1.86/1.90 WORST_CASE(?,O(n^2)) 1.86/1.90 1.86/1.90 Preprocessing Cost Relations 1.86/1.90 ===================================== 1.86/1.90 1.86/1.90 #### Computed strongly connected components 1.86/1.90 0. recursive : [eval3/6] 1.86/1.90 1. recursive : [eval2/5,eval3_loop_cont/6,eval4/5] 1.86/1.90 2. non_recursive : [exit_location/1] 1.86/1.90 3. non_recursive : [eval2_loop_cont/2] 1.86/1.90 4. non_recursive : [eval1/5] 1.86/1.90 1.86/1.90 #### Obtained direct recursion through partial evaluation 1.86/1.90 0. SCC is partially evaluated into eval3/6 1.86/1.90 1. SCC is partially evaluated into eval2/5 1.86/1.90 2. SCC is completely evaluated into other SCCs 1.86/1.90 3. SCC is completely evaluated into other SCCs 1.86/1.90 4. SCC is partially evaluated into eval1/5 1.86/1.90 1.86/1.90 Control-Flow Refinement of Cost Relations 1.86/1.90 ===================================== 1.86/1.90 1.86/1.90 ### Specialization of cost equations eval3/6 1.86/1.90 * CE 13 is refined into CE [14] 1.86/1.90 * CE 7 is refined into CE [15] 1.86/1.90 * CE 8 is refined into CE [16] 1.86/1.90 * CE 11 is refined into CE [17] 1.86/1.90 * CE 9 is refined into CE [18] 1.86/1.90 * CE 10 is refined into CE [19] 1.86/1.90 * CE 12 is refined into CE [20] 1.86/1.90 1.86/1.90 1.86/1.90 ### Cost equations --> "Loop" of eval3/6 1.86/1.90 * CEs [18] --> Loop 14 1.86/1.90 * CEs [19] --> Loop 15 1.86/1.90 * CEs [20] --> Loop 16 1.86/1.90 * CEs [14] --> Loop 17 1.86/1.90 * CEs [15] --> Loop 18 1.86/1.90 * CEs [16] --> Loop 19 1.86/1.90 * CEs [17] --> Loop 20 1.86/1.90 1.86/1.90 ### Ranking functions of CR eval3(B,C,D,E,F,G) 1.86/1.90 * RF of phase [14,15]: [B-2*C] 1.86/1.90 1.86/1.90 #### Partial ranking functions of CR eval3(B,C,D,E,F,G) 1.86/1.90 * Partial RF of phase [14,15]: 1.86/1.90 - RF of loop [14:1]: 1.86/1.90 B-2*C 1.86/1.90 B-D 1.86/1.90 - RF of loop [15:1]: 1.86/1.90 B/3-2/3*C 1.86/1.90 B/3-D/3 1.86/1.90 1.86/1.90 1.86/1.90 ### Specialization of cost equations eval2/5 1.86/1.90 * CE 3 is refined into CE [21,22,23,24] 1.86/1.90 * CE 6 is refined into CE [25] 1.86/1.90 * CE 4 is refined into CE [26,27,28,29,30,31] 1.86/1.90 * CE 5 is refined into CE [32,33,34,35,36,37] 1.86/1.90 1.86/1.90 1.86/1.90 ### Cost equations --> "Loop" of eval2/5 1.86/1.90 * CEs [31] --> Loop 21 1.86/1.90 * CEs [30] --> Loop 22 1.86/1.90 * CEs [27] --> Loop 23 1.86/1.90 * CEs [28] --> Loop 24 1.86/1.90 * CEs [26] --> Loop 25 1.86/1.90 * CEs [29] --> Loop 26 1.86/1.90 * CEs [33] --> Loop 27 1.86/1.90 * CEs [34] --> Loop 28 1.86/1.90 * CEs [32] --> Loop 29 1.86/1.90 * CEs [36] --> Loop 30 1.86/1.90 * CEs [37] --> Loop 31 1.86/1.90 * CEs [35] --> Loop 32 1.86/1.90 * CEs [24] --> Loop 33 1.86/1.90 * CEs [23] --> Loop 34 1.86/1.90 * CEs [22] --> Loop 35 1.86/1.90 * CEs [21] --> Loop 36 1.86/1.90 * CEs [25] --> Loop 37 1.86/1.90 1.86/1.90 ### Ranking functions of CR eval2(A,B,C,D,E) 1.86/1.90 * RF of phase [21,22,23,24,25]: [A-1] 1.86/1.90 * RF of phase [27,28,29,30,31]: [B-2] 1.86/1.90 1.86/1.90 #### Partial ranking functions of CR eval2(A,B,C,D,E) 1.86/1.90 * Partial RF of phase [21,22,23,24,25]: 1.86/1.90 - RF of loop [21:1,22:1,23:1,24:1,25:1]: 1.86/1.90 A-1 1.86/1.90 * Partial RF of phase [27,28,29,30,31]: 1.86/1.90 - RF of loop [27:1,28:1]: 1.86/1.90 B-4 1.86/1.90 - RF of loop [29:1]: 1.86/1.90 B-3 1.86/1.90 - RF of loop [30:1,31:1]: 1.86/1.90 B-2 1.86/1.90 1.86/1.90 1.86/1.90 ### Specialization of cost equations eval1/5 1.86/1.90 * CE 1 is refined into CE [38,39,40,41,42,43,44,45,46,47,48,49,50] 1.86/1.90 * CE 2 is refined into CE [51,52,53,54,55,56,57,58,59] 1.86/1.90 1.86/1.90 1.86/1.90 ### Cost equations --> "Loop" of eval1/5 1.86/1.90 * CEs [47] --> Loop 38 1.86/1.90 * CEs [50] --> Loop 39 1.86/1.90 * CEs [49] --> Loop 40 1.86/1.90 * CEs [48] --> Loop 41 1.86/1.90 * CEs [43] --> Loop 42 1.86/1.90 * CEs [59] --> Loop 43 1.86/1.90 * CEs [58] --> Loop 44 1.86/1.90 * CEs [57] --> Loop 45 1.86/1.90 * CEs [55] --> Loop 46 1.86/1.90 * CEs [46] --> Loop 47 1.86/1.90 * CEs [45] --> Loop 48 1.86/1.90 * CEs [44] --> Loop 49 1.86/1.90 * CEs [42] --> Loop 50 1.86/1.90 * CEs [41] --> Loop 51 1.86/1.90 * CEs [40] --> Loop 52 1.86/1.90 * CEs [39] --> Loop 53 1.86/1.90 * CEs [38] --> Loop 54 1.86/1.90 * CEs [54] --> Loop 55 1.86/1.90 * CEs [53] --> Loop 56 1.86/1.90 * CEs [52] --> Loop 57 1.86/1.90 * CEs [51,56] --> Loop 58 1.86/1.90 1.86/1.90 ### Ranking functions of CR eval1(A,B,C,D,E) 1.86/1.90 1.86/1.90 #### Partial ranking functions of CR eval1(A,B,C,D,E) 1.86/1.90 1.86/1.90 1.86/1.90 Computing Bounds 1.86/1.90 ===================================== 1.86/1.90 1.86/1.90 #### Cost of chains of eval3(B,C,D,E,F,G): 1.86/1.90 * Chain [[14,15],20]: 1*it(14)+1*it(15)+0 1.86/1.90 Such that:it(15) =< -D/3+G/3 1.86/1.90 aux(5) =< -D+G 1.86/1.90 it(14) =< aux(5) 1.86/1.90 it(15) =< aux(5) 1.86/1.90 1.86/1.90 with precondition: [E=2,D=2*C,B=2*F,B=G,D>=1,B>=2*D] 1.86/1.90 1.86/1.90 * Chain [[14,15],19]: 1*it(14)+1*it(15)+0 1.86/1.90 Such that:it(15) =< -2/3*C+G/3 1.86/1.90 aux(6) =< B-2*C 1.86/1.90 aux(7) =< -2*C+G 1.86/1.90 it(14) =< aux(6) 1.86/1.90 it(15) =< aux(6) 1.86/1.90 it(14) =< aux(7) 1.86/1.90 it(15) =< aux(7) 1.86/1.90 1.86/1.90 with precondition: [E=2,D=2*C,2*F+1=G,D>=1,B>=2*F+1,F>=D] 1.86/1.90 1.86/1.90 * Chain [[14,15],18]: 1*it(14)+1*it(15)+0 1.86/1.90 Such that:it(15) =< -2/3*C+G/3 1.86/1.90 aux(8) =< B-2*C 1.86/1.90 aux(9) =< -2*C+G 1.86/1.90 it(14) =< aux(8) 1.86/1.90 it(15) =< aux(8) 1.86/1.90 it(14) =< aux(9) 1.86/1.90 it(15) =< aux(9) 1.86/1.90 1.86/1.90 with precondition: [E=2,D=2*C,2*F=G,D>=1,B>=2*F+1,F>=D] 1.86/1.90 1.86/1.90 * Chain [[14,15],17]: 1*it(14)+1*it(15)+0 1.86/1.90 Such that:it(15) =< B/3-D/3 1.86/1.90 aux(10) =< B-D 1.86/1.90 aux(11) =< 2*B-D 1.86/1.90 it(14) =< aux(10) 1.86/1.90 it(15) =< aux(10) 1.86/1.90 it(14) =< aux(11) 1.86/1.90 it(15) =< aux(11) 1.86/1.90 1.86/1.90 with precondition: [E=3,D=2*C,D>=1,B>=D+1] 1.86/1.90 1.86/1.90 * Chain [[14,15],16,17]: 1*it(14)+1*it(15)+1 1.86/1.90 Such that:it(15) =< B/3-D/3 1.86/1.90 aux(12) =< B-D 1.86/1.90 it(14) =< aux(12) 1.86/1.90 it(15) =< aux(12) 1.86/1.90 1.86/1.90 with precondition: [E=3,D=2*C,D>=1,B>=2*D] 1.86/1.90 1.86/1.90 * Chain [20]: 0 1.86/1.90 with precondition: [E=2,2*C=B,2*C=D,C=F,2*C=G,C>=1] 1.86/1.90 1.86/1.90 * Chain [19]: 0 1.86/1.90 with precondition: [E=2,2*C=D,C=F,2*C+1=G,B>=2,B>=2*C+1] 1.86/1.90 1.86/1.90 * Chain [18]: 0 1.86/1.90 with precondition: [E=2,2*C=D,C=F,2*C=G,B>=2,B>=2*C+1] 1.86/1.90 1.86/1.90 * Chain [17]: 0 1.86/1.90 with precondition: [E=3,D=2*C,B>=2] 1.86/1.90 1.86/1.90 * Chain [16,17]: 1 1.86/1.90 with precondition: [E=3,B=2*C,B=D,B>=2] 1.86/1.90 1.86/1.90 1.86/1.90 #### Cost of chains of eval2(A,B,C,D,E): 1.86/1.90 * Chain [[27,28,29,30,31],37]: 5*it(27)+1*s(23)+1*s(24)+2*s(27)+2*s(28)+0 1.86/1.90 Such that:aux(23) =< B 1.86/1.90 it(27) =< aux(23) 1.86/1.90 aux(14) =< aux(23) 1.86/1.90 s(26) =< it(27)*aux(23) 1.86/1.90 aux(15) =< it(27)*aux(14) 1.86/1.90 s(27) =< aux(15)*(1/3) 1.86/1.90 s(23) =< aux(15)*(1/3) 1.86/1.90 s(28) =< aux(15) 1.86/1.90 s(27) =< aux(15) 1.86/1.90 s(24) =< s(26) 1.86/1.90 s(23) =< s(26) 1.86/1.90 s(24) =< aux(15) 1.86/1.90 s(23) =< aux(15) 1.86/1.90 1.86/1.90 with precondition: [A=1,E=3,B>=3] 1.86/1.90 1.86/1.90 * Chain [[27,28,29,30,31],36]: 5*it(27)+1*s(23)+1*s(24)+2*s(27)+2*s(28)+1 1.86/1.90 Such that:aux(24) =< B 1.86/1.90 it(27) =< aux(24) 1.86/1.90 aux(14) =< aux(24) 1.86/1.90 s(26) =< it(27)*aux(24) 1.86/1.90 aux(15) =< it(27)*aux(14) 1.86/1.90 s(27) =< aux(15)*(1/3) 1.86/1.90 s(23) =< aux(15)*(1/3) 1.86/1.90 s(28) =< aux(15) 1.86/1.90 s(27) =< aux(15) 1.86/1.90 s(24) =< s(26) 1.86/1.90 s(23) =< s(26) 1.86/1.90 s(24) =< aux(15) 1.86/1.90 s(23) =< aux(15) 1.86/1.90 1.86/1.90 with precondition: [A=1,E=3,B>=3] 1.86/1.90 1.86/1.90 * Chain [[27,28,29,30,31],35]: 5*it(27)+1*s(23)+1*s(24)+2*s(27)+2*s(28)+0 1.86/1.90 Such that:aux(25) =< B 1.86/1.90 it(27) =< aux(25) 1.86/1.90 aux(14) =< aux(25) 1.86/1.90 s(26) =< it(27)*aux(25) 1.86/1.90 aux(15) =< it(27)*aux(14) 1.86/1.90 s(27) =< aux(15)*(1/3) 1.86/1.90 s(23) =< aux(15)*(1/3) 1.86/1.90 s(28) =< aux(15) 1.86/1.90 s(27) =< aux(15) 1.86/1.90 s(24) =< s(26) 1.86/1.90 s(23) =< s(26) 1.86/1.90 s(24) =< aux(15) 1.86/1.90 s(23) =< aux(15) 1.86/1.90 1.86/1.90 with precondition: [A=1,E=3,B>=3] 1.86/1.90 1.86/1.90 * Chain [[27,28,29,30,31],34]: 6*it(27)+1*s(23)+1*s(24)+2*s(27)+2*s(28)+1*s(34)+1 1.86/1.90 Such that:s(34) =< B/3 1.86/1.90 aux(26) =< B 1.86/1.90 s(34) =< aux(26) 1.86/1.90 it(27) =< aux(26) 1.86/1.90 aux(14) =< aux(26) 1.86/1.90 s(26) =< it(27)*aux(26) 1.86/1.90 aux(15) =< it(27)*aux(14) 1.86/1.90 s(27) =< aux(15)*(1/3) 1.86/1.90 s(23) =< aux(15)*(1/3) 1.86/1.90 s(28) =< aux(15) 1.86/1.90 s(27) =< aux(15) 1.86/1.90 s(24) =< s(26) 1.86/1.90 s(23) =< s(26) 1.86/1.90 s(24) =< aux(15) 1.86/1.90 s(23) =< aux(15) 1.86/1.90 1.86/1.90 with precondition: [A=1,E=3,B>=5] 1.86/1.90 1.86/1.90 * Chain [[27,28,29,30,31],33]: 5*it(27)+1*s(23)+1*s(24)+2*s(27)+2*s(28)+1*s(37)+1*s(40)+0 1.86/1.90 Such that:s(37) =< B/3 1.86/1.90 aux(27) =< B 1.86/1.90 aux(28) =< 2*B 1.86/1.90 aux(22) =< aux(27) 1.86/1.90 s(37) =< aux(27) 1.86/1.90 aux(22) =< aux(28) 1.86/1.90 s(40) =< aux(27) 1.86/1.90 s(40) =< aux(28) 1.86/1.90 s(37) =< aux(28) 1.86/1.90 it(27) =< aux(27) 1.86/1.90 it(27) =< aux(22) 1.86/1.90 aux(14) =< aux(27) 1.86/1.90 s(26) =< it(27)*aux(27) 1.86/1.90 aux(15) =< it(27)*aux(14) 1.86/1.90 s(27) =< aux(15)*(1/3) 1.86/1.90 s(23) =< aux(15)*(1/3) 1.86/1.90 s(28) =< aux(15) 1.86/1.90 s(27) =< aux(15) 1.86/1.90 s(24) =< s(26) 1.86/1.90 s(23) =< s(26) 1.86/1.90 s(24) =< aux(15) 1.86/1.90 s(23) =< aux(15) 1.86/1.90 1.86/1.90 with precondition: [A=1,E=3,B>=4] 1.86/1.90 1.86/1.90 * Chain [[27,28,29,30,31],32,37]: 5*it(27)+1*s(23)+1*s(24)+2*s(27)+2*s(28)+1 1.86/1.90 Such that:aux(29) =< B 1.86/1.90 it(27) =< aux(29) 1.86/1.90 aux(14) =< aux(29) 1.86/1.90 s(26) =< it(27)*aux(29) 1.86/1.90 aux(15) =< it(27)*aux(14) 1.86/1.90 s(27) =< aux(15)*(1/3) 1.86/1.90 s(23) =< aux(15)*(1/3) 1.86/1.90 s(28) =< aux(15) 1.86/1.90 s(27) =< aux(15) 1.86/1.90 s(24) =< s(26) 1.86/1.90 s(23) =< s(26) 1.86/1.90 s(24) =< aux(15) 1.86/1.90 s(23) =< aux(15) 1.86/1.90 1.86/1.90 with precondition: [A=1,E=3,B>=3] 1.86/1.90 1.86/1.90 * Chain [[21,22,23,24,25],[27,28,29,30,31],37]: 5*it(21)+5*it(27)+1*s(23)+1*s(24)+2*s(27)+2*s(28)+1*s(63)+1*s(64)+1*s(67)+1*s(68)+1*s(71)+1*s(72)+0 1.86/1.90 Such that:aux(40) =< A 1.86/1.90 aux(41) =< B 1.86/1.90 it(27) =< aux(41) 1.86/1.90 aux(14) =< aux(41) 1.86/1.90 s(26) =< it(27)*aux(41) 1.86/1.90 aux(15) =< it(27)*aux(14) 1.86/1.90 s(27) =< aux(15)*(1/3) 1.86/1.90 s(23) =< aux(15)*(1/3) 1.86/1.90 s(28) =< aux(15) 1.86/1.90 s(27) =< aux(15) 1.86/1.90 s(24) =< s(26) 1.86/1.90 s(23) =< s(26) 1.86/1.90 s(24) =< aux(15) 1.86/1.90 s(23) =< aux(15) 1.86/1.90 it(21) =< aux(40) 1.86/1.90 aux(31) =< aux(41)-1 1.86/1.90 s(66) =< it(21)*aux(41) 1.86/1.90 aux(37) =< it(21)*aux(14) 1.86/1.90 aux(32) =< it(21)*aux(31) 1.86/1.90 s(71) =< aux(37)*(1/3) 1.86/1.90 s(67) =< aux(32)*(1/3) 1.86/1.90 s(63) =< aux(32)*(1/3) 1.86/1.90 s(72) =< aux(37) 1.86/1.90 s(71) =< aux(37) 1.86/1.90 s(68) =< aux(37) 1.86/1.90 s(67) =< aux(37) 1.86/1.90 s(68) =< aux(32) 1.86/1.90 s(67) =< aux(32) 1.86/1.90 s(64) =< s(66) 1.86/1.90 s(63) =< s(66) 1.86/1.90 s(64) =< aux(32) 1.86/1.90 s(63) =< aux(32) 1.86/1.90 1.86/1.90 with precondition: [E=3,A>=2,B>=2*A+1] 1.86/1.90 1.86/1.90 * Chain [[21,22,23,24,25],[27,28,29,30,31],36]: 5*it(21)+5*it(27)+1*s(23)+1*s(24)+2*s(27)+2*s(28)+1*s(63)+1*s(64)+1*s(67)+1*s(68)+1*s(71)+1*s(72)+1 1.86/1.90 Such that:aux(42) =< A 1.86/1.90 aux(43) =< B 1.86/1.90 it(27) =< aux(43) 1.86/1.90 aux(14) =< aux(43) 1.86/1.90 s(26) =< it(27)*aux(43) 1.86/1.90 aux(15) =< it(27)*aux(14) 1.86/1.90 s(27) =< aux(15)*(1/3) 1.86/1.90 s(23) =< aux(15)*(1/3) 1.86/1.90 s(28) =< aux(15) 1.86/1.90 s(27) =< aux(15) 1.86/1.90 s(24) =< s(26) 1.86/1.90 s(23) =< s(26) 1.86/1.90 s(24) =< aux(15) 1.86/1.90 s(23) =< aux(15) 1.86/1.90 it(21) =< aux(42) 1.86/1.90 aux(31) =< aux(43)-1 1.86/1.90 s(66) =< it(21)*aux(43) 1.86/1.90 aux(37) =< it(21)*aux(14) 1.86/1.90 aux(32) =< it(21)*aux(31) 1.86/1.90 s(71) =< aux(37)*(1/3) 1.86/1.90 s(67) =< aux(32)*(1/3) 1.86/1.90 s(63) =< aux(32)*(1/3) 1.86/1.90 s(72) =< aux(37) 1.86/1.90 s(71) =< aux(37) 1.86/1.90 s(68) =< aux(37) 1.86/1.90 s(67) =< aux(37) 1.86/1.90 s(68) =< aux(32) 1.86/1.90 s(67) =< aux(32) 1.86/1.90 s(64) =< s(66) 1.86/1.90 s(63) =< s(66) 1.86/1.90 s(64) =< aux(32) 1.86/1.90 s(63) =< aux(32) 1.86/1.90 1.86/1.90 with precondition: [E=3,A>=2,B>=2*A+1] 1.86/1.90 1.86/1.90 * Chain [[21,22,23,24,25],[27,28,29,30,31],35]: 5*it(21)+5*it(27)+1*s(23)+1*s(24)+2*s(27)+2*s(28)+1*s(63)+1*s(64)+1*s(67)+1*s(68)+1*s(71)+1*s(72)+0 1.86/1.90 Such that:aux(44) =< A 1.86/1.90 aux(45) =< B 1.86/1.90 it(27) =< aux(45) 1.86/1.90 aux(14) =< aux(45) 1.86/1.90 s(26) =< it(27)*aux(45) 1.86/1.90 aux(15) =< it(27)*aux(14) 1.86/1.90 s(27) =< aux(15)*(1/3) 1.86/1.90 s(23) =< aux(15)*(1/3) 1.86/1.90 s(28) =< aux(15) 1.86/1.90 s(27) =< aux(15) 1.86/1.90 s(24) =< s(26) 1.86/1.90 s(23) =< s(26) 1.86/1.90 s(24) =< aux(15) 1.86/1.90 s(23) =< aux(15) 1.86/1.90 it(21) =< aux(44) 1.86/1.90 aux(31) =< aux(45)-1 1.86/1.90 s(66) =< it(21)*aux(45) 1.86/1.90 aux(37) =< it(21)*aux(14) 1.86/1.90 aux(32) =< it(21)*aux(31) 1.86/1.90 s(71) =< aux(37)*(1/3) 1.86/1.90 s(67) =< aux(32)*(1/3) 1.86/1.90 s(63) =< aux(32)*(1/3) 1.86/1.90 s(72) =< aux(37) 1.86/1.90 s(71) =< aux(37) 1.86/1.90 s(68) =< aux(37) 1.86/1.90 s(67) =< aux(37) 1.86/1.90 s(68) =< aux(32) 1.86/1.90 s(67) =< aux(32) 1.86/1.90 s(64) =< s(66) 1.86/1.90 s(63) =< s(66) 1.86/1.90 s(64) =< aux(32) 1.86/1.90 s(63) =< aux(32) 1.86/1.90 1.86/1.90 with precondition: [E=3,A>=2,B>=2*A+1] 1.86/1.90 1.86/1.90 * Chain [[21,22,23,24,25],[27,28,29,30,31],34]: 5*it(21)+6*it(27)+1*s(23)+1*s(24)+2*s(27)+2*s(28)+1*s(34)+1*s(63)+1*s(64)+1*s(67)+1*s(68)+1*s(71)+1*s(72)+1 1.86/1.90 Such that:s(34) =< B/3 1.86/1.90 aux(46) =< A 1.86/1.90 aux(47) =< B 1.86/1.90 s(34) =< aux(47) 1.86/1.90 it(27) =< aux(47) 1.86/1.90 aux(14) =< aux(47) 1.86/1.90 s(26) =< it(27)*aux(47) 1.86/1.90 aux(15) =< it(27)*aux(14) 1.86/1.90 s(27) =< aux(15)*(1/3) 1.86/1.90 s(23) =< aux(15)*(1/3) 1.86/1.90 s(28) =< aux(15) 1.86/1.90 s(27) =< aux(15) 1.86/1.90 s(24) =< s(26) 1.86/1.90 s(23) =< s(26) 1.86/1.90 s(24) =< aux(15) 1.86/1.90 s(23) =< aux(15) 1.86/1.90 it(21) =< aux(46) 1.86/1.90 aux(31) =< aux(47)-1 1.86/1.90 s(66) =< it(21)*aux(47) 1.86/1.90 aux(37) =< it(21)*aux(14) 1.86/1.90 aux(32) =< it(21)*aux(31) 1.86/1.90 s(71) =< aux(37)*(1/3) 1.86/1.90 s(67) =< aux(32)*(1/3) 1.86/1.90 s(63) =< aux(32)*(1/3) 1.86/1.90 s(72) =< aux(37) 1.86/1.90 s(71) =< aux(37) 1.86/1.90 s(68) =< aux(37) 1.86/1.90 s(67) =< aux(37) 1.86/1.90 s(68) =< aux(32) 1.86/1.90 s(67) =< aux(32) 1.86/1.90 s(64) =< s(66) 1.86/1.90 s(63) =< s(66) 1.86/1.90 s(64) =< aux(32) 1.86/1.90 s(63) =< aux(32) 1.86/1.90 1.86/1.90 with precondition: [E=3,A>=2,B>=2*A+1] 1.86/1.90 1.86/1.90 * Chain [[21,22,23,24,25],[27,28,29,30,31],33]: 5*it(21)+5*it(27)+1*s(23)+1*s(24)+2*s(27)+2*s(28)+1*s(37)+1*s(40)+1*s(63)+1*s(64)+1*s(67)+1*s(68)+1*s(71)+1*s(72)+0 1.86/1.90 Such that:aux(28) =< 2*B 1.86/1.90 s(37) =< B/3 1.86/1.90 aux(48) =< A 1.86/1.90 aux(49) =< B 1.86/1.90 aux(22) =< aux(49) 1.86/1.90 s(37) =< aux(49) 1.86/1.90 aux(22) =< aux(28) 1.86/1.90 s(40) =< aux(49) 1.86/1.90 s(40) =< aux(28) 1.86/1.90 s(37) =< aux(28) 1.86/1.90 it(27) =< aux(49) 1.86/1.90 it(27) =< aux(22) 1.86/1.90 aux(14) =< aux(49) 1.86/1.90 s(26) =< it(27)*aux(49) 1.86/1.90 aux(15) =< it(27)*aux(14) 1.86/1.90 s(27) =< aux(15)*(1/3) 1.86/1.90 s(23) =< aux(15)*(1/3) 1.86/1.90 s(28) =< aux(15) 1.86/1.90 s(27) =< aux(15) 1.86/1.90 s(24) =< s(26) 1.86/1.90 s(23) =< s(26) 1.86/1.90 s(24) =< aux(15) 1.86/1.90 s(23) =< aux(15) 1.86/1.90 it(21) =< aux(48) 1.86/1.90 aux(31) =< aux(49)-1 1.86/1.90 s(66) =< it(21)*aux(49) 1.86/1.90 aux(37) =< it(21)*aux(14) 1.86/1.90 aux(32) =< it(21)*aux(31) 1.86/1.90 s(71) =< aux(37)*(1/3) 1.86/1.90 s(67) =< aux(32)*(1/3) 1.86/1.90 s(63) =< aux(32)*(1/3) 1.86/1.90 s(72) =< aux(37) 1.86/1.90 s(71) =< aux(37) 1.86/1.90 s(68) =< aux(37) 1.86/1.90 s(67) =< aux(37) 1.86/1.90 s(68) =< aux(32) 1.86/1.90 s(67) =< aux(32) 1.86/1.90 s(64) =< s(66) 1.86/1.90 s(63) =< s(66) 1.86/1.90 s(64) =< aux(32) 1.86/1.90 s(63) =< aux(32) 1.86/1.90 1.86/1.90 with precondition: [E=3,A>=2,B>=2*A+1] 1.86/1.90 1.86/1.90 * Chain [[21,22,23,24,25],[27,28,29,30,31],32,37]: 5*it(21)+5*it(27)+1*s(23)+1*s(24)+2*s(27)+2*s(28)+1*s(63)+1*s(64)+1*s(67)+1*s(68)+1*s(71)+1*s(72)+1 1.86/1.90 Such that:aux(50) =< A 1.86/1.90 aux(51) =< B 1.86/1.90 it(27) =< aux(51) 1.86/1.90 aux(14) =< aux(51) 1.86/1.90 s(26) =< it(27)*aux(51) 1.86/1.90 aux(15) =< it(27)*aux(14) 1.86/1.90 s(27) =< aux(15)*(1/3) 1.86/1.90 s(23) =< aux(15)*(1/3) 1.86/1.90 s(28) =< aux(15) 1.86/1.90 s(27) =< aux(15) 1.86/1.90 s(24) =< s(26) 1.86/1.90 s(23) =< s(26) 1.86/1.90 s(24) =< aux(15) 1.86/1.90 s(23) =< aux(15) 1.86/1.90 it(21) =< aux(50) 1.86/1.90 aux(31) =< aux(51)-1 1.86/1.90 s(66) =< it(21)*aux(51) 1.86/1.90 aux(37) =< it(21)*aux(14) 1.86/1.90 aux(32) =< it(21)*aux(31) 1.86/1.90 s(71) =< aux(37)*(1/3) 1.86/1.90 s(67) =< aux(32)*(1/3) 1.86/1.90 s(63) =< aux(32)*(1/3) 1.86/1.90 s(72) =< aux(37) 1.86/1.90 s(71) =< aux(37) 1.86/1.90 s(68) =< aux(37) 1.86/1.90 s(67) =< aux(37) 1.86/1.90 s(68) =< aux(32) 1.86/1.90 s(67) =< aux(32) 1.86/1.90 s(64) =< s(66) 1.86/1.90 s(63) =< s(66) 1.86/1.90 s(64) =< aux(32) 1.86/1.90 s(63) =< aux(32) 1.86/1.90 1.86/1.90 with precondition: [E=3,A>=2,B>=2*A+1] 1.86/1.90 1.86/1.90 * Chain [[21,22,23,24,25],37]: 5*it(21)+1*s(63)+1*s(64)+1*s(67)+1*s(68)+1*s(71)+1*s(72)+0 1.86/1.90 Such that:aux(30) =< B 1.86/1.90 aux(52) =< A 1.86/1.90 it(21) =< aux(52) 1.86/1.90 aux(33) =< aux(30) 1.86/1.90 aux(31) =< aux(30)-1 1.86/1.90 s(66) =< it(21)*aux(30) 1.86/1.90 aux(37) =< it(21)*aux(33) 1.86/1.90 aux(32) =< it(21)*aux(31) 1.86/1.90 s(71) =< aux(37)*(1/3) 1.86/1.90 s(67) =< aux(32)*(1/3) 1.86/1.90 s(63) =< aux(32)*(1/3) 1.86/1.90 s(72) =< aux(37) 1.86/1.90 s(71) =< aux(37) 1.86/1.90 s(68) =< aux(37) 1.86/1.90 s(67) =< aux(37) 1.86/1.90 s(68) =< aux(32) 1.86/1.90 s(67) =< aux(32) 1.86/1.90 s(64) =< s(66) 1.86/1.90 s(63) =< s(66) 1.86/1.90 s(64) =< aux(32) 1.86/1.90 s(63) =< aux(32) 1.86/1.90 1.86/1.90 with precondition: [E=3,A>=2,B>=2*A+1] 1.86/1.90 1.86/1.90 * Chain [[21,22,23,24,25],35]: 5*it(21)+1*s(63)+1*s(64)+1*s(67)+1*s(68)+1*s(71)+1*s(72)+0 1.86/1.90 Such that:aux(30) =< B 1.86/1.90 aux(53) =< A 1.86/1.90 it(21) =< aux(53) 1.86/1.90 aux(33) =< aux(30) 1.86/1.90 aux(31) =< aux(30)-1 1.86/1.90 s(66) =< it(21)*aux(30) 1.86/1.90 aux(37) =< it(21)*aux(33) 1.86/1.90 aux(32) =< it(21)*aux(31) 1.86/1.90 s(71) =< aux(37)*(1/3) 1.86/1.90 s(67) =< aux(32)*(1/3) 1.86/1.90 s(63) =< aux(32)*(1/3) 1.86/1.90 s(72) =< aux(37) 1.86/1.90 s(71) =< aux(37) 1.86/1.90 s(68) =< aux(37) 1.86/1.90 s(67) =< aux(37) 1.86/1.90 s(68) =< aux(32) 1.86/1.90 s(67) =< aux(32) 1.86/1.90 s(64) =< s(66) 1.86/1.90 s(63) =< s(66) 1.86/1.90 s(64) =< aux(32) 1.86/1.90 s(63) =< aux(32) 1.86/1.90 1.86/1.90 with precondition: [E=3,A>=2,B>=2*A+1] 1.86/1.90 1.86/1.90 * Chain [[21,22,23,24,25],34]: 5*it(21)+1*s(34)+1*s(36)+1*s(63)+1*s(64)+1*s(67)+1*s(68)+1*s(71)+1*s(72)+1 1.86/1.90 Such that:s(34) =< B/3 1.86/1.90 aux(54) =< A 1.86/1.90 aux(55) =< B 1.86/1.90 s(36) =< aux(55) 1.86/1.90 s(34) =< aux(55) 1.86/1.90 it(21) =< aux(54) 1.86/1.90 aux(33) =< aux(55) 1.86/1.90 aux(31) =< aux(55)-1 1.86/1.90 s(66) =< it(21)*aux(55) 1.86/1.90 aux(37) =< it(21)*aux(33) 1.86/1.90 aux(32) =< it(21)*aux(31) 1.86/1.90 s(71) =< aux(37)*(1/3) 1.86/1.90 s(67) =< aux(32)*(1/3) 1.86/1.90 s(63) =< aux(32)*(1/3) 1.86/1.90 s(72) =< aux(37) 1.86/1.90 s(71) =< aux(37) 1.86/1.90 s(68) =< aux(37) 1.86/1.90 s(67) =< aux(37) 1.86/1.90 s(68) =< aux(32) 1.86/1.90 s(67) =< aux(32) 1.86/1.90 s(64) =< s(66) 1.86/1.90 s(63) =< s(66) 1.86/1.90 s(64) =< aux(32) 1.86/1.90 s(63) =< aux(32) 1.86/1.90 1.86/1.90 with precondition: [E=3,A>=2,B>=2*A+1] 1.86/1.90 1.86/1.90 * Chain [[21,22,23,24,25],33]: 5*it(21)+1*s(37)+1*s(40)+1*s(63)+1*s(64)+1*s(67)+1*s(68)+1*s(71)+1*s(72)+0 1.86/1.90 Such that:s(39) =< 2*B 1.86/1.90 s(37) =< B/3 1.86/1.90 aux(56) =< A 1.86/1.90 aux(57) =< B 1.86/1.90 s(40) =< aux(57) 1.86/1.90 s(37) =< aux(57) 1.86/1.90 s(40) =< s(39) 1.86/1.90 s(37) =< s(39) 1.86/1.90 it(21) =< aux(56) 1.86/1.90 aux(33) =< aux(57) 1.86/1.90 aux(31) =< aux(57)-1 1.86/1.90 s(66) =< it(21)*aux(57) 1.86/1.90 aux(37) =< it(21)*aux(33) 1.86/1.90 aux(32) =< it(21)*aux(31) 1.86/1.90 s(71) =< aux(37)*(1/3) 1.86/1.90 s(67) =< aux(32)*(1/3) 1.86/1.90 s(63) =< aux(32)*(1/3) 1.86/1.90 s(72) =< aux(37) 1.86/1.90 s(71) =< aux(37) 1.86/1.90 s(68) =< aux(37) 1.86/1.90 s(67) =< aux(37) 1.86/1.90 s(68) =< aux(32) 1.86/1.90 s(67) =< aux(32) 1.86/1.90 s(64) =< s(66) 1.86/1.90 s(63) =< s(66) 1.86/1.90 s(64) =< aux(32) 1.86/1.90 s(63) =< aux(32) 1.86/1.90 1.86/1.90 with precondition: [E=3,A>=2,B>=2*A+1] 1.86/1.90 1.86/1.90 * Chain [37]: 0 1.86/1.90 with precondition: [E=3] 1.86/1.90 1.86/1.90 * Chain [36]: 1 1.86/1.90 with precondition: [E=3,2*A=B,A>=1] 1.86/1.90 1.86/1.90 * Chain [35]: 0 1.86/1.90 with precondition: [E=3,B>=2] 1.86/1.90 1.86/1.90 * Chain [34]: 1*s(34)+1*s(36)+1 1.86/1.90 Such that:s(35) =< -2*A+B 1.86/1.90 s(34) =< -2/3*A+B/3 1.86/1.90 s(36) =< s(35) 1.86/1.90 s(34) =< s(35) 1.86/1.90 1.86/1.90 with precondition: [E=3,2*A>=1,B>=4*A] 1.86/1.90 1.86/1.91 * Chain [33]: 1*s(37)+1*s(40)+0 1.86/1.91 Such that:s(38) =< -2*A+B 1.86/1.91 s(39) =< -2*A+2*B 1.86/1.91 s(37) =< -2/3*A+B/3 1.86/1.91 s(40) =< s(38) 1.86/1.91 s(37) =< s(38) 1.86/1.91 s(40) =< s(39) 1.86/1.91 s(37) =< s(39) 1.86/1.91 1.86/1.91 with precondition: [E=3,2*A>=1,B>=2*A+1] 1.86/1.91 1.86/1.91 * Chain [32,37]: 1 1.86/1.91 with precondition: [A=1,B=2,E=3] 1.86/1.91 1.86/1.91 * Chain [26,[27,28,29,30,31],37]: 5*it(27)+1*s(23)+1*s(24)+2*s(27)+2*s(28)+1 1.86/1.91 Such that:aux(23) =< 4 1.86/1.91 it(27) =< aux(23) 1.86/1.91 aux(14) =< aux(23) 1.86/1.91 s(26) =< it(27)*aux(23) 1.86/1.91 aux(15) =< it(27)*aux(14) 1.86/1.91 s(27) =< aux(15)*(1/3) 1.86/1.91 s(23) =< aux(15)*(1/3) 1.86/1.91 s(28) =< aux(15) 1.86/1.91 s(27) =< aux(15) 1.86/1.91 s(24) =< s(26) 1.86/1.91 s(23) =< s(26) 1.86/1.91 s(24) =< aux(15) 1.86/1.91 s(23) =< aux(15) 1.86/1.91 1.86/1.91 with precondition: [A=2,B=4,E=3] 1.86/1.91 1.86/1.91 * Chain [26,[27,28,29,30,31],36]: 5*it(27)+1*s(23)+1*s(24)+2*s(27)+2*s(28)+2 1.86/1.91 Such that:aux(24) =< 4 1.86/1.91 it(27) =< aux(24) 1.86/1.91 aux(14) =< aux(24) 1.86/1.91 s(26) =< it(27)*aux(24) 1.86/1.91 aux(15) =< it(27)*aux(14) 1.86/1.91 s(27) =< aux(15)*(1/3) 1.86/1.91 s(23) =< aux(15)*(1/3) 1.86/1.91 s(28) =< aux(15) 1.86/1.91 s(27) =< aux(15) 1.86/1.91 s(24) =< s(26) 1.86/1.91 s(23) =< s(26) 1.86/1.91 s(24) =< aux(15) 1.86/1.91 s(23) =< aux(15) 1.86/1.91 1.86/1.91 with precondition: [A=2,B=4,E=3] 1.86/1.91 1.86/1.91 * Chain [26,[27,28,29,30,31],35]: 5*it(27)+1*s(23)+1*s(24)+2*s(27)+2*s(28)+1 1.86/1.91 Such that:aux(25) =< 4 1.86/1.91 it(27) =< aux(25) 1.86/1.91 aux(14) =< aux(25) 1.86/1.91 s(26) =< it(27)*aux(25) 1.86/1.91 aux(15) =< it(27)*aux(14) 1.86/1.91 s(27) =< aux(15)*(1/3) 1.86/1.91 s(23) =< aux(15)*(1/3) 1.86/1.91 s(28) =< aux(15) 1.86/1.91 s(27) =< aux(15) 1.86/1.91 s(24) =< s(26) 1.86/1.91 s(23) =< s(26) 1.86/1.91 s(24) =< aux(15) 1.86/1.91 s(23) =< aux(15) 1.86/1.91 1.86/1.91 with precondition: [A=2,B=4,E=3] 1.86/1.91 1.86/1.91 * Chain [26,[27,28,29,30,31],33]: 5*it(27)+1*s(23)+1*s(24)+2*s(27)+2*s(28)+1*s(37)+1*s(40)+1 1.86/1.91 Such that:aux(27) =< 4 1.86/1.91 aux(28) =< 8 1.86/1.91 s(37) =< 4/3 1.86/1.91 aux(22) =< aux(27) 1.86/1.91 s(37) =< aux(27) 1.86/1.91 aux(22) =< aux(28) 1.86/1.91 s(40) =< aux(27) 1.86/1.91 s(40) =< aux(28) 1.86/1.91 s(37) =< aux(28) 1.86/1.91 it(27) =< aux(27) 1.86/1.91 it(27) =< aux(22) 1.86/1.91 aux(14) =< aux(27) 1.86/1.91 s(26) =< it(27)*aux(27) 1.86/1.91 aux(15) =< it(27)*aux(14) 1.86/1.91 s(27) =< aux(15)*(1/3) 1.86/1.91 s(23) =< aux(15)*(1/3) 1.86/1.91 s(28) =< aux(15) 1.86/1.91 s(27) =< aux(15) 1.86/1.91 s(24) =< s(26) 1.86/1.91 s(23) =< s(26) 1.86/1.91 s(24) =< aux(15) 1.86/1.91 s(23) =< aux(15) 1.86/1.91 1.86/1.91 with precondition: [A=2,B=4,E=3] 1.86/1.91 1.86/1.91 * Chain [26,[27,28,29,30,31],32,37]: 5*it(27)+1*s(23)+1*s(24)+2*s(27)+2*s(28)+2 1.86/1.91 Such that:aux(29) =< 4 1.86/1.91 it(27) =< aux(29) 1.86/1.91 aux(14) =< aux(29) 1.86/1.91 s(26) =< it(27)*aux(29) 1.86/1.91 aux(15) =< it(27)*aux(14) 1.86/1.91 s(27) =< aux(15)*(1/3) 1.86/1.91 s(23) =< aux(15)*(1/3) 1.86/1.91 s(28) =< aux(15) 1.86/1.91 s(27) =< aux(15) 1.86/1.91 s(24) =< s(26) 1.86/1.91 s(23) =< s(26) 1.86/1.91 s(24) =< aux(15) 1.86/1.91 s(23) =< aux(15) 1.86/1.91 1.86/1.91 with precondition: [A=2,B=4,E=3] 1.86/1.91 1.86/1.91 * Chain [26,[21,22,23,24,25],[27,28,29,30,31],37]: 5*it(21)+5*it(27)+1*s(23)+1*s(24)+2*s(27)+2*s(28)+1*s(63)+1*s(64)+1*s(67)+1*s(68)+1*s(71)+1*s(72)+1 1.86/1.91 Such that:aux(41) =< B 1.86/1.91 aux(40) =< B/2 1.86/1.91 it(27) =< aux(41) 1.86/1.91 aux(14) =< aux(41) 1.86/1.91 s(26) =< it(27)*aux(41) 1.86/1.91 aux(15) =< it(27)*aux(14) 1.86/1.91 s(27) =< aux(15)*(1/3) 1.86/1.91 s(23) =< aux(15)*(1/3) 1.86/1.91 s(28) =< aux(15) 1.86/1.91 s(27) =< aux(15) 1.86/1.91 s(24) =< s(26) 1.86/1.91 s(23) =< s(26) 1.86/1.91 s(24) =< aux(15) 1.86/1.91 s(23) =< aux(15) 1.86/1.91 it(21) =< aux(40) 1.86/1.91 aux(31) =< aux(41)-1 1.86/1.91 s(66) =< it(21)*aux(41) 1.86/1.91 aux(37) =< it(21)*aux(14) 1.86/1.91 aux(32) =< it(21)*aux(31) 1.86/1.91 s(71) =< aux(37)*(1/3) 1.86/1.91 s(67) =< aux(32)*(1/3) 1.86/1.91 s(63) =< aux(32)*(1/3) 1.86/1.91 s(72) =< aux(37) 1.86/1.91 s(71) =< aux(37) 1.86/1.91 s(68) =< aux(37) 1.86/1.91 s(67) =< aux(37) 1.86/1.91 s(68) =< aux(32) 1.86/1.91 s(67) =< aux(32) 1.86/1.91 s(64) =< s(66) 1.86/1.91 s(63) =< s(66) 1.86/1.91 s(64) =< aux(32) 1.86/1.91 s(63) =< aux(32) 1.86/1.91 1.86/1.91 with precondition: [E=3,2*A=B,A>=3] 1.86/1.91 1.86/1.91 * Chain [26,[21,22,23,24,25],[27,28,29,30,31],36]: 5*it(21)+5*it(27)+1*s(23)+1*s(24)+2*s(27)+2*s(28)+1*s(63)+1*s(64)+1*s(67)+1*s(68)+1*s(71)+1*s(72)+2 1.86/1.91 Such that:aux(43) =< B 1.86/1.91 aux(42) =< B/2 1.86/1.91 it(27) =< aux(43) 1.86/1.91 aux(14) =< aux(43) 1.86/1.91 s(26) =< it(27)*aux(43) 1.86/1.91 aux(15) =< it(27)*aux(14) 1.86/1.91 s(27) =< aux(15)*(1/3) 1.86/1.91 s(23) =< aux(15)*(1/3) 1.86/1.91 s(28) =< aux(15) 1.86/1.91 s(27) =< aux(15) 1.86/1.91 s(24) =< s(26) 1.86/1.91 s(23) =< s(26) 1.86/1.91 s(24) =< aux(15) 1.86/1.91 s(23) =< aux(15) 1.86/1.91 it(21) =< aux(42) 1.86/1.91 aux(31) =< aux(43)-1 1.86/1.91 s(66) =< it(21)*aux(43) 1.86/1.91 aux(37) =< it(21)*aux(14) 1.86/1.91 aux(32) =< it(21)*aux(31) 1.86/1.91 s(71) =< aux(37)*(1/3) 1.86/1.91 s(67) =< aux(32)*(1/3) 1.86/1.91 s(63) =< aux(32)*(1/3) 1.86/1.91 s(72) =< aux(37) 1.86/1.91 s(71) =< aux(37) 1.86/1.91 s(68) =< aux(37) 1.86/1.91 s(67) =< aux(37) 1.86/1.91 s(68) =< aux(32) 1.86/1.91 s(67) =< aux(32) 1.86/1.91 s(64) =< s(66) 1.86/1.91 s(63) =< s(66) 1.86/1.91 s(64) =< aux(32) 1.86/1.91 s(63) =< aux(32) 1.86/1.91 1.86/1.91 with precondition: [E=3,2*A=B,A>=3] 1.86/1.91 1.86/1.91 * Chain [26,[21,22,23,24,25],[27,28,29,30,31],35]: 5*it(21)+5*it(27)+1*s(23)+1*s(24)+2*s(27)+2*s(28)+1*s(63)+1*s(64)+1*s(67)+1*s(68)+1*s(71)+1*s(72)+1 1.86/1.91 Such that:aux(45) =< B 1.86/1.91 aux(44) =< B/2 1.86/1.91 it(27) =< aux(45) 1.86/1.91 aux(14) =< aux(45) 1.86/1.91 s(26) =< it(27)*aux(45) 1.86/1.91 aux(15) =< it(27)*aux(14) 1.86/1.91 s(27) =< aux(15)*(1/3) 1.86/1.91 s(23) =< aux(15)*(1/3) 1.86/1.91 s(28) =< aux(15) 1.86/1.91 s(27) =< aux(15) 1.86/1.91 s(24) =< s(26) 1.86/1.91 s(23) =< s(26) 1.86/1.91 s(24) =< aux(15) 1.86/1.91 s(23) =< aux(15) 1.86/1.91 it(21) =< aux(44) 1.86/1.91 aux(31) =< aux(45)-1 1.86/1.91 s(66) =< it(21)*aux(45) 1.86/1.91 aux(37) =< it(21)*aux(14) 1.86/1.91 aux(32) =< it(21)*aux(31) 1.86/1.91 s(71) =< aux(37)*(1/3) 1.86/1.91 s(67) =< aux(32)*(1/3) 1.86/1.91 s(63) =< aux(32)*(1/3) 1.86/1.91 s(72) =< aux(37) 1.86/1.91 s(71) =< aux(37) 1.86/1.91 s(68) =< aux(37) 1.86/1.91 s(67) =< aux(37) 1.86/1.91 s(68) =< aux(32) 1.86/1.91 s(67) =< aux(32) 1.86/1.91 s(64) =< s(66) 1.86/1.91 s(63) =< s(66) 1.86/1.91 s(64) =< aux(32) 1.86/1.91 s(63) =< aux(32) 1.86/1.91 1.86/1.91 with precondition: [E=3,2*A=B,A>=3] 1.86/1.91 1.86/1.91 * Chain [26,[21,22,23,24,25],[27,28,29,30,31],34]: 5*it(21)+6*it(27)+1*s(23)+1*s(24)+2*s(27)+2*s(28)+1*s(34)+1*s(63)+1*s(64)+1*s(67)+1*s(68)+1*s(71)+1*s(72)+2 1.86/1.91 Such that:aux(46) =< A 1.86/1.91 aux(47) =< 2*A 1.86/1.91 s(34) =< 2/3*A 1.86/1.91 s(34) =< aux(47) 1.86/1.91 it(27) =< aux(47) 1.86/1.91 aux(14) =< aux(47) 1.86/1.91 s(26) =< it(27)*aux(47) 1.86/1.91 aux(15) =< it(27)*aux(14) 1.86/1.91 s(27) =< aux(15)*(1/3) 1.86/1.91 s(23) =< aux(15)*(1/3) 1.86/1.91 s(28) =< aux(15) 1.86/1.91 s(27) =< aux(15) 1.86/1.91 s(24) =< s(26) 1.86/1.91 s(23) =< s(26) 1.86/1.91 s(24) =< aux(15) 1.86/1.91 s(23) =< aux(15) 1.86/1.91 it(21) =< aux(46) 1.86/1.91 aux(31) =< aux(47)-1 1.86/1.91 s(66) =< it(21)*aux(47) 1.86/1.91 aux(37) =< it(21)*aux(14) 1.86/1.91 aux(32) =< it(21)*aux(31) 1.86/1.91 s(71) =< aux(37)*(1/3) 1.86/1.91 s(67) =< aux(32)*(1/3) 1.86/1.91 s(63) =< aux(32)*(1/3) 1.86/1.91 s(72) =< aux(37) 1.86/1.91 s(71) =< aux(37) 1.86/1.91 s(68) =< aux(37) 1.86/1.91 s(67) =< aux(37) 1.86/1.91 s(68) =< aux(32) 1.86/1.91 s(67) =< aux(32) 1.86/1.91 s(64) =< s(66) 1.86/1.91 s(63) =< s(66) 1.86/1.91 s(64) =< aux(32) 1.86/1.91 s(63) =< aux(32) 1.86/1.91 1.86/1.91 with precondition: [E=3,2*A=B,A>=3] 1.86/1.91 1.86/1.91 * Chain [26,[21,22,23,24,25],[27,28,29,30,31],33]: 5*it(21)+5*it(27)+1*s(23)+1*s(24)+2*s(27)+2*s(28)+1*s(37)+1*s(40)+1*s(63)+1*s(64)+1*s(67)+1*s(68)+1*s(71)+1*s(72)+1 1.86/1.91 Such that:aux(48) =< A 1.86/1.91 aux(49) =< 2*A 1.86/1.91 aux(28) =< 4*A 1.86/1.91 s(37) =< 2/3*A 1.86/1.91 aux(22) =< aux(49) 1.86/1.91 s(37) =< aux(49) 1.86/1.91 aux(22) =< aux(28) 1.86/1.91 s(40) =< aux(49) 1.86/1.91 s(40) =< aux(28) 1.86/1.91 s(37) =< aux(28) 1.86/1.91 it(27) =< aux(49) 1.86/1.91 it(27) =< aux(22) 1.86/1.91 aux(14) =< aux(49) 1.86/1.91 s(26) =< it(27)*aux(49) 1.86/1.91 aux(15) =< it(27)*aux(14) 1.86/1.91 s(27) =< aux(15)*(1/3) 1.86/1.91 s(23) =< aux(15)*(1/3) 1.86/1.91 s(28) =< aux(15) 1.86/1.91 s(27) =< aux(15) 1.86/1.91 s(24) =< s(26) 1.86/1.91 s(23) =< s(26) 1.86/1.91 s(24) =< aux(15) 1.86/1.91 s(23) =< aux(15) 1.86/1.91 it(21) =< aux(48) 1.86/1.91 aux(31) =< aux(49)-1 1.86/1.91 s(66) =< it(21)*aux(49) 1.86/1.91 aux(37) =< it(21)*aux(14) 1.86/1.91 aux(32) =< it(21)*aux(31) 1.86/1.91 s(71) =< aux(37)*(1/3) 1.86/1.91 s(67) =< aux(32)*(1/3) 1.86/1.91 s(63) =< aux(32)*(1/3) 1.86/1.91 s(72) =< aux(37) 1.86/1.91 s(71) =< aux(37) 1.86/1.91 s(68) =< aux(37) 1.86/1.91 s(67) =< aux(37) 1.86/1.91 s(68) =< aux(32) 1.86/1.91 s(67) =< aux(32) 1.86/1.91 s(64) =< s(66) 1.86/1.91 s(63) =< s(66) 1.86/1.91 s(64) =< aux(32) 1.86/1.91 s(63) =< aux(32) 1.86/1.91 1.86/1.91 with precondition: [E=3,2*A=B,A>=3] 1.86/1.91 1.86/1.91 * Chain [26,[21,22,23,24,25],[27,28,29,30,31],32,37]: 5*it(21)+5*it(27)+1*s(23)+1*s(24)+2*s(27)+2*s(28)+1*s(63)+1*s(64)+1*s(67)+1*s(68)+1*s(71)+1*s(72)+2 1.86/1.91 Such that:aux(51) =< B 1.86/1.91 aux(50) =< B/2 1.86/1.91 it(27) =< aux(51) 1.86/1.91 aux(14) =< aux(51) 1.86/1.91 s(26) =< it(27)*aux(51) 1.86/1.91 aux(15) =< it(27)*aux(14) 1.86/1.91 s(27) =< aux(15)*(1/3) 1.86/1.91 s(23) =< aux(15)*(1/3) 1.86/1.91 s(28) =< aux(15) 1.86/1.91 s(27) =< aux(15) 1.86/1.91 s(24) =< s(26) 1.86/1.91 s(23) =< s(26) 1.86/1.91 s(24) =< aux(15) 1.86/1.91 s(23) =< aux(15) 1.86/1.91 it(21) =< aux(50) 1.86/1.91 aux(31) =< aux(51)-1 1.86/1.91 s(66) =< it(21)*aux(51) 1.86/1.91 aux(37) =< it(21)*aux(14) 1.86/1.91 aux(32) =< it(21)*aux(31) 1.86/1.91 s(71) =< aux(37)*(1/3) 1.86/1.91 s(67) =< aux(32)*(1/3) 1.86/1.91 s(63) =< aux(32)*(1/3) 1.86/1.91 s(72) =< aux(37) 1.86/1.91 s(71) =< aux(37) 1.86/1.91 s(68) =< aux(37) 1.86/1.91 s(67) =< aux(37) 1.86/1.91 s(68) =< aux(32) 1.86/1.91 s(67) =< aux(32) 1.86/1.91 s(64) =< s(66) 1.86/1.91 s(63) =< s(66) 1.86/1.91 s(64) =< aux(32) 1.86/1.91 s(63) =< aux(32) 1.86/1.91 1.86/1.91 with precondition: [E=3,2*A=B,A>=3] 1.86/1.91 1.86/1.91 * Chain [26,[21,22,23,24,25],37]: 5*it(21)+1*s(63)+1*s(64)+1*s(67)+1*s(68)+1*s(71)+1*s(72)+1 1.86/1.91 Such that:aux(30) =< B 1.86/1.91 aux(52) =< B/2 1.86/1.91 it(21) =< aux(52) 1.86/1.91 aux(33) =< aux(30) 1.86/1.91 aux(31) =< aux(30)-1 1.86/1.91 s(66) =< it(21)*aux(30) 1.86/1.91 aux(37) =< it(21)*aux(33) 1.86/1.91 aux(32) =< it(21)*aux(31) 1.86/1.91 s(71) =< aux(37)*(1/3) 1.86/1.91 s(67) =< aux(32)*(1/3) 1.86/1.91 s(63) =< aux(32)*(1/3) 1.86/1.91 s(72) =< aux(37) 1.86/1.91 s(71) =< aux(37) 1.86/1.91 s(68) =< aux(37) 1.86/1.91 s(67) =< aux(37) 1.86/1.91 s(68) =< aux(32) 1.86/1.91 s(67) =< aux(32) 1.86/1.91 s(64) =< s(66) 1.86/1.91 s(63) =< s(66) 1.86/1.91 s(64) =< aux(32) 1.86/1.91 s(63) =< aux(32) 1.86/1.91 1.86/1.91 with precondition: [E=3,2*A=B,A>=3] 1.86/1.91 1.86/1.91 * Chain [26,[21,22,23,24,25],35]: 5*it(21)+1*s(63)+1*s(64)+1*s(67)+1*s(68)+1*s(71)+1*s(72)+1 1.86/1.91 Such that:aux(30) =< B 1.86/1.91 aux(53) =< B/2 1.86/1.91 it(21) =< aux(53) 1.86/1.91 aux(33) =< aux(30) 1.86/1.91 aux(31) =< aux(30)-1 1.86/1.91 s(66) =< it(21)*aux(30) 1.86/1.91 aux(37) =< it(21)*aux(33) 1.86/1.91 aux(32) =< it(21)*aux(31) 1.86/1.91 s(71) =< aux(37)*(1/3) 1.86/1.91 s(67) =< aux(32)*(1/3) 1.86/1.91 s(63) =< aux(32)*(1/3) 1.86/1.91 s(72) =< aux(37) 1.86/1.91 s(71) =< aux(37) 1.86/1.91 s(68) =< aux(37) 1.86/1.91 s(67) =< aux(37) 1.86/1.91 s(68) =< aux(32) 1.86/1.91 s(67) =< aux(32) 1.86/1.91 s(64) =< s(66) 1.86/1.91 s(63) =< s(66) 1.86/1.91 s(64) =< aux(32) 1.86/1.91 s(63) =< aux(32) 1.86/1.91 1.86/1.91 with precondition: [E=3,2*A=B,A>=3] 1.86/1.91 1.86/1.91 * Chain [26,[21,22,23,24,25],34]: 5*it(21)+1*s(34)+1*s(36)+1*s(63)+1*s(64)+1*s(67)+1*s(68)+1*s(71)+1*s(72)+2 1.86/1.91 Such that:aux(54) =< A 1.86/1.91 aux(55) =< 2*A 1.86/1.91 s(34) =< 2/3*A 1.86/1.91 s(36) =< aux(55) 1.86/1.91 s(34) =< aux(55) 1.86/1.91 it(21) =< aux(54) 1.86/1.91 aux(33) =< aux(55) 1.86/1.91 aux(31) =< aux(55)-1 1.86/1.91 s(66) =< it(21)*aux(55) 1.86/1.91 aux(37) =< it(21)*aux(33) 1.86/1.91 aux(32) =< it(21)*aux(31) 1.86/1.91 s(71) =< aux(37)*(1/3) 1.86/1.91 s(67) =< aux(32)*(1/3) 1.86/1.91 s(63) =< aux(32)*(1/3) 1.86/1.91 s(72) =< aux(37) 1.86/1.91 s(71) =< aux(37) 1.86/1.91 s(68) =< aux(37) 1.86/1.91 s(67) =< aux(37) 1.86/1.91 s(68) =< aux(32) 1.86/1.91 s(67) =< aux(32) 1.86/1.91 s(64) =< s(66) 1.86/1.91 s(63) =< s(66) 1.86/1.91 s(64) =< aux(32) 1.86/1.91 s(63) =< aux(32) 1.86/1.91 1.86/1.91 with precondition: [E=3,2*A=B,A>=3] 1.86/1.91 1.86/1.91 * Chain [26,[21,22,23,24,25],33]: 5*it(21)+1*s(37)+1*s(40)+1*s(63)+1*s(64)+1*s(67)+1*s(68)+1*s(71)+1*s(72)+1 1.86/1.91 Such that:aux(56) =< A 1.86/1.91 aux(57) =< 2*A 1.86/1.91 s(39) =< 4*A 1.86/1.91 s(37) =< 2/3*A 1.86/1.91 s(40) =< aux(57) 1.86/1.91 s(37) =< aux(57) 1.86/1.91 s(40) =< s(39) 1.86/1.91 s(37) =< s(39) 1.86/1.91 it(21) =< aux(56) 1.86/1.91 aux(33) =< aux(57) 1.86/1.91 aux(31) =< aux(57)-1 1.86/1.91 s(66) =< it(21)*aux(57) 1.86/1.91 aux(37) =< it(21)*aux(33) 1.86/1.91 aux(32) =< it(21)*aux(31) 1.86/1.91 s(71) =< aux(37)*(1/3) 1.86/1.91 s(67) =< aux(32)*(1/3) 1.86/1.91 s(63) =< aux(32)*(1/3) 1.86/1.91 s(72) =< aux(37) 1.86/1.91 s(71) =< aux(37) 1.86/1.91 s(68) =< aux(37) 1.86/1.91 s(67) =< aux(37) 1.86/1.91 s(68) =< aux(32) 1.86/1.91 s(67) =< aux(32) 1.86/1.91 s(64) =< s(66) 1.86/1.91 s(63) =< s(66) 1.86/1.91 s(64) =< aux(32) 1.86/1.91 s(63) =< aux(32) 1.86/1.91 1.86/1.91 with precondition: [E=3,2*A=B,A>=3] 1.86/1.91 1.86/1.91 * Chain [26,37]: 1 1.86/1.91 with precondition: [E=3,2*A=B,A>=2] 1.86/1.91 1.86/1.91 * Chain [26,35]: 1 1.86/1.91 with precondition: [E=3,2*A=B,A>=2] 1.86/1.91 1.86/1.91 * Chain [26,34]: 1*s(34)+1*s(36)+2 1.86/1.91 Such that:s(35) =< 2 1.86/1.91 s(34) =< 2/3 1.86/1.91 s(36) =< s(35) 1.86/1.91 s(34) =< s(35) 1.86/1.91 1.86/1.91 with precondition: [A=2,B=4,E=3] 1.86/1.91 1.86/1.91 * Chain [26,33]: 1*s(37)+1*s(40)+1 1.86/1.91 Such that:s(38) =< 2 1.86/1.91 s(37) =< 2/3 1.86/1.91 s(39) =< B+2 1.86/1.91 s(40) =< s(38) 1.86/1.91 s(37) =< s(38) 1.86/1.91 s(40) =< s(39) 1.86/1.91 s(37) =< s(39) 1.86/1.91 1.86/1.91 with precondition: [E=3,2*A=B,A>=2] 1.86/1.91 1.86/1.91 1.86/1.91 #### Cost of chains of eval1(A,B,C,D,E): 1.86/1.91 * Chain [58]: 1 1.86/1.91 with precondition: [A=1,B=3] 1.86/1.91 1.86/1.91 * Chain [57]: 20*s(551)+8*s(555)+4*s(556)+8*s(557)+4*s(558)+1 1.86/1.91 Such that:s(550) =< B 1.86/1.91 s(551) =< s(550) 1.86/1.91 s(552) =< s(550) 1.86/1.91 s(553) =< s(551)*s(550) 1.86/1.91 s(554) =< s(551)*s(552) 1.86/1.91 s(555) =< s(554)*(1/3) 1.86/1.91 s(556) =< s(554)*(1/3) 1.86/1.91 s(557) =< s(554) 1.86/1.91 s(555) =< s(554) 1.86/1.91 s(558) =< s(553) 1.86/1.91 s(556) =< s(553) 1.86/1.91 s(558) =< s(554) 1.86/1.91 s(556) =< s(554) 1.86/1.91 1.86/1.91 with precondition: [A=1,B>=4] 1.86/1.91 1.86/1.91 * Chain [56]: 1*s(559)+1*s(563)+5*s(564)+2*s(568)+1*s(569)+2*s(570)+1*s(571)+0 1.86/1.91 Such that:s(560) =< B 1.86/1.91 s(561) =< 2*B 1.86/1.91 s(559) =< B/3 1.86/1.91 s(562) =< s(560) 1.86/1.91 s(559) =< s(560) 1.86/1.91 s(562) =< s(561) 1.86/1.91 s(563) =< s(560) 1.86/1.91 s(563) =< s(561) 1.86/1.91 s(559) =< s(561) 1.86/1.91 s(564) =< s(560) 1.86/1.91 s(564) =< s(562) 1.86/1.91 s(565) =< s(560) 1.86/1.91 s(566) =< s(564)*s(560) 1.86/1.91 s(567) =< s(564)*s(565) 1.86/1.91 s(568) =< s(567)*(1/3) 1.86/1.91 s(569) =< s(567)*(1/3) 1.86/1.91 s(570) =< s(567) 1.86/1.91 s(568) =< s(567) 1.86/1.91 s(571) =< s(566) 1.86/1.91 s(569) =< s(566) 1.86/1.91 s(571) =< s(567) 1.86/1.91 s(569) =< s(567) 1.86/1.91 1.86/1.91 with precondition: [A=1,B>=5] 1.86/1.91 1.86/1.91 * Chain [55]: 1*s(572)+6*s(574)+2*s(578)+1*s(579)+2*s(580)+1*s(581)+1 1.86/1.91 Such that:s(573) =< B 1.86/1.91 s(572) =< B/3 1.86/1.91 s(572) =< s(573) 1.86/1.91 s(574) =< s(573) 1.86/1.91 s(575) =< s(573) 1.86/1.91 s(576) =< s(574)*s(573) 1.86/1.91 s(577) =< s(574)*s(575) 1.86/1.91 s(578) =< s(577)*(1/3) 1.86/1.91 s(579) =< s(577)*(1/3) 1.86/1.91 s(580) =< s(577) 1.86/1.91 s(578) =< s(577) 1.86/1.91 s(581) =< s(576) 1.86/1.91 s(579) =< s(576) 1.86/1.91 s(581) =< s(577) 1.86/1.91 s(579) =< s(577) 1.86/1.91 1.86/1.91 with precondition: [A=1,B>=6] 1.86/1.91 1.86/1.91 * Chain [54]: 1 1.86/1.91 with precondition: [A=2,B=2] 1.86/1.91 1.86/1.91 * Chain [53]: 20*s(583)+8*s(587)+4*s(588)+8*s(589)+4*s(590)+1 1.86/1.91 Such that:s(582) =< B 1.86/1.91 s(583) =< s(582) 1.86/1.91 s(584) =< s(582) 1.86/1.91 s(585) =< s(583)*s(582) 1.86/1.91 s(586) =< s(583)*s(584) 1.86/1.91 s(587) =< s(586)*(1/3) 1.86/1.91 s(588) =< s(586)*(1/3) 1.86/1.91 s(589) =< s(586) 1.86/1.91 s(587) =< s(586) 1.86/1.91 s(590) =< s(585) 1.86/1.91 s(588) =< s(585) 1.86/1.91 s(590) =< s(586) 1.86/1.91 s(588) =< s(586) 1.86/1.91 1.86/1.91 with precondition: [A=2,B>=3] 1.86/1.91 1.86/1.91 * Chain [52]: 1*s(591)+1*s(595)+5*s(596)+2*s(600)+1*s(601)+2*s(602)+1*s(603)+0 1.86/1.91 Such that:s(592) =< B 1.86/1.91 s(593) =< 2*B 1.86/1.91 s(591) =< B/3 1.86/1.91 s(594) =< s(592) 1.86/1.91 s(591) =< s(592) 1.86/1.91 s(594) =< s(593) 1.86/1.91 s(595) =< s(592) 1.86/1.91 s(595) =< s(593) 1.86/1.91 s(591) =< s(593) 1.86/1.91 s(596) =< s(592) 1.86/1.91 s(596) =< s(594) 1.86/1.91 s(597) =< s(592) 1.86/1.91 s(598) =< s(596)*s(592) 1.86/1.91 s(599) =< s(596)*s(597) 1.86/1.91 s(600) =< s(599)*(1/3) 1.86/1.91 s(601) =< s(599)*(1/3) 1.86/1.91 s(602) =< s(599) 1.86/1.91 s(600) =< s(599) 1.86/1.91 s(603) =< s(598) 1.86/1.91 s(601) =< s(598) 1.86/1.91 s(603) =< s(599) 1.86/1.91 s(601) =< s(599) 1.86/1.91 1.86/1.91 with precondition: [A=2,B>=4] 1.86/1.91 1.86/1.91 * Chain [51]: 1*s(604)+6*s(606)+2*s(610)+1*s(611)+2*s(612)+1*s(613)+1 1.86/1.91 Such that:s(605) =< B 1.86/1.91 s(604) =< B/3 1.86/1.91 s(604) =< s(605) 1.86/1.91 s(606) =< s(605) 1.86/1.91 s(607) =< s(605) 1.86/1.91 s(608) =< s(606)*s(605) 1.86/1.91 s(609) =< s(606)*s(607) 1.86/1.91 s(610) =< s(609)*(1/3) 1.86/1.91 s(611) =< s(609)*(1/3) 1.86/1.91 s(612) =< s(609) 1.86/1.91 s(610) =< s(609) 1.86/1.91 s(613) =< s(608) 1.86/1.91 s(611) =< s(608) 1.86/1.91 s(613) =< s(609) 1.86/1.91 s(611) =< s(609) 1.86/1.91 1.86/1.91 with precondition: [A=2,B>=5] 1.86/1.91 1.86/1.91 * Chain [50]: 430 1.86/1.91 with precondition: [A=3,B=4] 1.86/1.91 1.86/1.91 * Chain [49]: 1 1.86/1.91 with precondition: [2*A=B+2,A>=2] 1.86/1.91 1.86/1.91 * Chain [48]: 1*s(615)+1*s(617)+1 1.86/1.91 Such that:s(614) =< 2 1.86/1.91 s(615) =< 2/3 1.86/1.91 s(616) =< 2*A 1.86/1.91 s(617) =< s(614) 1.86/1.91 s(615) =< s(614) 1.86/1.91 s(617) =< s(616) 1.86/1.91 s(615) =< s(616) 1.86/1.91 1.86/1.91 with precondition: [2*A=B+2,A>=3] 1.86/1.91 1.86/1.91 * Chain [47]: 2*s(624)+2*s(625)+2*s(626)+50*s(627)+10*s(633)+10*s(634)+10*s(635)+10*s(636)+10*s(637)+10*s(638)+27*s(639)+5*s(641)+2*s(644)+1*s(645)+2*s(646)+1*s(647)+10*s(650)+5*s(651)+10*s(652)+5*s(653)+2 1.86/1.91 Such that:s(620) =< 2*B 1.86/1.91 s(621) =< B/3 1.86/1.91 aux(70) =< B 1.86/1.91 aux(71) =< B/2 1.86/1.91 s(624) =< s(621) 1.86/1.91 s(625) =< s(621) 1.86/1.91 s(626) =< aux(70) 1.86/1.91 s(624) =< aux(70) 1.86/1.91 s(626) =< s(620) 1.86/1.91 s(624) =< s(620) 1.86/1.91 s(627) =< aux(71) 1.86/1.91 s(628) =< aux(70) 1.86/1.91 s(629) =< aux(70)-1 1.86/1.91 s(630) =< s(627)*aux(70) 1.86/1.91 s(631) =< s(627)*s(628) 1.86/1.91 s(632) =< s(627)*s(629) 1.86/1.91 s(633) =< s(631)*(1/3) 1.86/1.91 s(634) =< s(632)*(1/3) 1.86/1.91 s(635) =< s(632)*(1/3) 1.86/1.91 s(636) =< s(631) 1.86/1.91 s(633) =< s(631) 1.86/1.91 s(637) =< s(631) 1.86/1.91 s(634) =< s(631) 1.86/1.91 s(637) =< s(632) 1.86/1.91 s(634) =< s(632) 1.86/1.91 s(638) =< s(630) 1.86/1.91 s(635) =< s(630) 1.86/1.91 s(638) =< s(632) 1.86/1.91 s(635) =< s(632) 1.86/1.91 s(639) =< aux(70) 1.86/1.91 s(625) =< aux(70) 1.86/1.91 s(640) =< aux(70) 1.86/1.91 s(640) =< s(620) 1.86/1.91 s(641) =< aux(70) 1.86/1.91 s(641) =< s(640) 1.86/1.91 s(642) =< s(641)*aux(70) 1.86/1.91 s(643) =< s(641)*s(628) 1.86/1.91 s(644) =< s(643)*(1/3) 1.86/1.91 s(645) =< s(643)*(1/3) 1.86/1.91 s(646) =< s(643) 1.86/1.91 s(644) =< s(643) 1.86/1.91 s(647) =< s(642) 1.86/1.91 s(645) =< s(642) 1.86/1.91 s(647) =< s(643) 1.86/1.91 s(645) =< s(643) 1.86/1.91 s(648) =< s(639)*aux(70) 1.86/1.91 s(649) =< s(639)*s(628) 1.86/1.91 s(650) =< s(649)*(1/3) 1.86/1.91 s(651) =< s(649)*(1/3) 1.86/1.91 s(652) =< s(649) 1.86/1.91 s(650) =< s(649) 1.86/1.91 s(653) =< s(648) 1.86/1.91 s(651) =< s(648) 1.86/1.91 s(653) =< s(649) 1.86/1.91 s(651) =< s(649) 1.86/1.91 1.86/1.91 with precondition: [2*A=B+2,A>=4] 1.86/1.91 1.86/1.91 * Chain [46]: 0 1.86/1.91 with precondition: [1>=A] 1.86/1.91 1.86/1.91 * Chain [45]: 0 1.86/1.91 with precondition: [1>=A,B>=3] 1.86/1.91 1.86/1.91 * Chain [44]: 1*s(674)+1*s(675)+1 1.86/1.91 Such that:s(673) =< -2*A+B 1.86/1.91 s(674) =< -2/3*A+B/3 1.86/1.91 s(675) =< s(673) 1.86/1.91 s(674) =< s(673) 1.86/1.91 1.86/1.91 with precondition: [1>=A,2*A>=1,B>=4*A+1] 1.86/1.91 1.86/1.91 * Chain [43]: 1*s(678)+1*s(679)+0 1.86/1.91 Such that:s(676) =< -2*A+B 1.86/1.91 s(677) =< -2*A+2*B 1.86/1.91 s(678) =< -2/3*A+B/3 1.86/1.91 s(679) =< s(676) 1.86/1.91 s(678) =< s(676) 1.86/1.91 s(679) =< s(677) 1.86/1.91 s(678) =< s(677) 1.86/1.91 1.86/1.91 with precondition: [1>=A,2*A>=1,B>=2*A+2] 1.86/1.91 1.86/1.91 * Chain [42]: 0 1.86/1.91 with precondition: [A>=2] 1.86/1.91 1.86/1.91 * Chain [41]: 0 1.86/1.91 with precondition: [A>=2,B>=2] 1.86/1.91 1.86/1.91 * Chain [40]: 1*s(681)+1*s(682)+1 1.86/1.91 Such that:s(680) =< -2*A+B+2 1.86/1.91 s(681) =< -2/3*A+B/3+2/3 1.86/1.91 s(682) =< s(680) 1.86/1.91 s(681) =< s(680) 1.86/1.91 1.86/1.91 with precondition: [A>=2,B+4>=4*A] 1.86/1.91 1.86/1.91 * Chain [39]: 1*s(685)+1*s(686)+0 1.86/1.91 Such that:s(683) =< -2*A+B+2 1.86/1.91 s(684) =< -2*A+2*B+2 1.86/1.91 s(685) =< -2/3*A+B/3+2/3 1.86/1.91 s(686) =< s(683) 1.86/1.91 s(685) =< s(683) 1.86/1.91 s(686) =< s(684) 1.86/1.91 s(685) =< s(684) 1.86/1.91 1.86/1.91 with precondition: [A>=2,B+1>=2*A] 1.86/1.91 1.86/1.91 * Chain [38]: 2*s(691)+2*s(692)+27*s(693)+10*s(697)+5*s(698)+10*s(699)+5*s(700)+50*s(701)+10*s(706)+10*s(707)+10*s(708)+10*s(709)+10*s(710)+10*s(711)+2*s(712)+5*s(714)+2*s(717)+1*s(718)+2*s(719)+1*s(720)+1 1.86/1.91 Such that:s(687) =< A 1.86/1.91 s(688) =< B 1.86/1.91 s(689) =< 2*B 1.86/1.91 s(690) =< B/3 1.86/1.91 s(691) =< s(690) 1.86/1.91 s(692) =< s(690) 1.86/1.91 s(693) =< s(688) 1.86/1.91 s(694) =< s(688) 1.86/1.91 s(695) =< s(693)*s(688) 1.86/1.91 s(696) =< s(693)*s(694) 1.86/1.91 s(697) =< s(696)*(1/3) 1.86/1.91 s(698) =< s(696)*(1/3) 1.86/1.91 s(699) =< s(696) 1.86/1.91 s(697) =< s(696) 1.86/1.91 s(700) =< s(695) 1.86/1.91 s(698) =< s(695) 1.86/1.91 s(700) =< s(696) 1.86/1.91 s(698) =< s(696) 1.86/1.91 s(701) =< s(687) 1.86/1.91 s(702) =< s(688)-1 1.86/1.91 s(703) =< s(701)*s(688) 1.86/1.91 s(704) =< s(701)*s(694) 1.86/1.91 s(705) =< s(701)*s(702) 1.86/1.91 s(706) =< s(704)*(1/3) 1.86/1.91 s(707) =< s(705)*(1/3) 1.86/1.91 s(708) =< s(705)*(1/3) 1.86/1.91 s(709) =< s(704) 1.86/1.91 s(706) =< s(704) 1.86/1.91 s(710) =< s(704) 1.86/1.91 s(707) =< s(704) 1.86/1.91 s(710) =< s(705) 1.86/1.91 s(707) =< s(705) 1.86/1.91 s(711) =< s(703) 1.86/1.91 s(708) =< s(703) 1.86/1.91 s(711) =< s(705) 1.86/1.91 s(708) =< s(705) 1.86/1.91 s(712) =< s(688) 1.86/1.91 s(691) =< s(688) 1.86/1.91 s(712) =< s(689) 1.86/1.91 s(691) =< s(689) 1.86/1.91 s(713) =< s(688) 1.86/1.91 s(713) =< s(689) 1.86/1.91 s(714) =< s(688) 1.86/1.91 s(714) =< s(713) 1.86/1.91 s(715) =< s(714)*s(688) 1.86/1.91 s(716) =< s(714)*s(694) 1.86/1.91 s(717) =< s(716)*(1/3) 1.86/1.91 s(718) =< s(716)*(1/3) 1.86/1.91 s(719) =< s(716) 1.86/1.91 s(717) =< s(716) 1.86/1.91 s(720) =< s(715) 1.86/1.91 s(718) =< s(715) 1.86/1.91 s(720) =< s(716) 1.86/1.91 s(718) =< s(716) 1.86/1.91 s(692) =< s(688) 1.86/1.91 1.86/1.91 with precondition: [A>=3,B+1>=2*A] 1.86/1.91 1.86/1.91 1.86/1.91 Closed-form bounds of eval1(A,B,C,D,E): 1.86/1.91 ------------------------------------- 1.86/1.91 * Chain [58] with precondition: [A=1,B=3] 1.86/1.91 - Upper bound: 1 1.86/1.91 - Complexity: constant 1.86/1.91 * Chain [57] with precondition: [A=1,B>=4] 1.86/1.91 - Upper bound: 20*B+1+16*B*B 1.86/1.91 - Complexity: n^2 1.86/1.91 * Chain [56] with precondition: [A=1,B>=5] 1.86/1.91 - Upper bound: B/3+(4*B*B+6*B) 1.86/1.91 - Complexity: n^2 1.86/1.91 * Chain [55] with precondition: [A=1,B>=6] 1.86/1.91 - Upper bound: B/3+(6*B+1+4*B*B) 1.86/1.91 - Complexity: n^2 1.86/1.91 * Chain [54] with precondition: [A=2,B=2] 1.86/1.91 - Upper bound: 1 1.86/1.91 - Complexity: constant 1.86/1.91 * Chain [53] with precondition: [A=2,B>=3] 1.86/1.91 - Upper bound: 20*B+1+16*B*B 1.86/1.91 - Complexity: n^2 1.86/1.91 * Chain [52] with precondition: [A=2,B>=4] 1.86/1.91 - Upper bound: B/3+(4*B*B+6*B) 1.86/1.91 - Complexity: n^2 1.86/1.91 * Chain [51] with precondition: [A=2,B>=5] 1.86/1.91 - Upper bound: B/3+(6*B+1+4*B*B) 1.86/1.91 - Complexity: n^2 1.86/1.91 * Chain [50] with precondition: [A=3,B=4] 1.86/1.91 - Upper bound: 430 1.86/1.91 - Complexity: constant 1.86/1.91 * Chain [49] with precondition: [2*A=B+2,A>=2] 1.86/1.91 - Upper bound: 1 1.86/1.91 - Complexity: constant 1.86/1.91 * Chain [48] with precondition: [2*A=B+2,A>=3] 1.86/1.91 - Upper bound: 11/3 1.86/1.91 - Complexity: constant 1.86/1.91 * Chain [47] with precondition: [2*A=B+2,A>=4] 1.86/1.91 - Upper bound: 34*B+2+24*B*B+B/2*(100/3*B)+B/2*(20/3*B-20/3)+25*B+4/3*B 1.86/1.91 - Complexity: n^2 1.86/1.91 * Chain [46] with precondition: [1>=A] 1.86/1.91 - Upper bound: 0 1.86/1.91 - Complexity: constant 1.86/1.91 * Chain [45] with precondition: [1>=A,B>=3] 1.86/1.91 - Upper bound: 0 1.86/1.91 - Complexity: constant 1.86/1.91 * Chain [44] with precondition: [1>=A,2*A>=1,B>=4*A+1] 1.86/1.91 - Upper bound: -8/3*A+4/3*B+1 1.86/1.91 - Complexity: n 1.86/1.91 * Chain [43] with precondition: [1>=A,2*A>=1,B>=2*A+2] 1.86/1.91 - Upper bound: -8/3*A+4/3*B 1.86/1.91 - Complexity: n 1.86/1.91 * Chain [42] with precondition: [A>=2] 1.86/1.91 - Upper bound: 0 1.86/1.91 - Complexity: constant 1.86/1.91 * Chain [41] with precondition: [A>=2,B>=2] 1.86/1.91 - Upper bound: 0 1.86/1.91 - Complexity: constant 1.86/1.91 * Chain [40] with precondition: [A>=2,B+4>=4*A] 1.86/1.91 - Upper bound: -8/3*A+4/3*B+11/3 1.86/1.91 - Complexity: n 1.86/1.91 * Chain [39] with precondition: [A>=2,B+1>=2*A] 1.86/1.91 - Upper bound: -8/3*A+4/3*B+8/3 1.86/1.91 - Complexity: n 1.86/1.91 * Chain [38] with precondition: [A>=3,B+1>=2*A] 1.86/1.91 - Upper bound: 50*A+1+100/3*A*B+(B-1)*(20/3*A)+34*B+24*B*B+4/3*B 1.86/1.91 - Complexity: n^2 1.86/1.91 1.86/1.91 ### Maximum cost of eval1(A,B,C,D,E): max([max([max([430,nat(-2/3*A+B/3+2/3)+nat(-2*A+B+2)+1]),nat(-2/3*A+B/3)+nat(-2*A+B)+1]),nat(B)*4*nat(B)+nat(B)*6+max([nat(B)*14+1+nat(B)*12*nat(B),nat(B)*20*nat(B)+nat(B)*28+nat(B/3)*3+max([100/3*nat(A)*nat(B)+nat(A)*50+20/3*nat(A)*nat(nat(B)+ -1),100/3*nat(B)*nat(B/2)+1+20/3*nat(nat(B)+ -1)*nat(B/2)+nat(B/2)*50])+(nat(B/3)+1)])]) 1.86/1.91 Asymptotic class: n^2 1.86/1.91 * Total analysis performed in 1746 ms. 1.86/1.91 1.92/2.01 EOF