2.55/2.54 WORST_CASE(?,O(n^2)) 2.55/2.54 2.55/2.54 Preprocessing Cost Relations 2.55/2.54 ===================================== 2.55/2.54 2.55/2.54 #### Computed strongly connected components 2.55/2.54 0. recursive : [lbl121/17] 2.55/2.54 1. recursive : [lbl121_loop_cont/18,lbl82/17] 2.55/2.54 2. non_recursive : [exit_location/1] 2.55/2.54 3. non_recursive : [stop/9] 2.55/2.54 4. non_recursive : [lbl82_loop_cont/10] 2.55/2.54 5. non_recursive : [start/9] 2.55/2.54 6. non_recursive : [start0/9] 2.55/2.54 2.55/2.54 #### Obtained direct recursion through partial evaluation 2.55/2.54 0. SCC is partially evaluated into lbl121/17 2.55/2.54 1. SCC is partially evaluated into lbl82/17 2.55/2.54 2. SCC is completely evaluated into other SCCs 2.55/2.54 3. SCC is completely evaluated into other SCCs 2.55/2.54 4. SCC is partially evaluated into lbl82_loop_cont/10 2.55/2.54 5. SCC is partially evaluated into start/9 2.55/2.54 6. SCC is partially evaluated into start0/9 2.55/2.54 2.55/2.54 Control-Flow Refinement of Cost Relations 2.55/2.54 ===================================== 2.55/2.54 2.55/2.54 ### Specialization of cost equations lbl121/17 2.55/2.54 * CE 10 is refined into CE [19] 2.55/2.54 * CE 8 is refined into CE [20] 2.55/2.54 * CE 7 is refined into CE [21] 2.55/2.54 * CE 9 is refined into CE [22] 2.55/2.54 2.55/2.54 2.55/2.54 ### Cost equations --> "Loop" of lbl121/17 2.55/2.54 * CEs [22] --> Loop 16 2.55/2.54 * CEs [19] --> Loop 17 2.55/2.54 * CEs [20] --> Loop 18 2.55/2.54 * CEs [21] --> Loop 19 2.55/2.54 2.55/2.54 ### Ranking functions of CR lbl121(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q) 2.55/2.54 * RF of phase [16]: [-A+E+1,-A+G+1,-D+E+1,-D+G+1,E,G] 2.55/2.54 2.55/2.54 #### Partial ranking functions of CR lbl121(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q) 2.55/2.54 * Partial RF of phase [16]: 2.55/2.54 - RF of loop [16:1]: 2.55/2.54 -A+E+1 2.55/2.54 -A+G+1 2.55/2.54 -D+E+1 2.55/2.54 -D+G+1 2.55/2.54 E 2.55/2.54 G 2.55/2.54 2.55/2.54 2.55/2.54 ### Specialization of cost equations lbl82/17 2.55/2.54 * CE 13 is refined into CE [23,24] 2.55/2.54 * CE 18 is refined into CE [25] 2.55/2.54 * CE 15 is refined into CE [26] 2.55/2.54 * CE 16 is refined into CE [27] 2.55/2.54 * CE 14 is refined into CE [28,29] 2.55/2.54 * CE 17 is refined into CE [30] 2.55/2.54 2.55/2.54 2.55/2.54 ### Cost equations --> "Loop" of lbl82/17 2.55/2.54 * CEs [29] --> Loop 20 2.55/2.54 * CEs [30] --> Loop 21 2.55/2.54 * CEs [28] --> Loop 22 2.55/2.54 * CEs [23,24] --> Loop 23 2.55/2.54 * CEs [25] --> Loop 24 2.55/2.54 * CEs [26] --> Loop 25 2.55/2.54 * CEs [27] --> Loop 26 2.55/2.54 2.55/2.54 ### Ranking functions of CR lbl82(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q) 2.55/2.54 2.55/2.54 #### Partial ranking functions of CR lbl82(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q) 2.55/2.54 * Partial RF of phase [20,21,22]: 2.55/2.54 - RF of loop [20:1]: 2.55/2.54 -A/2+E/2-1/2 2.55/2.54 -D/2+E/2-1/2 2.55/2.54 E/2-3/2 2.55/2.54 - RF of loop [21:1]: 2.55/2.54 -A+G+1 depends on loops [20:1,22:1] 2.55/2.54 -D+G+1 depends on loops [20:1,22:1] 2.55/2.54 -E/2+G+1/2 depends on loops [20:1,22:1] 2.55/2.54 G depends on loops [20:1,22:1] 2.55/2.54 - RF of loop [22:1]: 2.55/2.54 -A+E 2.55/2.54 -D+E 2.55/2.54 E-1 2.55/2.54 2.55/2.54 2.55/2.54 ### Specialization of cost equations lbl82_loop_cont/10 2.55/2.54 * CE 12 is refined into CE [31] 2.55/2.54 * CE 11 is refined into CE [32] 2.55/2.54 2.55/2.54 2.55/2.54 ### Cost equations --> "Loop" of lbl82_loop_cont/10 2.55/2.54 * CEs [31] --> Loop 27 2.55/2.54 * CEs [32] --> Loop 28 2.55/2.54 2.55/2.54 ### Ranking functions of CR lbl82_loop_cont(A,B,C,D,E,F,G,H,I,J) 2.55/2.54 2.55/2.54 #### Partial ranking functions of CR lbl82_loop_cont(A,B,C,D,E,F,G,H,I,J) 2.55/2.54 2.55/2.54 2.55/2.54 ### Specialization of cost equations start/9 2.55/2.54 * CE 2 is refined into CE [33,34] 2.55/2.54 * CE 3 is refined into CE [35,36,37,38,39,40,41,42,43,44,45,46,47,48] 2.55/2.54 * CE 4 is refined into CE [49,50] 2.55/2.54 * CE 6 is refined into CE [51,52,53,54,55,56,57] 2.55/2.54 * CE 5 is refined into CE [58] 2.55/2.54 2.55/2.54 2.55/2.54 ### Cost equations --> "Loop" of start/9 2.55/2.54 * CEs [44,47] --> Loop 29 2.55/2.54 * CEs [37,40,43,45,48] --> Loop 30 2.55/2.54 * CEs [36,38,41,42,46,53,56] --> Loop 31 2.55/2.54 * CEs [34,39,50,52,54,57] --> Loop 32 2.55/2.54 * CEs [33,55] --> Loop 33 2.55/2.54 * CEs [58] --> Loop 34 2.55/2.54 * CEs [35] --> Loop 35 2.55/2.54 * CEs [49,51] --> Loop 36 2.55/2.54 2.55/2.54 ### Ranking functions of CR start(A,B,C,D,E,F,G,H,I) 2.55/2.54 2.55/2.54 #### Partial ranking functions of CR start(A,B,C,D,E,F,G,H,I) 2.55/2.54 2.55/2.54 2.55/2.54 ### Specialization of cost equations start0/9 2.55/2.54 * CE 1 is refined into CE [59,60,61,62,63,64,65,66] 2.55/2.54 2.55/2.54 2.55/2.54 ### Cost equations --> "Loop" of start0/9 2.55/2.54 * CEs [66] --> Loop 37 2.55/2.54 * CEs [65] --> Loop 38 2.55/2.54 * CEs [64] --> Loop 39 2.55/2.54 * CEs [63] --> Loop 40 2.55/2.54 * CEs [62] --> Loop 41 2.55/2.54 * CEs [61] --> Loop 42 2.55/2.54 * CEs [60] --> Loop 43 2.55/2.54 * CEs [59] --> Loop 44 2.55/2.54 2.55/2.54 ### Ranking functions of CR start0(A,B,C,D,E,F,G,H,I) 2.55/2.54 2.55/2.54 #### Partial ranking functions of CR start0(A,B,C,D,E,F,G,H,I) 2.55/2.54 2.55/2.54 2.55/2.54 Computing Bounds 2.55/2.54 ===================================== 2.55/2.54 2.55/2.54 #### Cost of chains of lbl121(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q): 2.55/2.54 * Chain [[16],19]: 1*it(16)+0 2.55/2.54 Such that:it(16) =< E-N 2.55/2.54 2.55/2.54 with precondition: [I=2,A=D,E=G,A=J,A=K,C=L,A=M,A=N+1,F=O,A=P+1,H=Q,B>=A,E>=A,E+1>=B,2*A>=E+1] 2.55/2.54 2.55/2.54 * Chain [[16],18]: 1*it(16)+0 2.55/2.54 Such that:it(16) =< E-N 2.55/2.54 2.55/2.54 with precondition: [I=3,A=D,E=G,A=J,C=L,A=M,K=N+1,F=O,K=P+2,H=Q,B>=A,K>=A+1,E+1>=B,2*A>=E+1,E>=K] 2.55/2.54 2.55/2.54 * Chain [[16],17]: 1*it(16)+0 2.55/2.54 Such that:it(16) =< -A+E+1 2.55/2.54 2.55/2.54 with precondition: [I=4,A=D,E=G,B>=A,E>=A,E+1>=B,2*A>=E+1] 2.55/2.54 2.55/2.54 * Chain [19]: 0 2.55/2.54 with precondition: [I=2,E+1=A,E+1=B,L=C,E+1=D,O=F,E=G,Q=H,E+1=J,E+1=K,E+1=M,E=N,E=P,E+1>=0] 2.55/2.54 2.55/2.54 * Chain [18]: 0 2.55/2.54 with precondition: [I=3,D=A,L=C,G=E,O=F,Q=H,D=J,B=K,D=M,G=N,G=P+1,G+1>=B,B>=D,G>=D,2*D>=G+1] 2.55/2.54 2.55/2.54 * Chain [17]: 0 2.55/2.54 with precondition: [I=4,D=A,G=E,G+1>=B,B>=D,2*D>=G+1] 2.55/2.54 2.55/2.54 2.55/2.54 #### Cost of chains of lbl82(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q): 2.55/2.54 * Chain [[20,21,22],26]: 1*it(20)+1*it(21)+1*it(22)+1*s(3)+0 2.55/2.54 Such that:aux(24) =< -D-E/2+G+N/2+1 2.55/2.54 aux(69) =< E 2.55/2.54 aux(12) =< -E/2+G+1/2 2.55/2.54 aux(24) =< -E/2+G+N/2-P 2.55/2.54 aux(73) =< E/2 2.55/2.54 it(20) =< E/2-N/2 2.55/2.54 aux(74) =< E-J 2.55/2.54 aux(75) =< E-N 2.55/2.54 aux(76) =< J 2.55/2.54 it(22) =< aux(75) 2.55/2.54 it(22) =< aux(74) 2.55/2.54 aux(35) =< aux(76) 2.55/2.54 it(22) =< aux(69) 2.55/2.54 s(3) =< aux(69) 2.55/2.54 s(3) =< aux(75) 2.55/2.54 aux(35) =< aux(73) 2.55/2.54 it(20) =< aux(73) 2.55/2.54 aux(53) =< aux(76) 2.55/2.54 aux(35) =< aux(76) 2.55/2.54 aux(44) =< it(22)*aux(76) 2.55/2.54 aux(11) =< it(22)*aux(76) 2.55/2.54 aux(30) =< it(20)*aux(76) 2.55/2.54 aux(10) =< it(20)*aux(76) 2.55/2.54 aux(54) =< it(22)*aux(53) 2.55/2.54 aux(11) =< it(22)*aux(53) 2.55/2.54 aux(23) =< aux(44) 2.55/2.54 aux(36) =< it(20)*aux(35) 2.55/2.54 aux(10) =< it(20)*aux(35) 2.55/2.54 aux(22) =< aux(30) 2.55/2.54 aux(23) =< aux(54) 2.55/2.54 aux(22) =< aux(36) 2.55/2.54 it(21) =< aux(11)+aux(10)+aux(12) 2.55/2.54 it(21) =< aux(23)+aux(22)+aux(24) 2.55/2.54 2.55/2.54 with precondition: [I=2,A=D,A=J,C=L,A=M,F=O,A=P+1,H=Q,G>=A,N>=A,2*A>=E,E>=G+1,E>=N] 2.55/2.54 2.55/2.54 * Chain [[20,21,22],25]: 1*it(20)+1*it(21)+2*it(22)+1*s(4)+0 2.55/2.54 Such that:aux(69) =< E 2.55/2.54 aux(12) =< -E/2+G+1/2 2.55/2.54 aux(73) =< E/2 2.55/2.54 it(20) =< E/2-M/2 2.55/2.54 aux(24) =< G-P 2.55/2.54 aux(77) =< E-M 2.55/2.54 aux(78) =< M 2.55/2.54 aux(24) =< aux(77) 2.55/2.54 it(20) =< aux(77) 2.55/2.54 it(22) =< aux(77) 2.55/2.54 s(4) =< aux(77) 2.55/2.54 aux(35) =< aux(78) 2.55/2.54 it(22) =< aux(69) 2.55/2.54 aux(35) =< aux(73) 2.55/2.54 it(20) =< aux(73) 2.55/2.54 aux(53) =< aux(78) 2.55/2.54 aux(35) =< aux(78) 2.55/2.54 aux(44) =< it(22)*aux(78) 2.55/2.54 aux(11) =< it(22)*aux(78) 2.55/2.54 aux(30) =< it(20)*aux(78) 2.55/2.54 aux(10) =< it(20)*aux(78) 2.55/2.54 aux(54) =< it(22)*aux(53) 2.55/2.54 aux(11) =< it(22)*aux(53) 2.55/2.54 aux(23) =< aux(44) 2.55/2.54 aux(36) =< it(20)*aux(35) 2.55/2.54 aux(10) =< it(20)*aux(35) 2.55/2.54 aux(22) =< aux(30) 2.55/2.54 aux(23) =< aux(54) 2.55/2.54 aux(22) =< aux(36) 2.55/2.54 it(21) =< aux(11)+aux(10)+aux(12) 2.55/2.54 it(21) =< aux(23)+aux(22)+aux(24) 2.55/2.54 2.55/2.54 with precondition: [I=2,A=D,A=J,A=K,C=L,A=M,A=N+1,F=O,A=P+1,H=Q,E>=A+2,G>=A,2*A>=E,E>=G+1] 2.55/2.54 2.55/2.54 * Chain [[20,21,22],24]: 1*it(20)+1*it(21)+2*it(22)+0 2.55/2.54 Such that:aux(24) =< -A+G+1 2.55/2.54 aux(24) =< -D+G+1 2.55/2.54 it(20) =< -D/2+E/2 2.55/2.54 aux(69) =< E 2.55/2.54 aux(12) =< -E/2+G+1/2 2.55/2.54 aux(73) =< E/2 2.55/2.54 aux(79) =< -D+E 2.55/2.54 aux(80) =< D 2.55/2.54 it(22) =< aux(79) 2.55/2.54 aux(35) =< aux(80) 2.55/2.54 it(22) =< aux(69) 2.55/2.54 aux(35) =< aux(73) 2.55/2.54 it(20) =< aux(73) 2.55/2.54 aux(53) =< aux(80) 2.55/2.54 aux(35) =< aux(80) 2.55/2.54 aux(44) =< it(22)*aux(80) 2.55/2.54 aux(11) =< it(22)*aux(80) 2.55/2.54 aux(30) =< it(20)*aux(80) 2.55/2.54 aux(10) =< it(20)*aux(80) 2.55/2.54 aux(54) =< it(22)*aux(53) 2.55/2.54 aux(11) =< it(22)*aux(53) 2.55/2.54 aux(23) =< aux(44) 2.55/2.54 aux(36) =< it(20)*aux(35) 2.55/2.54 aux(10) =< it(20)*aux(35) 2.55/2.54 aux(22) =< aux(30) 2.55/2.54 aux(23) =< aux(54) 2.55/2.54 aux(22) =< aux(36) 2.55/2.54 it(21) =< aux(11)+aux(10)+aux(12) 2.55/2.54 it(21) =< aux(23)+aux(22)+aux(24) 2.55/2.54 2.55/2.54 with precondition: [I=4,A=D,G>=A,2*A>=E,E>=G+1] 2.55/2.54 2.55/2.54 * Chain [[20,21,22],23]: 1*it(20)+1*it(21)+2*it(22)+1*s(5)+0 2.55/2.54 Such that:aux(24) =< -A+G 2.55/2.54 aux(24) =< -D+G 2.55/2.54 it(20) =< -D/2+E/2 2.55/2.54 aux(69) =< E 2.55/2.54 aux(12) =< -E/2+G+1/2 2.55/2.54 aux(73) =< E/2 2.55/2.54 aux(81) =< -D+E 2.55/2.54 aux(82) =< D 2.55/2.54 it(20) =< aux(81) 2.55/2.54 it(22) =< aux(81) 2.55/2.54 s(5) =< aux(81) 2.55/2.54 aux(35) =< aux(82) 2.55/2.54 it(22) =< aux(69) 2.55/2.54 aux(35) =< aux(73) 2.55/2.54 it(20) =< aux(73) 2.55/2.54 aux(53) =< aux(82) 2.55/2.54 aux(35) =< aux(82) 2.55/2.54 aux(44) =< it(22)*aux(82) 2.55/2.54 aux(11) =< it(22)*aux(82) 2.55/2.54 aux(30) =< it(20)*aux(82) 2.55/2.54 aux(10) =< it(20)*aux(82) 2.55/2.54 aux(54) =< it(22)*aux(53) 2.55/2.54 aux(11) =< it(22)*aux(53) 2.55/2.54 aux(23) =< aux(44) 2.55/2.54 aux(36) =< it(20)*aux(35) 2.55/2.54 aux(10) =< it(20)*aux(35) 2.55/2.54 aux(22) =< aux(30) 2.55/2.54 aux(23) =< aux(54) 2.55/2.54 aux(22) =< aux(36) 2.55/2.54 it(21) =< aux(11)+aux(10)+aux(12) 2.55/2.54 it(21) =< aux(23)+aux(22)+aux(24) 2.55/2.54 2.55/2.54 with precondition: [I=4,A=D,E>=A+2,G>=A,2*A>=E,E>=G+1] 2.55/2.54 2.55/2.54 * Chain [26]: 0 2.55/2.54 with precondition: [I=2,K=B,L=C,A=D,O=F,A=G+1,Q=H,A=J,A=M,E=N,A=P+1,E>=A,2*A>=E] 2.55/2.54 2.55/2.54 * Chain [25]: 1*s(4)+0 2.55/2.54 Such that:s(4) =< -D+E 2.55/2.54 2.55/2.54 with precondition: [I=2,L=C,A=D,O=F,Q=H,A=J,A=K,A=M,A=N+1,A=P+1,G>=A,2*A>=E,E>=G+1] 2.55/2.54 2.55/2.54 * Chain [24]: 0 2.55/2.54 with precondition: [I=4] 2.55/2.54 2.55/2.54 * Chain [23]: 1*s(5)+0 2.55/2.55 Such that:s(5) =< -D+E 2.55/2.55 2.55/2.55 with precondition: [I=4,A=D,G>=A,2*A>=E,E>=G+1] 2.55/2.55 2.55/2.55 2.55/2.55 #### Cost of chains of lbl82_loop_cont(A,B,C,D,E,F,G,H,I,J): 2.55/2.55 * Chain [28]: 0 2.55/2.55 with precondition: [A=2] 2.55/2.55 2.55/2.55 * Chain [27]: 0 2.55/2.55 with precondition: [A=4] 2.55/2.55 2.55/2.55 2.55/2.55 #### Cost of chains of start(A,B,C,D,E,F,G,H,I): 2.55/2.55 * Chain [36]: 0 2.55/2.55 with precondition: [A=0,D=0,C=B,F=E,H=G] 2.55/2.55 2.55/2.55 * Chain [35]: 1 2.55/2.55 with precondition: [A=1,D=1,C=B,F=E,H=G] 2.55/2.55 2.55/2.55 * Chain [34]: 0 2.55/2.55 with precondition: [D=A,C=B,F=E,H=G,0>=D+1] 2.55/2.55 2.55/2.55 * Chain [33]: 0 2.55/2.55 with precondition: [D=A,C=B,F=E,H=G,D>=0] 2.55/2.55 2.55/2.55 * Chain [32]: 4*s(26)+1*s(33)+1*s(37)+1*s(39)+1*s(49)+1*s(52)+2*s(58)+1*s(69)+1 2.55/2.55 Such that:s(53) =< 2*A 2.55/2.55 s(52) =< A/2 2.55/2.55 aux(84) =< D 2.55/2.55 aux(85) =< 2*D 2.55/2.55 s(33) =< D/2 2.55/2.55 aux(87) =< A 2.55/2.55 s(26) =< aux(87) 2.55/2.55 s(58) =< aux(87) 2.55/2.55 s(59) =< aux(87) 2.55/2.55 s(58) =< s(53) 2.55/2.55 s(52) =< aux(87) 2.55/2.55 s(60) =< aux(87) 2.55/2.55 s(59) =< aux(87) 2.55/2.55 s(61) =< s(58)*aux(87) 2.55/2.55 s(62) =< s(58)*aux(87) 2.55/2.55 s(63) =< s(52)*aux(87) 2.55/2.55 s(64) =< s(52)*aux(87) 2.55/2.55 s(65) =< s(58)*s(60) 2.55/2.55 s(62) =< s(58)*s(60) 2.55/2.55 s(66) =< s(61) 2.55/2.55 s(67) =< s(52)*s(59) 2.55/2.55 s(64) =< s(52)*s(59) 2.55/2.55 s(68) =< s(63) 2.55/2.55 s(66) =< s(65) 2.55/2.55 s(68) =< s(67) 2.55/2.55 s(69) =< s(62)+s(64)+aux(87) 2.55/2.55 s(69) =< s(66)+s(68)+aux(87) 2.55/2.55 s(29) =< aux(84) 2.55/2.55 s(33) =< aux(84) 2.55/2.55 s(29) =< aux(85) 2.55/2.55 s(37) =< s(29) 2.55/2.55 s(37) =< aux(84) 2.55/2.55 s(38) =< aux(84) 2.55/2.55 s(37) =< aux(85) 2.55/2.55 s(39) =< aux(85) 2.55/2.55 s(39) =< s(29) 2.55/2.55 s(40) =< aux(84) 2.55/2.55 s(38) =< aux(84) 2.55/2.55 s(41) =< s(37)*aux(84) 2.55/2.55 s(42) =< s(37)*aux(84) 2.55/2.55 s(43) =< s(33)*aux(84) 2.55/2.55 s(44) =< s(33)*aux(84) 2.55/2.55 s(45) =< s(37)*s(40) 2.55/2.55 s(42) =< s(37)*s(40) 2.55/2.55 s(46) =< s(41) 2.55/2.55 s(47) =< s(33)*s(38) 2.55/2.55 s(44) =< s(33)*s(38) 2.55/2.55 s(48) =< s(43) 2.55/2.55 s(46) =< s(45) 2.55/2.55 s(48) =< s(47) 2.55/2.55 s(49) =< s(42)+s(44)+aux(84) 2.55/2.55 s(49) =< s(46)+s(48)+s(29) 2.55/2.55 2.55/2.55 with precondition: [D=A,C=B,F=E,H=G,D>=1] 2.55/2.55 2.55/2.55 * Chain [31]: 3*s(70)+4*s(75)+1*s(79)+1*s(81)+1*s(91)+3*s(99)+6*s(100)+3*s(111)+1 2.55/2.55 Such that:aux(93) =< A 2.55/2.55 aux(94) =< D 2.55/2.55 aux(95) =< 2*D 2.55/2.55 aux(96) =< D/2 2.55/2.55 s(70) =< aux(93) 2.55/2.55 s(75) =< aux(96) 2.55/2.55 s(99) =< aux(94) 2.55/2.55 s(100) =< aux(94) 2.55/2.55 s(80) =< aux(94) 2.55/2.55 s(100) =< aux(95) 2.55/2.55 s(75) =< aux(94) 2.55/2.55 s(82) =< aux(94) 2.55/2.55 s(80) =< aux(94) 2.55/2.55 s(103) =< s(100)*aux(94) 2.55/2.55 s(104) =< s(100)*aux(94) 2.55/2.55 s(85) =< s(75)*aux(94) 2.55/2.55 s(86) =< s(75)*aux(94) 2.55/2.55 s(107) =< s(100)*s(82) 2.55/2.55 s(104) =< s(100)*s(82) 2.55/2.55 s(108) =< s(103) 2.55/2.55 s(89) =< s(75)*s(80) 2.55/2.55 s(86) =< s(75)*s(80) 2.55/2.55 s(90) =< s(85) 2.55/2.55 s(108) =< s(107) 2.55/2.55 s(90) =< s(89) 2.55/2.55 s(111) =< s(104)+s(86)+aux(94) 2.55/2.55 s(111) =< s(108)+s(90)+aux(94) 2.55/2.55 s(71) =< aux(94) 2.55/2.55 s(71) =< aux(95) 2.55/2.55 s(79) =< s(71) 2.55/2.55 s(79) =< aux(94) 2.55/2.55 s(79) =< aux(95) 2.55/2.55 s(81) =< aux(95) 2.55/2.55 s(81) =< s(71) 2.55/2.55 s(83) =< s(79)*aux(94) 2.55/2.55 s(84) =< s(79)*aux(94) 2.55/2.55 s(87) =< s(79)*s(82) 2.55/2.55 s(84) =< s(79)*s(82) 2.55/2.55 s(88) =< s(83) 2.55/2.55 s(88) =< s(87) 2.55/2.55 s(91) =< s(84)+s(86)+aux(94) 2.55/2.55 s(91) =< s(88)+s(90)+s(71) 2.55/2.55 2.55/2.55 with precondition: [D=A,C=B,F=E,H=G,D>=2] 2.55/2.55 2.55/2.55 * Chain [30]: 2*s(157)+8*s(161)+6*s(162)+2*s(173)+1*s(201)+1*s(207)+1*s(217)+1*s(221)+1*s(238)+1 2.55/2.55 Such that:aux(104) =< D 2.55/2.55 aux(105) =< 2*D 2.55/2.55 aux(106) =< D/2 2.55/2.55 s(157) =< aux(106) 2.55/2.55 s(221) =< aux(106) 2.55/2.55 s(162) =< aux(104) 2.55/2.55 s(161) =< aux(104) 2.55/2.55 s(197) =< aux(104) 2.55/2.55 s(201) =< aux(104) 2.55/2.55 s(161) =< aux(105) 2.55/2.55 s(197) =< aux(105) 2.55/2.55 s(206) =< aux(104) 2.55/2.55 s(207) =< aux(105) 2.55/2.55 s(206) =< s(197) 2.55/2.55 s(201) =< s(197) 2.55/2.55 s(164) =< aux(104) 2.55/2.55 s(206) =< aux(104) 2.55/2.55 s(165) =< s(161)*aux(104) 2.55/2.55 s(166) =< s(161)*aux(104) 2.55/2.55 s(211) =< s(201)*aux(104) 2.55/2.55 s(212) =< s(201)*aux(104) 2.55/2.55 s(169) =< s(161)*s(164) 2.55/2.55 s(166) =< s(161)*s(164) 2.55/2.55 s(170) =< s(165) 2.55/2.55 s(215) =< s(201)*s(206) 2.55/2.55 s(212) =< s(201)*s(206) 2.55/2.55 s(216) =< s(211) 2.55/2.55 s(170) =< s(169) 2.55/2.55 s(216) =< s(215) 2.55/2.55 s(217) =< s(166)+s(212)+s(197) 2.55/2.55 s(217) =< s(170)+s(216)+s(197) 2.55/2.55 s(157) =< aux(104) 2.55/2.55 s(163) =< aux(104) 2.55/2.55 s(163) =< aux(104) 2.55/2.55 s(167) =< s(157)*aux(104) 2.55/2.55 s(168) =< s(157)*aux(104) 2.55/2.55 s(171) =< s(157)*s(163) 2.55/2.55 s(168) =< s(157)*s(163) 2.55/2.55 s(172) =< s(167) 2.55/2.55 s(172) =< s(171) 2.55/2.55 s(173) =< s(166)+s(168)+aux(104) 2.55/2.55 s(173) =< s(170)+s(172)+aux(104) 2.55/2.55 s(221) =< aux(104) 2.55/2.55 s(221) =< s(197) 2.55/2.55 s(232) =< s(221)*aux(104) 2.55/2.55 s(233) =< s(221)*aux(104) 2.55/2.55 s(236) =< s(221)*s(206) 2.55/2.55 s(233) =< s(221)*s(206) 2.55/2.55 s(237) =< s(232) 2.55/2.55 s(237) =< s(236) 2.55/2.55 s(238) =< s(166)+s(233)+s(197) 2.55/2.55 s(238) =< s(170)+s(237)+aux(104) 2.55/2.55 2.55/2.55 with precondition: [D=A,C=B,F=E,H=G,D>=3] 2.55/2.55 2.55/2.55 * Chain [29]: 5*s(239)+2*s(243)+3*s(248)+2*s(259)+1 2.55/2.55 Such that:aux(111) =< D 2.55/2.55 aux(112) =< 2*D 2.55/2.55 aux(113) =< D/2 2.55/2.55 s(243) =< aux(113) 2.55/2.55 s(239) =< aux(111) 2.55/2.55 s(241) =< aux(111) 2.55/2.55 s(243) =< aux(111) 2.55/2.55 s(239) =< aux(112) 2.55/2.55 s(241) =< aux(112) 2.55/2.55 s(248) =< aux(111) 2.55/2.55 s(249) =< aux(111) 2.55/2.55 s(249) =< s(241) 2.55/2.55 s(243) =< s(241) 2.55/2.55 s(250) =< aux(111) 2.55/2.55 s(249) =< aux(111) 2.55/2.55 s(251) =< s(239)*aux(111) 2.55/2.55 s(252) =< s(239)*aux(111) 2.55/2.55 s(253) =< s(243)*aux(111) 2.55/2.55 s(254) =< s(243)*aux(111) 2.55/2.55 s(255) =< s(239)*s(250) 2.55/2.55 s(252) =< s(239)*s(250) 2.55/2.55 s(256) =< s(251) 2.55/2.55 s(257) =< s(243)*s(249) 2.55/2.55 s(254) =< s(243)*s(249) 2.55/2.55 s(258) =< s(253) 2.55/2.55 s(256) =< s(255) 2.55/2.55 s(258) =< s(257) 2.55/2.55 s(259) =< s(252)+s(254)+s(241) 2.55/2.55 s(259) =< s(256)+s(258)+aux(111) 2.55/2.55 2.55/2.55 with precondition: [D=A,C=B,F=E,H=G,D>=4] 2.55/2.55 2.55/2.55 2.55/2.55 #### Cost of chains of start0(A,B,C,D,E,F,G,H,I): 2.55/2.55 * Chain [44]: 0 2.55/2.55 with precondition: [A=0] 2.55/2.55 2.55/2.55 * Chain [43]: 1 2.55/2.55 with precondition: [A=1] 2.55/2.55 2.55/2.55 * Chain [42]: 0 2.55/2.55 with precondition: [0>=A+1] 2.55/2.55 2.55/2.55 * Chain [41]: 0 2.55/2.55 with precondition: [A>=0] 2.55/2.55 2.55/2.55 * Chain [40]: 2*s(282)+4*s(287)+2*s(288)+1*s(299)+1*s(301)+1*s(303)+1*s(313)+1 2.55/2.55 Such that:aux(114) =< A 2.55/2.55 aux(115) =< 2*A 2.55/2.55 aux(116) =< A/2 2.55/2.55 s(282) =< aux(116) 2.55/2.55 s(287) =< aux(114) 2.55/2.55 s(288) =< aux(114) 2.55/2.55 s(289) =< aux(114) 2.55/2.55 s(288) =< aux(115) 2.55/2.55 s(282) =< aux(114) 2.55/2.55 s(290) =< aux(114) 2.55/2.55 s(289) =< aux(114) 2.55/2.55 s(291) =< s(288)*aux(114) 2.55/2.55 s(292) =< s(288)*aux(114) 2.55/2.55 s(293) =< s(282)*aux(114) 2.55/2.55 s(294) =< s(282)*aux(114) 2.55/2.55 s(295) =< s(288)*s(290) 2.55/2.55 s(292) =< s(288)*s(290) 2.55/2.55 s(296) =< s(291) 2.55/2.55 s(297) =< s(282)*s(289) 2.55/2.55 s(294) =< s(282)*s(289) 2.55/2.55 s(298) =< s(293) 2.55/2.55 s(296) =< s(295) 2.55/2.55 s(298) =< s(297) 2.55/2.55 s(299) =< s(292)+s(294)+aux(114) 2.55/2.55 s(299) =< s(296)+s(298)+aux(114) 2.55/2.55 s(300) =< aux(114) 2.55/2.55 s(300) =< aux(115) 2.55/2.55 s(301) =< s(300) 2.55/2.55 s(301) =< aux(114) 2.55/2.55 s(301) =< aux(115) 2.55/2.55 s(303) =< aux(115) 2.55/2.55 s(303) =< s(300) 2.55/2.55 s(305) =< s(301)*aux(114) 2.55/2.55 s(306) =< s(301)*aux(114) 2.55/2.55 s(309) =< s(301)*s(290) 2.55/2.55 s(306) =< s(301)*s(290) 2.55/2.55 s(310) =< s(305) 2.55/2.55 s(310) =< s(309) 2.55/2.55 s(313) =< s(306)+s(294)+aux(114) 2.55/2.55 s(313) =< s(310)+s(298)+s(300) 2.55/2.55 2.55/2.55 with precondition: [A>=1] 2.55/2.55 2.55/2.55 * Chain [39]: 6*s(318)+4*s(319)+6*s(321)+3*s(332)+1*s(334)+1*s(335)+1*s(340)+1 2.55/2.55 Such that:s(316) =< 2*A 2.55/2.55 s(317) =< A/2 2.55/2.55 aux(117) =< A 2.55/2.55 s(318) =< aux(117) 2.55/2.55 s(319) =< s(317) 2.55/2.55 s(321) =< aux(117) 2.55/2.55 s(322) =< aux(117) 2.55/2.55 s(321) =< s(316) 2.55/2.55 s(319) =< aux(117) 2.55/2.55 s(323) =< aux(117) 2.55/2.55 s(322) =< aux(117) 2.55/2.55 s(324) =< s(321)*aux(117) 2.55/2.55 s(325) =< s(321)*aux(117) 2.55/2.55 s(326) =< s(319)*aux(117) 2.55/2.55 s(327) =< s(319)*aux(117) 2.55/2.55 s(328) =< s(321)*s(323) 2.55/2.55 s(325) =< s(321)*s(323) 2.55/2.55 s(329) =< s(324) 2.55/2.55 s(330) =< s(319)*s(322) 2.55/2.55 s(327) =< s(319)*s(322) 2.55/2.55 s(331) =< s(326) 2.55/2.55 s(329) =< s(328) 2.55/2.55 s(331) =< s(330) 2.55/2.55 s(332) =< s(325)+s(327)+aux(117) 2.55/2.55 s(332) =< s(329)+s(331)+aux(117) 2.55/2.55 s(333) =< aux(117) 2.55/2.55 s(333) =< s(316) 2.55/2.55 s(334) =< s(333) 2.55/2.55 s(334) =< aux(117) 2.55/2.55 s(334) =< s(316) 2.55/2.55 s(335) =< s(316) 2.55/2.55 s(335) =< s(333) 2.55/2.55 s(336) =< s(334)*aux(117) 2.55/2.55 s(337) =< s(334)*aux(117) 2.55/2.55 s(338) =< s(334)*s(323) 2.55/2.55 s(337) =< s(334)*s(323) 2.55/2.55 s(339) =< s(336) 2.55/2.55 s(339) =< s(338) 2.55/2.55 s(340) =< s(337)+s(327)+aux(117) 2.55/2.55 s(340) =< s(339)+s(331)+s(333) 2.55/2.55 2.55/2.55 with precondition: [A>=2] 2.55/2.55 2.55/2.55 * Chain [38]: 2*s(344)+1*s(345)+6*s(346)+8*s(347)+1*s(349)+1*s(351)+1*s(361)+2*s(367)+1*s(372)+1 2.55/2.55 Such that:s(341) =< A 2.55/2.55 s(342) =< 2*A 2.55/2.55 s(343) =< A/2 2.55/2.55 s(344) =< s(343) 2.55/2.55 s(345) =< s(343) 2.55/2.55 s(346) =< s(341) 2.55/2.55 s(347) =< s(341) 2.55/2.55 s(348) =< s(341) 2.55/2.55 s(349) =< s(341) 2.55/2.55 s(347) =< s(342) 2.55/2.55 s(348) =< s(342) 2.55/2.55 s(350) =< s(341) 2.55/2.55 s(351) =< s(342) 2.55/2.55 s(350) =< s(348) 2.55/2.55 s(349) =< s(348) 2.55/2.55 s(352) =< s(341) 2.55/2.55 s(350) =< s(341) 2.55/2.55 s(353) =< s(347)*s(341) 2.55/2.55 s(354) =< s(347)*s(341) 2.55/2.55 s(355) =< s(349)*s(341) 2.55/2.55 s(356) =< s(349)*s(341) 2.55/2.55 s(357) =< s(347)*s(352) 2.55/2.55 s(354) =< s(347)*s(352) 2.55/2.55 s(358) =< s(353) 2.55/2.55 s(359) =< s(349)*s(350) 2.55/2.55 s(356) =< s(349)*s(350) 2.55/2.55 s(360) =< s(355) 2.55/2.55 s(358) =< s(357) 2.55/2.55 s(360) =< s(359) 2.55/2.55 s(361) =< s(354)+s(356)+s(348) 2.55/2.55 s(361) =< s(358)+s(360)+s(348) 2.55/2.55 s(344) =< s(341) 2.55/2.55 s(362) =< s(341) 2.55/2.55 s(362) =< s(341) 2.55/2.55 s(363) =< s(344)*s(341) 2.55/2.55 s(364) =< s(344)*s(341) 2.55/2.55 s(365) =< s(344)*s(362) 2.55/2.55 s(364) =< s(344)*s(362) 2.55/2.55 s(366) =< s(363) 2.55/2.55 s(366) =< s(365) 2.55/2.55 s(367) =< s(354)+s(364)+s(341) 2.55/2.55 s(367) =< s(358)+s(366)+s(341) 2.55/2.55 s(345) =< s(341) 2.55/2.55 s(345) =< s(348) 2.55/2.55 s(368) =< s(345)*s(341) 2.55/2.55 s(369) =< s(345)*s(341) 2.55/2.55 s(370) =< s(345)*s(350) 2.55/2.55 s(369) =< s(345)*s(350) 2.55/2.55 s(371) =< s(368) 2.55/2.55 s(371) =< s(370) 2.55/2.55 s(372) =< s(354)+s(369)+s(348) 2.55/2.55 s(372) =< s(358)+s(371)+s(341) 2.55/2.55 2.55/2.55 with precondition: [A>=3] 2.55/2.55 2.55/2.55 * Chain [37]: 2*s(376)+5*s(377)+3*s(379)+2*s(390)+1 2.55/2.55 Such that:s(373) =< A 2.55/2.55 s(374) =< 2*A 2.55/2.55 s(375) =< A/2 2.55/2.55 s(376) =< s(375) 2.55/2.55 s(377) =< s(373) 2.55/2.55 s(378) =< s(373) 2.55/2.55 s(376) =< s(373) 2.55/2.55 s(377) =< s(374) 2.55/2.55 s(378) =< s(374) 2.55/2.55 s(379) =< s(373) 2.55/2.55 s(380) =< s(373) 2.55/2.55 s(380) =< s(378) 2.55/2.55 s(376) =< s(378) 2.55/2.55 s(381) =< s(373) 2.55/2.55 s(380) =< s(373) 2.55/2.55 s(382) =< s(377)*s(373) 2.55/2.55 s(383) =< s(377)*s(373) 2.55/2.55 s(384) =< s(376)*s(373) 2.55/2.55 s(385) =< s(376)*s(373) 2.55/2.55 s(386) =< s(377)*s(381) 2.55/2.55 s(383) =< s(377)*s(381) 2.55/2.55 s(387) =< s(382) 2.55/2.55 s(388) =< s(376)*s(380) 2.55/2.55 s(385) =< s(376)*s(380) 2.55/2.55 s(389) =< s(384) 2.55/2.55 s(387) =< s(386) 2.55/2.55 s(389) =< s(388) 2.55/2.55 s(390) =< s(383)+s(385)+s(378) 2.55/2.55 s(390) =< s(387)+s(389)+s(373) 2.55/2.55 2.55/2.55 with precondition: [A>=4] 2.55/2.55 2.55/2.55 2.55/2.55 Closed-form bounds of start0(A,B,C,D,E,F,G,H,I): 2.55/2.55 ------------------------------------- 2.55/2.55 * Chain [44] with precondition: [A=0] 2.55/2.55 - Upper bound: 0 2.55/2.55 - Complexity: constant 2.55/2.55 * Chain [43] with precondition: [A=1] 2.55/2.55 - Upper bound: 1 2.55/2.55 - Complexity: constant 2.55/2.55 * Chain [42] with precondition: [0>=A+1] 2.55/2.55 - Upper bound: 0 2.55/2.55 - Complexity: constant 2.55/2.55 * Chain [41] with precondition: [A>=0] 2.55/2.55 - Upper bound: 0 2.55/2.55 - Complexity: constant 2.55/2.55 * Chain [40] with precondition: [A>=1] 2.55/2.55 - Upper bound: 9*A+1+2*A*A+A/2*(2*A)+2*A+A 2.55/2.55 - Complexity: n^2 2.55/2.55 * Chain [39] with precondition: [A>=2] 2.55/2.55 - Upper bound: 17*A+1+4*A*A+A/2*(4*A)+2*A+2*A 2.55/2.55 - Complexity: n^2 2.55/2.55 * Chain [38] with precondition: [A>=3] 2.55/2.55 - Upper bound: 19*A+1+5*A*A+A/2*(3*A)+2*A+3/2*A 2.55/2.55 - Complexity: n^2 2.55/2.55 * Chain [37] with precondition: [A>=4] 2.55/2.55 - Upper bound: 10*A+1+2*A*A+A/2*(2*A)+A 2.55/2.55 - Complexity: n^2 2.55/2.55 2.55/2.55 ### Maximum cost of start0(A,B,C,D,E,F,G,H,I): nat(A)*2*nat(A)+nat(A)*9+nat(A)*2*nat(A/2)+nat(A/2)*2+max([nat(2*A),nat(A)*2*nat(A)+nat(A)*7+nat(A/2)*nat(A)+nat(2*A)+nat(A/2)+max([nat(A)*nat(A)+nat(A)*2,nat(A/2)*nat(A)+nat(A/2)])+nat(A)])+1 2.55/2.55 Asymptotic class: n^2 2.55/2.55 * Total analysis performed in 2354 ms. 2.55/2.55 2.55/2.65 EOF