116) =< s(112)+1 1.95/1.97 s(114) =< s(112)+2 1.95/1.97 s(117) =< s(113)*s(116) 1.95/1.97 s(118) =< s(113)*s(116) 1.95/1.97 s(119) =< s(113)*s(114) 1.95/1.97 s(120) =< s(113)*s(115) 1.95/1.97 s(118) =< s(113)*s(115) 1.95/1.97 s(121) =< s(113)*s(109) 1.95/1.97 s(122) =< s(113)*s(112) 1.95/1.97 s(123) =< s(113)*s(112) 1.95/1.97 s(123) =< s(113)*s(109) 1.95/1.97 s(124) =< s(122) 1.95/1.97 s(124) =< s(121) 1.95/1.97 s(125) =< s(117) 1.95/1.97 s(125) =< s(120) 1.95/1.97 s(126) =< s(119)+s(121)+s(107) 1.95/1.97 s(126) =< s(118)+s(123)+s(106) 1.95/1.97 s(126) =< s(125)+s(124)+s(106) 1.95/1.97 1.95/1.97 with precondition: [G=0,A=E,A>=2,A>=C+1] 1.95/1.97 1.95/1.97 * Chain [37]: 0 1.95/1.97 with precondition: [1>=A] 1.95/1.97 1.95/1.97 * Chain [36]: 4*s(133)+2*s(146)+0 1.95/1.97 Such that:s(128) =< 2 1.95/1.97 s(129) =< -A+3 1.95/1.97 s(130) =< A 1.95/1.97 aux(194) =< 1 1.95/1.97 s(129) =< aux(194) 1.95/1.97 s(131) =< s(128) 1.95/1.97 s(131) =< aux(194) 1.95/1.97 s(132) =< s(130) 1.95/1.97 s(133) =< s(130) 1.95/1.97 s(134) =< s(130)+2 1.95/1.97 s(135) =< s(130)+1 1.95/1.97 s(132) =< s(130) 1.95/1.97 s(136) =< s(132)+1 1.95/1.97 s(134) =< s(132)+2 1.95/1.97 s(137) =< s(133)*s(136) 1.95/1.97 s(138) =< s(133)*s(136) 1.95/1.97 s(139) =< s(133)*s(134) 1.95/1.97 s(140) =< s(133)*s(135) 1.95/1.97 s(138) =< s(133)*s(135) 1.95/1.97 s(141) =< s(133)*s(130) 1.95/1.97 s(142) =< s(133)*s(132) 1.95/1.97 s(143) =< s(133)*s(132) 1.95/1.97 s(143) =< s(133)*s(130) 1.95/1.97 s(144) =< s(142) 1.95/1.97 s(144) =< s(141) 1.95/1.97 s(145) =< s(137) 1.95/1.97 s(145) =< s(140) 1.95/1.97 s(146) =< s(139)+s(141)+s(129) 1.95/1.97 s(146) =< s(138)+s(143)+aux(194) 1.95/1.97 s(146) =< s(139)+s(141)+s(131) 1.95/1.97 s(146) =< s(145)+s(144)+aux(194) 1.95/1.97 1.95/1.97 with precondition: [A>=2] 1.95/1.97 1.95/1.97 * Chain [35]: 0 1.95/1.97 with precondition: [A>=3] 1.95/1.97 1.95/1.97 * Chain [34]: 2*s(152)+1*s(165)+0 1.95/1.97 Such that:s(149) =< 1 1.95/1.97 s(147) =< 2 1.95/1.97 s(150) =< A 1.95/1.97 s(147) =< s(149) 1.95/1.97 s(151) =< s(150) 1.95/1.97 s(152) =< s(150) 1.95/1.97 s(153) =< s(150)+2 1.95/1.97 s(154) =< s(150)+1 1.95/1.97 s(151) =< s(150) 1.95/1.97 s(155) =< s(151)+1 1.95/1.97 s(153) =< s(151)+2 1.95/1.97 s(156) =< s(152)*s(155) 1.95/1.97 s(157) =< s(152)*s(155) 1.95/1.97 s(158) =< s(152)*s(153) 1.95/1.97 s(159) =< s(152)*s(154) 1.95/1.97 s(157) =< s(152)*s(154) 1.95/1.97 s(160) =< s(152)*s(150) 1.95/1.97 s(161) =< s(152)*s(151) 1.95/1.97 s(162) =< s(152)*s(151) 1.95/1.97 s(162) =< s(152)*s(150) 1.95/1.97 s(163) =< s(161) 1.95/1.97 s(163) =< s(160) 1.95/1.97 s(164) =< s(156) 1.95/1.97 s(164) =< s(159) 1.95/1.97 s(165) =< s(158)+s(160) 1.95/1.97 s(165) =< s(157)+s(162)+s(149) 1.95/1.97 s(165) =< s(158)+s(160)+s(147) 1.95/1.97 s(165) =< s(164)+s(163)+s(149) 1.95/1.97 1.95/1.97 with precondition: [A>=5] 1.95/1.97 1.95/1.97 1.95/1.97 Closed-form bounds of start0(A,B,C,D,E,F,G,H,I): 1.95/1.97 ------------------------------------- 1.95/1.97 * Chain [38] with precondition: [G=0,A=E,A>=2,A>=C+1] 1.95/1.97 - Upper bound: 2*E*E+4*E+nat(-A+3) 1.95/1.97 - Complexity: n^2 1.95/1.97 * Chain [37] with precondition: [1>=A] 1.95/1.97 - Upper bound: 0 1.95/1.97 - Complexity: constant 1.95/1.97 * Chain [36] with precondition: [A>=2] 1.95/1.97 - Upper bound: 8*A+2+4*A*A 1.95/1.97 - Complexity: n^2 1.95/1.97 * Chain [35] with precondition: [A>=3] 1.95/1.97 - Upper bound: 0 1.95/1.97 - Complexity: constant 1.95/1.97 * Chain [34] with precondition: [A>=5] 1.95/1.97 - Upper bound: 2*A*A+4*A 1.95/1.97 - Complexity: n^2 1.95/1.97 1.95/1.97 ### Maximum cost of start0(A,B,C,D,E,F,G,H,I): max([nat(E)*2*nat(E)+nat(E)*4+nat(-A+3),nat(A)*4+2+nat(A)*2*nat(A)+(nat(A)*2*nat(A)+nat(A)*4)]) 1.95/1.97 Asymptotic class: n^2 1.95/1.97 * Total analysis performed in 1724 ms. 1.95/1.97 1.98/2.08 EOF