0.78/0.86 WORST_CASE(?,O(n^4)) 0.78/0.86 0.78/0.86 Preprocessing Cost Relations 0.78/0.86 ===================================== 0.78/0.86 0.78/0.86 #### Computed strongly connected components 0.78/0.86 0. recursive : [evalfbb3in/4,evalfbb4in/4] 0.78/0.86 1. recursive : [evalfbb4in_loop_cont/8,evalfbb5in/7,evalfbb6in/7] 0.78/0.86 2. recursive : [evalfbb6in_loop_cont/10,evalfbb7in/9,evalfbb8in/9] 0.78/0.86 3. recursive : [evalfbb10in/10,evalfbb8in_loop_cont/11,evalfbb9in/10] 0.78/0.86 4. non_recursive : [evalfstop/6] 0.78/0.86 5. non_recursive : [evalfreturnin/6] 0.78/0.86 6. non_recursive : [exit_location/1] 0.78/0.86 7. non_recursive : [evalfbb10in_loop_cont/7] 0.78/0.86 8. non_recursive : [evalfentryin/6] 0.78/0.86 9. non_recursive : [evalfstart/6] 0.78/0.86 0.78/0.86 #### Obtained direct recursion through partial evaluation 0.78/0.86 0. SCC is partially evaluated into evalfbb4in/4 0.78/0.86 1. SCC is partially evaluated into evalfbb6in/7 0.78/0.86 2. SCC is partially evaluated into evalfbb8in/9 0.78/0.86 3. SCC is partially evaluated into evalfbb10in/10 0.78/0.86 4. SCC is completely evaluated into other SCCs 0.78/0.86 5. SCC is completely evaluated into other SCCs 0.78/0.86 6. SCC is completely evaluated into other SCCs 0.78/0.86 7. SCC is partially evaluated into evalfbb10in_loop_cont/7 0.78/0.86 8. SCC is partially evaluated into evalfentryin/6 0.78/0.86 9. SCC is partially evaluated into evalfstart/6 0.78/0.86 0.78/0.86 Control-Flow Refinement of Cost Relations 0.78/0.86 ===================================== 0.78/0.86 0.78/0.86 ### Specialization of cost equations evalfbb4in/4 0.78/0.86 * CE 19 is refined into CE [20] 0.78/0.86 * CE 18 is refined into CE [21] 0.78/0.86 * CE 17 is refined into CE [22] 0.78/0.86 0.78/0.86 0.78/0.86 ### Cost equations --> "Loop" of evalfbb4in/4 0.78/0.86 * CEs [22] --> Loop 20 0.78/0.86 * CEs [20] --> Loop 21 0.78/0.86 * CEs [21] --> Loop 22 0.78/0.86 0.78/0.86 ### Ranking functions of CR evalfbb4in(D,E,F,G) 0.78/0.86 * RF of phase [20]: [D-E+1] 0.78/0.86 0.78/0.86 #### Partial ranking functions of CR evalfbb4in(D,E,F,G) 0.78/0.86 * Partial RF of phase [20]: 0.78/0.86 - RF of loop [20:1]: 0.78/0.86 D-E+1 0.78/0.86 0.78/0.86 0.78/0.86 ### Specialization of cost equations evalfbb6in/7 0.78/0.86 * CE 15 is refined into CE [23] 0.78/0.86 * CE 13 is refined into CE [24,25] 0.78/0.86 * CE 16 is refined into CE [26] 0.78/0.86 * CE 14 is refined into CE [27] 0.78/0.86 0.78/0.86 0.78/0.86 ### Cost equations --> "Loop" of evalfbb6in/7 0.78/0.86 * CEs [27] --> Loop 23 0.78/0.86 * CEs [23] --> Loop 24 0.78/0.86 * CEs [24,25] --> Loop 25 0.78/0.86 * CEs [26] --> Loop 26 0.78/0.86 0.78/0.86 ### Ranking functions of CR evalfbb6in(B,C,D,E,F,G,H) 0.78/0.86 * RF of phase [23]: [B+C-D+1] 0.78/0.86 0.78/0.86 #### Partial ranking functions of CR evalfbb6in(B,C,D,E,F,G,H) 0.78/0.86 * Partial RF of phase [23]: 0.78/0.86 - RF of loop [23:1]: 0.78/0.86 B+C-D+1 0.78/0.86 0.78/0.86 0.78/0.86 ### Specialization of cost equations evalfbb8in/9 0.78/0.86 * CE 11 is refined into CE [28] 0.78/0.86 * CE 9 is refined into CE [29,30,31] 0.78/0.86 * CE 12 is refined into CE [32] 0.78/0.86 * CE 10 is refined into CE [33] 0.78/0.86 0.78/0.86 0.78/0.86 ### Cost equations --> "Loop" of evalfbb8in/9 0.78/0.86 * CEs [33] --> Loop 27 0.78/0.86 * CEs [28] --> Loop 28 0.78/0.86 * CEs [29,30,31] --> Loop 29 0.78/0.86 * CEs [32] --> Loop 30 0.78/0.86 0.78/0.86 ### Ranking functions of CR evalfbb8in(A,B,C,D,E,F,G,H,I) 0.78/0.86 * RF of phase [27]: [A-C+1] 0.78/0.86 0.78/0.86 #### Partial ranking functions of CR evalfbb8in(A,B,C,D,E,F,G,H,I) 0.78/0.86 * Partial RF of phase [27]: 0.78/0.86 - RF of loop [27:1]: 0.78/0.86 A-C+1 0.78/0.86 0.78/0.86 0.78/0.86 ### Specialization of cost equations evalfbb10in/10 0.78/0.86 * CE 5 is refined into CE [34] 0.78/0.86 * CE 3 is refined into CE [35,36,37] 0.78/0.86 * CE 6 is refined into CE [38] 0.78/0.86 * CE 4 is refined into CE [39,40] 0.78/0.86 0.78/0.86 0.78/0.86 ### Cost equations --> "Loop" of evalfbb10in/10 0.78/0.86 * CEs [40] --> Loop 31 0.78/0.86 * CEs [39] --> Loop 32 0.78/0.86 * CEs [34] --> Loop 33 0.78/0.86 * CEs [35] --> Loop 34 0.78/0.86 * CEs [37] --> Loop 35 0.78/0.86 * CEs [36] --> Loop 36 0.78/0.86 * CEs [38] --> Loop 37 0.78/0.86 0.78/0.86 ### Ranking functions of CR evalfbb10in(A,B,C,D,E,F,G,H,I,J) 0.78/0.86 * RF of phase [31]: [B] 0.78/0.86 * RF of phase [32]: [B] 0.78/0.86 0.78/0.86 #### Partial ranking functions of CR evalfbb10in(A,B,C,D,E,F,G,H,I,J) 0.78/0.86 * Partial RF of phase [31]: 0.78/0.86 - RF of loop [31:1]: 0.78/0.86 B 0.78/0.86 * Partial RF of phase [32]: 0.78/0.86 - RF of loop [32:1]: 0.78/0.86 B 0.78/0.86 0.78/0.86 0.78/0.86 ### Specialization of cost equations evalfbb10in_loop_cont/7 0.78/0.86 * CE 7 is refined into CE [41] 0.78/0.86 * CE 8 is refined into CE [42] 0.78/0.86 0.78/0.86 0.78/0.86 ### Cost equations --> "Loop" of evalfbb10in_loop_cont/7 0.78/0.86 * CEs [41] --> Loop 38 0.78/0.86 * CEs [42] --> Loop 39 0.78/0.86 0.78/0.86 ### Ranking functions of CR evalfbb10in_loop_cont(A,B,C,D,E,F,G) 0.78/0.86 0.78/0.86 #### Partial ranking functions of CR evalfbb10in_loop_cont(A,B,C,D,E,F,G) 0.78/0.86 0.78/0.86 0.78/0.86 ### Specialization of cost equations evalfentryin/6 0.78/0.86 * CE 2 is refined into CE [43,44,45,46,47,48,49,50,51,52,53] 0.78/0.86 0.78/0.86 0.78/0.86 ### Cost equations --> "Loop" of evalfentryin/6 0.78/0.86 * CEs [49] --> Loop 40 0.78/0.86 * CEs [47] --> Loop 41 0.78/0.86 * CEs [48] --> Loop 42 0.78/0.86 * CEs [46,52] --> Loop 43 0.78/0.86 * CEs [50] --> Loop 44 0.78/0.86 * CEs [45] --> Loop 45 0.78/0.86 * CEs [44,51] --> Loop 46 0.78/0.86 * CEs [53] --> Loop 47 0.78/0.86 * CEs [43] --> Loop 48 0.78/0.86 0.78/0.86 ### Ranking functions of CR evalfentryin(A,B,C,D,E,F) 0.78/0.86 0.78/0.86 #### Partial ranking functions of CR evalfentryin(A,B,C,D,E,F) 0.78/0.86 0.78/0.86 0.78/0.86 ### Specialization of cost equations evalfstart/6 0.78/0.86 * CE 1 is refined into CE [54,55,56,57,58,59,60,61,62] 0.78/0.86 0.78/0.86 0.78/0.86 ### Cost equations --> "Loop" of evalfstart/6 0.78/0.86 * CEs [62] --> Loop 49 0.78/0.86 * CEs [61] --> Loop 50 0.78/0.86 * CEs [60] --> Loop 51 0.78/0.86 * CEs [59] --> Loop 52 0.78/0.86 * CEs [58] --> Loop 53 0.78/0.86 * CEs [57] --> Loop 54 0.78/0.86 * CEs [56] --> Loop 55 0.78/0.86 * CEs [55] --> Loop 56 0.78/0.86 * CEs [54] --> Loop 57 0.78/0.86 0.78/0.86 ### Ranking functions of CR evalfstart(A,B,C,D,E,F) 0.78/0.86 0.78/0.86 #### Partial ranking functions of CR evalfstart(A,B,C,D,E,F) 0.78/0.86 0.78/0.86 0.78/0.86 Computing Bounds 0.78/0.86 ===================================== 0.78/0.86 0.78/0.86 #### Cost of chains of evalfbb4in(D,E,F,G): 0.78/0.86 * Chain [[20],22]: 1*it(20)+0 0.78/0.86 Such that:it(20) =< -E+G 0.78/0.86 0.78/0.86 with precondition: [F=2,D+1=G,E>=1,D>=E] 0.78/0.86 0.78/0.86 * Chain [[20],21]: 1*it(20)+0 0.78/0.86 Such that:it(20) =< D-E+1 0.78/0.86 0.78/0.86 with precondition: [F=3,E>=1,D>=E] 0.78/0.86 0.78/0.86 * Chain [21]: 0 0.78/0.86 with precondition: [F=3,D>=1,E>=1] 0.78/0.86 0.78/0.86 0.78/0.86 #### Cost of chains of evalfbb6in(B,C,D,E,F,G,H): 0.78/0.86 * Chain [[23],26]: 1*it(23)+1*s(3)+0 0.78/0.86 Such that:aux(1) =< B+C+1 0.78/0.86 it(23) =< B+C-D+1 0.78/0.86 s(3) =< it(23)*aux(1) 0.78/0.86 0.78/0.86 with precondition: [F=3,B>=1,C>=1,D>=B,B+C>=D] 0.78/0.86 0.78/0.86 * Chain [[23],25]: 1*it(23)+1*s(3)+1*s(4)+0 0.78/0.86 Such that:s(4) =< B+C 0.78/0.86 aux(1) =< B+C+1 0.78/0.86 it(23) =< B+C-D 0.78/0.86 s(3) =< it(23)*aux(1) 0.78/0.86 0.78/0.86 with precondition: [F=3,B>=1,D>=B,B+C>=D+1] 0.78/0.86 0.78/0.86 * Chain [[23],24]: 1*it(23)+1*s(3)+0 0.78/0.86 Such that:it(23) =< -D+G 0.78/0.86 aux(1) =< G 0.78/0.86 s(3) =< it(23)*aux(1) 0.78/0.86 0.78/0.86 with precondition: [F=4,B+C+1=G,B+C+1=H,B>=1,C>=1,D>=B,B+C>=D] 0.78/0.86 0.78/0.86 * Chain [26]: 0 0.78/0.86 with precondition: [F=3,B>=1,C>=1,D>=B] 0.78/0.86 0.78/0.86 * Chain [25]: 1*s(4)+0 0.78/0.86 Such that:s(4) =< D 0.78/0.86 0.78/0.86 with precondition: [F=3,B>=1,C>=1,D>=B,B+C>=D] 0.78/0.86 0.78/0.86 0.78/0.86 #### Cost of chains of evalfbb8in(A,B,C,D,E,F,G,H,I): 0.78/0.86 * Chain [[27],30]: 1*it(27)+1*s(15)+1*s(16)+0 0.78/0.86 Such that:aux(2) =< A+1 0.78/0.86 s(12) =< A+B+1 0.78/0.86 it(27) =< A-C+1 0.78/0.86 s(15) =< it(27)*aux(2) 0.78/0.86 s(16) =< s(15)*s(12) 0.78/0.86 0.78/0.86 with precondition: [F=3,B>=1,C>=1,A>=C] 0.78/0.86 0.78/0.86 * Chain [[27],29]: 1*it(27)+1*s(15)+1*s(16)+1*s(18)+1*s(19)+1*s(20)+1*s(21)+1*s(23)+1*s(24)+0 0.78/0.86 Such that:s(23) =< A 0.78/0.86 s(21) =< A+B 0.78/0.86 it(27) =< A-C 0.78/0.86 s(19) =< B 0.78/0.86 aux(4) =< A+1 0.78/0.86 aux(5) =< A+B+1 0.78/0.86 s(18) =< aux(4) 0.78/0.86 s(20) =< s(18)*aux(5) 0.78/0.86 s(24) =< s(23)*aux(5) 0.78/0.86 s(15) =< it(27)*aux(4) 0.78/0.86 s(16) =< s(15)*aux(5) 0.78/0.86 0.78/0.86 with precondition: [F=3,B>=1,C>=1,A>=C+1] 0.78/0.86 0.78/0.86 * Chain [[27],28]: 1*it(27)+1*s(15)+1*s(16)+0 0.78/0.86 Such that:it(27) =< -C+G 0.78/0.86 aux(2) =< G 0.78/0.86 s(12) =< I 0.78/0.86 s(15) =< it(27)*aux(2) 0.78/0.86 s(16) =< s(15)*s(12) 0.78/0.86 0.78/0.86 with precondition: [F=5,A+1=G,A+B+1=H,A+B+1=I,B>=1,C>=1,A>=C] 0.78/0.86 0.78/0.86 * Chain [30]: 0 0.78/0.86 with precondition: [F=3,B>=1,C>=1] 0.78/0.86 0.78/0.86 * Chain [29]: 1*s(18)+1*s(19)+1*s(20)+1*s(21)+1*s(23)+1*s(24)+0 0.78/0.86 Such that:s(19) =< B 0.78/0.86 s(21) =< B+C 0.78/0.86 s(23) =< C 0.78/0.86 s(18) =< C+1 0.78/0.86 aux(3) =< B+C+1 0.78/0.86 s(20) =< s(18)*aux(3) 0.78/0.86 s(24) =< s(23)*aux(3) 0.78/0.86 0.78/0.86 with precondition: [F=3,B>=1,C>=1,A>=C] 0.78/0.86 0.78/0.86 * Chain [28]: 0 0.78/0.86 with precondition: [F=5,H=D,I=E,C=G,B>=1,C>=1,C>=A+1] 0.78/0.86 0.78/0.86 0.78/0.86 #### Cost of chains of evalfbb10in(A,B,C,D,E,F,G,H,I,J): 0.78/0.86 * Chain [[32],37]: 1*it(32)+0 0.78/0.86 Such that:it(32) =< B 0.78/0.86 0.78/0.86 with precondition: [F=3,0>=A,B>=1] 0.78/0.86 0.78/0.86 * Chain [[32],34]: 1*it(32)+0 0.78/0.86 Such that:it(32) =< B 0.78/0.86 0.78/0.86 with precondition: [F=3,0>=A,B>=2] 0.78/0.86 0.78/0.86 * Chain [[32],33]: 1*it(32)+0 0.78/0.86 Such that:it(32) =< B 0.78/0.86 0.78/0.86 with precondition: [F=6,G=0,H=1,D=I,E=J,0>=A,B>=1] 0.78/0.86 0.78/0.86 * Chain [[31],37]: 1*it(31)+1*s(47)+1*s(48)+1*s(49)+0 0.78/0.86 Such that:s(43) =< A+2 0.78/0.86 s(42) =< A+B+1 0.78/0.86 it(31) =< B 0.78/0.86 aux(7) =< s(43) 0.78/0.86 s(50) =< it(31)*aux(7) 0.78/0.86 s(47) =< s(50) 0.78/0.86 s(48) =< s(47)*s(43) 0.78/0.86 s(49) =< s(48)*s(42) 0.78/0.86 0.78/0.86 with precondition: [F=3,A>=1,B>=1] 0.78/0.86 0.78/0.86 * Chain [[31],36]: 1*it(31)+1*s(47)+1*s(48)+1*s(49)+1*s(53)+1*s(54)+1*s(55)+1*s(57)+1*s(58)+1*s(59)+1*s(60)+1*s(61)+1*s(62)+0 0.78/0.86 Such that:s(57) =< 1 0.78/0.86 s(58) =< 2 0.78/0.86 s(53) =< A 0.78/0.86 s(51) =< A+1 0.78/0.86 s(43) =< A+2 0.78/0.86 s(52) =< A+B 0.78/0.86 s(56) =< B+2 0.78/0.86 aux(8) =< A+B+1 0.78/0.86 aux(9) =< B 0.78/0.86 aux(10) =< B+1 0.78/0.86 it(31) =< aux(8) 0.78/0.86 s(52) =< aux(8) 0.78/0.86 it(31) =< aux(9) 0.78/0.86 s(54) =< aux(9) 0.78/0.86 s(55) =< aux(9) 0.78/0.86 s(55) =< aux(10) 0.78/0.86 s(56) =< aux(10) 0.78/0.86 s(59) =< s(53)*s(51) 0.78/0.86 s(60) =< s(59)*s(52) 0.78/0.86 s(61) =< s(58)*s(56) 0.78/0.86 s(62) =< s(57)*s(56) 0.78/0.86 aux(7) =< s(43) 0.78/0.86 s(50) =< it(31)*aux(7) 0.78/0.86 s(47) =< s(50) 0.78/0.86 s(48) =< s(47)*s(43) 0.78/0.86 s(49) =< s(48)*aux(8) 0.78/0.86 0.78/0.86 with precondition: [F=3,A>=1,B>=2] 0.78/0.86 0.78/0.86 * Chain [[31],35]: 1*it(31)+1*s(47)+1*s(48)+1*s(49)+2*s(63)+1*s(64)+1*s(66)+1*s(69)+1*s(70)+1*s(71)+1*s(72)+1*s(73)+0 0.78/0.86 Such that:aux(11) =< A 0.78/0.86 s(67) =< A+1 0.78/0.86 s(43) =< A+2 0.78/0.86 aux(12) =< A+B 0.78/0.86 aux(13) =< A+B+1 0.78/0.86 aux(14) =< B 0.78/0.86 it(31) =< aux(12) 0.78/0.86 s(64) =< aux(12) 0.78/0.86 s(68) =< aux(12) 0.78/0.86 s(68) =< aux(13) 0.78/0.86 it(31) =< aux(14) 0.78/0.86 s(66) =< aux(14) 0.78/0.86 s(63) =< aux(11) 0.78/0.86 s(69) =< s(67) 0.78/0.86 s(70) =< s(69)*s(68) 0.78/0.86 s(71) =< s(63)*s(68) 0.78/0.86 s(72) =< s(63)*s(67) 0.78/0.86 s(73) =< s(72)*s(68) 0.78/0.86 aux(7) =< s(43) 0.78/0.86 s(50) =< it(31)*aux(7) 0.78/0.86 s(47) =< s(50) 0.78/0.86 s(48) =< s(47)*s(43) 0.78/0.86 s(49) =< s(48)*aux(13) 0.78/0.86 0.78/0.86 with precondition: [F=3,A>=2,B>=2] 0.78/0.86 0.78/0.86 * Chain [[31],34]: 1*it(31)+1*s(47)+1*s(48)+1*s(49)+0 0.78/0.86 Such that:s(43) =< A+2 0.78/0.86 s(42) =< A+B+1 0.78/0.86 it(31) =< B 0.78/0.86 aux(7) =< s(43) 0.78/0.86 s(50) =< it(31)*aux(7) 0.78/0.86 s(47) =< s(50) 0.78/0.86 s(48) =< s(47)*s(43) 0.78/0.86 s(49) =< s(48)*s(42) 0.78/0.86 0.78/0.86 with precondition: [F=3,A>=1,B>=2] 0.78/0.86 0.78/0.86 * Chain [[31],33]: 1*it(31)+1*s(47)+1*s(48)+1*s(49)+0 0.78/0.86 Such that:it(31) =< B 0.78/0.86 s(42) =< B+J 0.78/0.86 s(43) =< J 0.78/0.86 aux(7) =< s(43) 0.78/0.86 s(50) =< it(31)*aux(7) 0.78/0.86 s(47) =< s(50) 0.78/0.86 s(48) =< s(47)*s(43) 0.78/0.86 s(49) =< s(48)*s(42) 0.78/0.86 0.78/0.86 with precondition: [F=6,G=0,A+1=H,A+2=I,A+2=J,A>=1,B>=1] 0.78/0.86 0.78/0.86 * Chain [37]: 0 0.78/0.86 with precondition: [F=3] 0.78/0.86 0.78/0.86 * Chain [36]: 1*s(53)+1*s(54)+1*s(55)+1*s(57)+1*s(58)+1*s(59)+1*s(60)+1*s(61)+1*s(62)+0 0.78/0.86 Such that:s(57) =< 1 0.78/0.86 s(58) =< 2 0.78/0.86 s(53) =< A 0.78/0.86 s(51) =< A+1 0.78/0.86 s(52) =< A+B+1 0.78/0.86 s(54) =< B 0.78/0.86 s(55) =< B+1 0.78/0.86 s(56) =< B+2 0.78/0.86 s(59) =< s(53)*s(51) 0.78/0.86 s(60) =< s(59)*s(52) 0.78/0.86 s(61) =< s(58)*s(56) 0.78/0.86 s(62) =< s(57)*s(56) 0.78/0.86 0.78/0.86 with precondition: [F=3,A>=1,B>=1] 0.78/0.86 0.78/0.86 * Chain [35]: 2*s(63)+1*s(64)+1*s(66)+1*s(69)+1*s(70)+1*s(71)+1*s(72)+1*s(73)+0 0.78/0.86 Such that:s(67) =< A+1 0.78/0.86 s(64) =< A+B 0.78/0.86 s(68) =< A+B+1 0.78/0.86 s(66) =< B 0.78/0.86 aux(11) =< A 0.78/0.86 s(63) =< aux(11) 0.78/0.86 s(69) =< s(67) 0.78/0.86 s(70) =< s(69)*s(68) 0.78/0.86 s(71) =< s(63)*s(68) 0.78/0.86 s(72) =< s(63)*s(67) 0.78/0.86 s(73) =< s(72)*s(68) 0.78/0.86 0.78/0.86 with precondition: [F=3,A>=2,B>=1] 0.78/0.86 0.78/0.86 * Chain [34]: 0 0.78/0.86 with precondition: [F=3,B>=1] 0.78/0.86 0.78/0.86 * Chain [33]: 0 0.78/0.86 with precondition: [F=6,H=C,I=D,J=E,B=G,0>=B] 0.78/0.86 0.78/0.86 0.78/0.86 #### Cost of chains of evalfbb10in_loop_cont(A,B,C,D,E,F,G): 0.78/0.86 * Chain [39]: 0 0.78/0.86 with precondition: [A=3] 0.78/0.86 0.78/0.86 * Chain [38]: 0 0.78/0.86 with precondition: [A=6] 0.78/0.86 0.78/0.86 0.78/0.86 #### Cost of chains of evalfentryin(A,B,C,D,E,F): 0.78/0.86 * Chain [48]: 0 0.78/0.86 with precondition: [] 0.78/0.86 0.78/0.86 * Chain [47]: 0 0.78/0.86 with precondition: [0>=A] 0.78/0.86 0.78/0.86 * Chain [46]: 2*s(124)+0 0.78/0.86 Such that:aux(20) =< A 0.78/0.86 s(124) =< aux(20) 0.78/0.86 0.78/0.86 with precondition: [0>=B,A>=1] 0.78/0.86 0.78/0.86 * Chain [45]: 1*s(126)+0 0.78/0.86 Such that:s(126) =< A 0.78/0.86 0.78/0.86 with precondition: [0>=B,A>=2] 0.78/0.86 0.78/0.86 * Chain [44]: 0 0.78/0.86 with precondition: [A>=1] 0.78/0.86 0.78/0.86 * Chain [43]: 1*s(127)+1*s(128)+1*s(129)+1*s(132)+3*s(136)+1*s(137)+1*s(138)+1*s(139)+1*s(140)+2*s(143)+2*s(144)+1*s(145)+1*s(153)+0 0.78/0.86 Such that:s(127) =< 1 0.78/0.86 s(128) =< 2 0.78/0.86 s(132) =< A+1 0.78/0.86 s(133) =< A+2 0.78/0.86 s(134) =< A+B+1 0.78/0.86 s(147) =< A+B+2 0.78/0.86 s(129) =< B 0.78/0.86 s(130) =< B+1 0.78/0.86 aux(21) =< A 0.78/0.86 aux(22) =< B+2 0.78/0.86 s(136) =< aux(21) 0.78/0.86 s(137) =< s(129)*s(130) 0.78/0.86 s(138) =< s(137)*s(134) 0.78/0.86 s(139) =< s(128)*s(133) 0.78/0.86 s(140) =< s(127)*s(133) 0.78/0.86 s(141) =< aux(22) 0.78/0.86 s(142) =< s(136)*s(141) 0.78/0.86 s(143) =< s(142) 0.78/0.86 s(144) =< s(143)*aux(22) 0.78/0.86 s(145) =< s(144)*s(134) 0.78/0.86 s(153) =< s(144)*s(147) 0.78/0.86 0.78/0.86 with precondition: [A>=1,B>=1] 0.78/0.86 0.78/0.86 * Chain [42]: 1*s(155)+1*s(157)+2*s(159)+1*s(160)+1*s(161)+1*s(162)+1*s(163)+1*s(164)+0 0.78/0.86 Such that:s(157) =< A 0.78/0.86 s(155) =< A+B 0.78/0.86 s(156) =< A+B+1 0.78/0.86 s(158) =< B 0.78/0.86 s(154) =< B+1 0.78/0.86 s(159) =< s(158) 0.78/0.86 s(160) =< s(154) 0.78/0.86 s(161) =< s(160)*s(156) 0.78/0.86 s(162) =< s(159)*s(156) 0.78/0.86 s(163) =< s(159)*s(154) 0.78/0.86 s(164) =< s(163)*s(156) 0.78/0.86 0.78/0.86 with precondition: [A>=1,B>=2] 0.78/0.86 0.78/0.86 * Chain [41]: 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(180)+1*s(181)+1*s(184)+1*s(185)+1*s(186)+1*s(188)+1*s(189)+1*s(190)+0 0.78/0.86 Such that:s(165) =< 1 0.78/0.86 s(166) =< 2 0.78/0.86 s(174) =< A 0.78/0.86 s(170) =< A+1 0.78/0.86 s(171) =< A+2 0.78/0.86 s(169) =< A+B 0.78/0.86 s(173) =< A+B+1 0.78/0.86 s(167) =< B 0.78/0.86 s(168) =< B+1 0.78/0.86 s(172) =< B+2 0.78/0.86 s(175) =< s(174) 0.78/0.86 s(176) =< s(173) 0.78/0.86 s(169) =< s(173) 0.78/0.86 s(176) =< s(174) 0.78/0.86 s(177) =< s(174) 0.78/0.86 s(177) =< s(170) 0.78/0.86 s(171) =< s(170) 0.78/0.86 s(178) =< s(167)*s(168) 0.78/0.86 s(179) =< s(178)*s(169) 0.78/0.86 s(180) =< s(166)*s(171) 0.78/0.86 s(181) =< s(165)*s(171) 0.78/0.86 s(182) =< s(172) 0.78/0.86 s(183) =< s(176)*s(182) 0.78/0.86 s(184) =< s(183) 0.78/0.86 s(185) =< s(184)*s(172) 0.78/0.86 s(186) =< s(185)*s(173) 0.78/0.86 s(187) =< s(175)*s(182) 0.78/0.86 s(188) =< s(187) 0.78/0.86 s(189) =< s(188)*s(172) 0.78/0.86 s(190) =< s(189)*s(173) 0.78/0.86 0.78/0.86 with precondition: [A>=2,B>=1] 0.78/0.86 0.78/0.86 * Chain [40]: 1*s(197)+1*s(198)+1*s(200)+2*s(201)+1*s(202)+1*s(203)+1*s(204)+1*s(205)+1*s(206)+1*s(209)+1*s(210)+1*s(211)+0 0.78/0.86 Such that:s(196) =< A 0.78/0.86 s(194) =< A+B 0.78/0.86 s(195) =< A+B+1 0.78/0.86 s(191) =< B 0.78/0.86 s(192) =< B+1 0.78/0.86 s(193) =< B+2 0.78/0.86 s(197) =< s(194) 0.78/0.86 s(198) =< s(194) 0.78/0.86 s(199) =< s(194) 0.78/0.86 s(199) =< s(195) 0.78/0.86 s(197) =< s(196) 0.78/0.86 s(200) =< s(196) 0.78/0.86 s(201) =< s(191) 0.78/0.86 s(202) =< s(192) 0.78/0.86 s(203) =< s(202)*s(199) 0.78/0.86 s(204) =< s(201)*s(199) 0.78/0.86 s(205) =< s(201)*s(192) 0.78/0.86 s(206) =< s(205)*s(199) 0.78/0.86 s(207) =< s(193) 0.78/0.86 s(208) =< s(197)*s(207) 0.78/0.86 s(209) =< s(208) 0.78/0.86 s(210) =< s(209)*s(193) 0.78/0.86 s(211) =< s(210)*s(195) 0.78/0.86 0.78/0.86 with precondition: [A>=2,B>=2] 0.78/0.86 0.78/0.86 0.78/0.86 #### Cost of chains of evalfstart(A,B,C,D,E,F): 0.78/0.86 * Chain [57]: 0 0.78/0.86 with precondition: [] 0.78/0.86 0.78/0.86 * Chain [56]: 0 0.78/0.86 with precondition: [0>=A] 0.78/0.86 0.78/0.86 * Chain [55]: 2*s(213)+0 0.78/0.86 Such that:s(212) =< A 0.78/0.86 s(213) =< s(212) 0.78/0.86 0.78/0.86 with precondition: [0>=B,A>=1] 0.78/0.86 0.78/0.86 * Chain [54]: 1*s(214)+0 0.78/0.86 Such that:s(214) =< A 0.78/0.86 0.78/0.86 with precondition: [0>=B,A>=2] 0.78/0.86 0.78/0.86 * Chain [53]: 0 0.78/0.86 with precondition: [A>=1] 0.78/0.86 0.78/0.86 * Chain [52]: 1*s(215)+1*s(216)+1*s(217)+1*s(221)+3*s(225)+1*s(226)+1*s(227)+1*s(228)+1*s(229)+2*s(232)+2*s(233)+1*s(234)+1*s(235)+0 0.78/0.86 Such that:s(215) =< 1 0.78/0.86 s(216) =< 2 0.78/0.86 s(223) =< A 0.78/0.86 s(217) =< A+1 0.78/0.86 s(218) =< A+2 0.78/0.86 s(219) =< A+B+1 0.78/0.86 s(220) =< A+B+2 0.78/0.86 s(221) =< B 0.78/0.86 s(222) =< B+1 0.78/0.86 s(224) =< B+2 0.78/0.86 s(225) =< s(223) 0.78/0.86 s(226) =< s(221)*s(222) 0.78/0.86 s(227) =< s(226)*s(219) 0.78/0.86 s(228) =< s(216)*s(218) 0.78/0.86 s(229) =< s(215)*s(218) 0.78/0.86 s(230) =< s(224) 0.78/0.86 s(231) =< s(225)*s(230) 0.78/0.86 s(232) =< s(231) 0.78/0.86 s(233) =< s(232)*s(224) 0.78/0.86 s(234) =< s(233)*s(219) 0.78/0.86 s(235) =< s(233)*s(220) 0.78/0.86 0.78/0.86 with precondition: [A>=1,B>=1] 0.78/0.86 0.78/0.86 * Chain [51]: 1*s(236)+1*s(237)+2*s(241)+1*s(242)+1*s(243)+1*s(244)+1*s(245)+1*s(246)+0 0.78/0.86 Such that:s(236) =< A 0.78/0.86 s(237) =< A+B 0.78/0.87 s(238) =< A+B+1 0.78/0.87 s(239) =< B 0.78/0.87 s(240) =< B+1 0.78/0.87 s(241) =< s(239) 0.78/0.87 s(242) =< s(240) 0.78/0.87 s(243) =< s(242)*s(238) 0.78/0.87 s(244) =< s(241)*s(238) 0.78/0.87 s(245) =< s(241)*s(240) 0.78/0.87 s(246) =< s(245)*s(238) 0.78/0.87 0.78/0.87 with precondition: [A>=1,B>=2] 0.78/0.87 0.78/0.87 * Chain [50]: 1*s(247)+1*s(248)+1*s(254)+2*s(257)+1*s(258)+1*s(259)+1*s(260)+1*s(261)+1*s(262)+1*s(263)+1*s(266)+1*s(267)+1*s(268)+1*s(270)+1*s(271)+1*s(272)+0 0.78/0.87 Such that:s(247) =< 1 0.78/0.87 s(248) =< 2 0.78/0.87 s(249) =< A 0.78/0.87 s(250) =< A+1 0.78/0.87 s(251) =< A+2 0.78/0.87 s(252) =< A+B 0.78/0.87 s(253) =< A+B+1 0.78/0.87 s(254) =< B 0.78/0.87 s(255) =< B+1 0.78/0.87 s(256) =< B+2 0.78/0.87 s(257) =< s(249) 0.78/0.87 s(258) =< s(253) 0.78/0.87 s(252) =< s(253) 0.78/0.87 s(258) =< s(249) 0.78/0.87 s(259) =< s(249) 0.78/0.87 s(259) =< s(250) 0.78/0.87 s(251) =< s(250) 0.78/0.87 s(260) =< s(254)*s(255) 0.78/0.87 s(261) =< s(260)*s(252) 0.78/0.87 s(262) =< s(248)*s(251) 0.78/0.87 s(263) =< s(247)*s(251) 0.78/0.87 s(264) =< s(256) 0.78/0.87 s(265) =< s(258)*s(264) 0.78/0.87 s(266) =< s(265) 0.78/0.87 s(267) =< s(266)*s(256) 0.78/0.87 s(268) =< s(267)*s(253) 0.78/0.87 s(269) =< s(257)*s(264) 0.78/0.87 s(270) =< s(269) 0.78/0.87 s(271) =< s(270)*s(256) 0.78/0.87 s(272) =< s(271)*s(253) 0.78/0.87 0.78/0.87 with precondition: [A>=2,B>=1] 0.78/0.87 0.78/0.87 * Chain [49]: 1*s(279)+1*s(280)+1*s(282)+2*s(283)+1*s(284)+1*s(285)+1*s(286)+1*s(287)+1*s(288)+1*s(291)+1*s(292)+1*s(293)+0 0.78/0.87 Such that:s(273) =< A 0.78/0.87 s(274) =< A+B 0.78/0.87 s(275) =< A+B+1 0.78/0.87 s(276) =< B 0.78/0.87 s(277) =< B+1 0.78/0.87 s(278) =< B+2 0.78/0.87 s(279) =< s(274) 0.78/0.87 s(280) =< s(274) 0.78/0.87 s(281) =< s(274) 0.78/0.87 s(281) =< s(275) 0.78/0.87 s(279) =< s(273) 0.78/0.87 s(282) =< s(273) 0.78/0.87 s(283) =< s(276) 0.78/0.87 s(284) =< s(277) 0.78/0.87 s(285) =< s(284)*s(281) 0.78/0.87 s(286) =< s(283)*s(281) 0.78/0.87 s(287) =< s(283)*s(277) 0.78/0.87 s(288) =< s(287)*s(281) 0.78/0.87 s(289) =< s(278) 0.78/0.87 s(290) =< s(279)*s(289) 0.78/0.87 s(291) =< s(290) 0.78/0.87 s(292) =< s(291)*s(278) 0.78/0.87 s(293) =< s(292)*s(275) 0.78/0.87 0.78/0.87 with precondition: [A>=2,B>=2] 0.78/0.87 0.78/0.87 0.78/0.87 Closed-form bounds of evalfstart(A,B,C,D,E,F): 0.78/0.87 ------------------------------------- 0.78/0.87 * Chain [57] with precondition: [] 0.78/0.87 - Upper bound: 0 0.78/0.87 - Complexity: constant 0.78/0.87 * Chain [56] with precondition: [0>=A] 0.78/0.87 - Upper bound: 0 0.78/0.87 - Complexity: constant 0.78/0.87 * Chain [55] with precondition: [0>=B,A>=1] 0.78/0.87 - Upper bound: 2*A 0.78/0.87 - Complexity: n 0.78/0.87 * Chain [54] with precondition: [0>=B,A>=2] 0.78/0.87 - Upper bound: A 0.78/0.87 - Complexity: n 0.78/0.87 * Chain [53] with precondition: [A>=1] 0.78/0.87 - Upper bound: 0 0.78/0.87 - Complexity: constant 0.78/0.87 * Chain [52] with precondition: [A>=1,B>=1] 0.78/0.87 - Upper bound: 3*A+3+(B+2)*(2*A)+(B+2)*((B+2)*(2*A))+(A+B+1)*((B+2)*((B+2)*A))+(A+B+2)*((B+2)*((B+2)*A))+B+(B+1)*B+(A+B+1)*((B+1)*B)+(A+1)+(3*A+6) 0.78/0.87 - Complexity: n^4 0.78/0.87 * Chain [51] with precondition: [A>=1,B>=2] 0.78/0.87 - Upper bound: A+2*B+(B+1)*B+(A+B+1)*((B+1)*B)+(A+B+1)*B+(A+B)+(B+1)+(A+B+1)*(B+1) 0.78/0.87 - Complexity: n^3 0.78/0.87 * Chain [50] with precondition: [A>=2,B>=1] 0.78/0.87 - Upper bound: 3*A+3+(B+2)*A+(B+2)*((B+2)*A)+(A+B+1)*((B+2)*((B+2)*A))+B+(B+1)*((A+B)*B)+(B+1)*B+(3*A+6)+(A+B+1)*((B+2)*(B+2))+(A+B+1)*((A+B+1)*((B+2)*(B+2)))+(A+B+1)*(B+2)+(A+B+1) 0.78/0.87 - Complexity: n^4 0.78/0.87 * Chain [49] with precondition: [A>=2,B>=2] 0.78/0.87 - Upper bound: A+2*B+(A+B)*B+(B+1)*((A+B)*B)+(B+1)*B+(2*A+2*B)+(B+1)*(A+B)+(B+2)*(A+B)+(B+2)*((B+2)*(A+B))+(A+B+1)*((B+2)*((B+2)*(A+B)))+(B+1) 0.78/0.87 - Complexity: n^4 0.78/0.87 0.78/0.87 ### Maximum cost of evalfstart(A,B,C,D,E,F): nat(A)+max([nat(A),nat(B+1)*nat(B)+nat(B)+max([nat(A+B)+nat(B)+nat(B+1)+max([nat(B+1)*nat(B)*nat(A+B+1)+nat(A+B+1)*nat(B)+nat(A+B+1)*nat(B+1),nat(A+B)*nat(B)*nat(B+1)+nat(A+B)*nat(B)+nat(A+B)+nat(B+1)*nat(A+B)+nat(B+2)*nat(A+B)+nat(B+2)*nat(A+B)*nat(B+2)+nat(B+2)*nat(A+B)*nat(B+2)*nat(A+B+1)]),nat(A)*2+3+nat(B+2)*nat(A)+nat(B+2)*nat(A)*nat(B+2)+nat(B+2)*nat(A)*nat(B+2)*nat(A+B+1)+nat(A+2)*3+max([nat(B+2)*nat(A)*nat(B+2)+nat(B+2)*nat(A)+nat(B+2)*nat(A)*nat(B+2)*nat(A+B+2)+nat(B+1)*nat(B)*nat(A+B+1)+nat(A+1),nat(B+2)*nat(B+2)*nat(A+B+1)+nat(A+B)*nat(B)*nat(B+1)+nat(B+2)*nat(B+2)*nat(A+B+1)*nat(A+B+1)+nat(A+B+1)*nat(B+2)+nat(A+B+1)])])]) 0.78/0.87 Asymptotic class: n^4 0.78/0.87 * Total analysis performed in 758 ms. 0.78/0.87 0.87/0.97 EOF