4.09/4.13 WORST_CASE(?,O(n^1)) 4.09/4.13 4.14/4.85 Preprocessing Cost Relations 4.14/4.85 ===================================== 4.14/4.85 4.14/4.85 #### Computed strongly connected components 4.14/4.85 0. recursive : [f1/7,f2/7,f3/7] 4.14/4.85 1. non_recursive : [exit_location/1] 4.14/4.85 2. non_recursive : [f1_loop_cont/2] 4.14/4.85 3. non_recursive : [f0/8] 4.14/4.85 4.14/4.85 #### Obtained direct recursion through partial evaluation 4.14/4.85 0. SCC is partially evaluated into f1/7 4.14/4.85 1. SCC is completely evaluated into other SCCs 4.14/4.85 2. SCC is completely evaluated into other SCCs 4.14/4.85 3. SCC is partially evaluated into f0/8 4.14/4.85 4.14/4.85 Control-Flow Refinement of Cost Relations 4.14/4.85 ===================================== 4.14/4.85 4.14/4.85 ### Specialization of cost equations f1/7 4.14/4.85 * CE 14 is refined into CE [15] 4.14/4.85 * CE 9 is refined into CE [16] 4.14/4.85 * CE 8 is refined into CE [17] 4.14/4.85 * CE 6 is refined into CE [18] 4.14/4.85 * CE 7 is refined into CE [19] 4.14/4.85 * CE 5 is refined into CE [20] 4.14/4.85 * CE 4 is refined into CE [21] 4.14/4.85 * CE 2 is refined into CE [22] 4.14/4.85 * CE 3 is refined into CE [23] 4.14/4.85 * CE 12 is refined into CE [24] 4.14/4.85 * CE 10 is refined into CE [25] 4.14/4.85 * CE 13 is refined into CE [26] 4.14/4.85 * CE 11 is refined into CE [27] 4.14/4.85 4.14/4.85 4.14/4.85 ### Cost equations --> "Loop" of f1/7 4.14/4.85 * CEs [16] --> Loop 15 4.14/4.85 * CEs [17] --> Loop 16 4.14/4.85 * CEs [18] --> Loop 17 4.14/4.85 * CEs [19] --> Loop 18 4.14/4.85 * CEs [20] --> Loop 19 4.14/4.85 * CEs [21] --> Loop 20 4.14/4.85 * CEs [22] --> Loop 21 4.14/4.85 * CEs [23] --> Loop 22 4.14/4.85 * CEs [24] --> Loop 23 4.14/4.85 * CEs [25] --> Loop 24 4.14/4.85 * CEs [26] --> Loop 25 4.14/4.85 * CEs [27] --> Loop 26 4.14/4.85 * CEs [15] --> Loop 27 4.14/4.85 4.14/4.85 ### Ranking functions of CR f1(A,B,D,E,F,G,H) 4.14/4.85 * RF of phase [16,17]: [B/2-D+1,-D+3] 4.14/4.85 * RF of phase [18]: [-A-D+5,-A/2+E-1/2,-A/3-D/3+2/3*E-1/3,B/2-D+1,-D+3,-D/3+2/3*E-1/3,E] 4.14/4.85 * RF of phase [19,22]: [-B/2+D-3/2,D-1] 4.14/4.85 * RF of phase [21]: [A+D-1,A/3+D/3-2/3*E,-B/2+D-3/2,D-1,D/3-2/3*E+1] 4.14/4.85 * RF of phase [23]: [A/2+B/4-E+1/2,A/2+D/2-E,A/2-E+3/2,B/4-E+2,D/2-E+3/2,-E+4] 4.14/4.85 * RF of phase [24]: [-A/2-B/4+E-3/2,-A/2-D/2+E-1/2,-A/2+E-1,-B/4+E-3/2,-D/2+E-1/2,E] 4.14/4.85 * RF of phase [25]: [A/2+B/4-E+1/4,A/2+D/2-E,A/2-E+3/2,B/4-E+7/4,D/2-E+3/2,-E+4] 4.14/4.85 * RF of phase [26]: [-A/2-B/4+E-5/4,-A/2-D/2+E-1/2,-A/2+E-1,-B/4+E-5/4,-D/2+E-1/2,E] 4.14/4.85 4.14/4.85 #### Partial ranking functions of CR f1(A,B,D,E,F,G,H) 4.14/4.85 * Partial RF of phase [16,17]: 4.14/4.85 - RF of loop [16:1]: 4.14/4.85 -A-D+2*E+1 depends on loops [17:1] 4.14/4.85 -D+2*E+1 depends on loops [17:1] 4.14/4.85 - RF of loop [16:1,17:1]: 4.14/4.85 B/2-D+1 4.14/4.85 -D+3 4.14/4.85 - RF of loop [17:1]: 4.14/4.85 A+D-2*E depends on loops [16:1] 4.14/4.85 A/2+B/4-E 4.14/4.85 A/2-E+1 4.14/4.85 B/4-E+3/2 4.14/4.85 D-2*E+3 depends on loops [16:1] 4.14/4.85 -E+3 4.14/4.85 * Partial RF of phase [18]: 4.14/4.85 - RF of loop [18:1]: 4.14/4.85 -A-D+5 4.14/4.85 -A/2+E-1/2 4.14/4.85 -A/3-D/3+2/3*E-1/3 4.14/4.85 B/2-D+1 4.14/4.85 -D+3 4.14/4.85 -D/3+2/3*E-1/3 4.14/4.85 E 4.14/4.85 * Partial RF of phase [19,22]: 4.14/4.85 - RF of loop [19:1]: 4.14/4.85 A+D-2*E+2 depends on loops [22:1] 4.14/4.85 D-2*E+5 depends on loops [22:1] 4.14/4.85 - RF of loop [19:1,22:1]: 4.14/4.85 -B/2+D-3/2 4.14/4.85 D-1 4.14/4.85 - RF of loop [22:1]: 4.14/4.85 -A-D+2*E-1 depends on loops [19:1] 4.14/4.85 -A/2-B/4+E-7/4 4.14/4.85 -A/2+E-3/2 4.14/4.85 -B/4+E-7/4 4.14/4.85 -D+2*E-1 depends on loops [19:1] 4.14/4.85 E-1 4.14/4.85 * Partial RF of phase [21]: 4.14/4.85 - RF of loop [21:1]: 4.14/4.85 A+D-1 4.14/4.85 A/3+D/3-2/3*E 4.14/4.85 -B/2+D-3/2 4.14/4.85 D-1 4.14/4.85 D/3-2/3*E+1 4.14/4.85 * Partial RF of phase [23]: 4.14/4.85 - RF of loop [23:1]: 4.14/4.85 A/2+B/4-E+1/2 4.14/4.85 A/2+D/2-E 4.14/4.85 A/2-E+3/2 4.14/4.85 B/4-E+2 4.14/4.85 D/2-E+3/2 4.14/4.85 -E+4 4.14/4.85 * Partial RF of phase [24]: 4.14/4.85 - RF of loop [24:1]: 4.14/4.85 -A/2-B/4+E-3/2 4.14/4.85 -A/2-D/2+E-1/2 4.14/4.85 -A/2+E-1 4.14/4.85 -B/4+E-3/2 4.14/4.85 -D/2+E-1/2 4.14/4.85 E 4.14/4.85 * Partial RF of phase [25]: 4.14/4.85 - RF of loop [25:1]: 4.14/4.85 A/2+B/4-E+1/4 4.14/4.85 A/2+D/2-E 4.14/4.85 A/2-E+3/2 4.14/4.85 B/4-E+7/4 4.14/4.85 D/2-E+3/2 4.14/4.85 -E+4 4.14/4.85 * Partial RF of phase [26]: 4.14/4.85 - RF of loop [26:1]: 4.14/4.85 -A/2-B/4+E-5/4 4.14/4.85 -A/2-D/2+E-1/2 4.14/4.85 -A/2+E-1 4.14/4.85 -B/4+E-5/4 4.14/4.85 -D/2+E-1/2 4.14/4.85 E 4.14/4.85 4.14/4.85 4.14/4.85 ### Specialization of cost equations f0/8 4.14/4.85 * CE 1 is refined into CE [28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63] 4.14/4.85 4.14/4.85 4.14/4.85 ### Cost equations --> "Loop" of f0/8 4.14/4.85 * CEs [59] --> Loop 28 4.14/4.85 * CEs [58] --> Loop 29 4.14/4.85 * CEs [63] --> Loop 30 4.14/4.85 * CEs [62] --> Loop 31 4.14/4.85 * CEs [61] --> Loop 32 4.14/4.85 * CEs [60] --> Loop 33 4.14/4.85 * CEs [51] --> Loop 34 4.14/4.85 * CEs [49] --> Loop 35 4.14/4.85 * CEs [48] --> Loop 36 4.14/4.85 * CEs [47] --> Loop 37 4.14/4.85 * CEs [57] --> Loop 38 4.14/4.85 * CEs [56] --> Loop 39 4.14/4.85 * CEs [55] --> Loop 40 4.14/4.85 * CEs [54] --> Loop 41 4.14/4.85 * CEs [53] --> Loop 42 4.14/4.85 * CEs [52] --> Loop 43 4.14/4.85 * CEs [46] --> Loop 44 4.14/4.85 * CEs [50] --> Loop 45 4.14/4.85 * CEs [44] --> Loop 46 4.14/4.85 * CEs [45] --> Loop 47 4.14/4.85 * CEs [43] --> Loop 48 4.14/4.85 * CEs [42] --> Loop 49 4.14/4.85 * CEs [41] --> Loop 50 4.14/4.85 * CEs [40] --> Loop 51 4.14/4.85 * CEs [39] --> Loop 52 4.14/4.85 * CEs [38] --> Loop 53 4.14/4.85 * CEs [37] --> Loop 54 4.14/4.85 * CEs [36] --> Loop 55 4.14/4.85 * CEs [35] --> Loop 56 4.14/4.85 * CEs [34] --> Loop 57 4.14/4.85 * CEs [33] --> Loop 58 4.14/4.85 * CEs [32] --> Loop 59 4.14/4.85 * CEs [30] --> Loop 60 4.14/4.85 * CEs [31] --> Loop 61 4.14/4.85 * CEs [29] --> Loop 62 4.14/4.85 * CEs [28] --> Loop 63 4.14/4.85 4.14/4.85 ### Ranking functions of CR f0(A,B,C,D,E,F,G,H) 4.14/4.85 4.14/4.85 #### Partial ranking functions of CR f0(A,B,C,D,E,F,G,H) 4.14/4.85 4.14/4.85 4.14/4.85 Computing Bounds 4.14/4.85 ===================================== 4.14/4.85 4.14/4.85 #### Cost of chains of f1(A,B,D,E,F,G,H): 4.14/4.85 * Chain [[26],27]: 1*it(26)+0 4.14/4.85 Such that:it(26) =< -A/2-D/2+E 4.14/4.85 4.14/4.85 with precondition: [H=2,2*D=B+2,5>=2*D,3>=A,A>=0,D>=1,2*E>=A+D+2] 4.14/4.85 4.14/4.85 * Chain [[25],27]: 1*it(25)+0 4.14/4.85 Such that:it(25) =< A/2+D/2-E 4.14/4.85 4.14/4.85 with precondition: [H=2,B+2=2*D,3>=A,3>=B,A>=0,B>=0,E>=0,B+2*A>=4*E] 4.14/4.85 4.14/4.85 * Chain [[24],27]: 1*it(24)+0 4.14/4.85 Such that:it(24) =< -A/2-D/2+E 4.14/4.85 4.14/4.85 with precondition: [H=2,2*D=B+3,3>=A,3>=D,A>=0,2*D>=3,2*E>=A+D+2] 4.14/4.85 4.14/4.85 * Chain [[23],27]: 1*it(23)+0 4.14/4.85 Such that:it(23) =< A/2+D/2-E 4.14/4.85 4.14/4.85 with precondition: [H=2,2*D=B+3,3>=A,3>=D,A>=0,E>=0,2*D>=3,A+D>=2*E+1] 4.14/4.85 4.14/4.85 * Chain [[21],[26],27]: 1*it(21)+1*it(26)+0 4.14/4.85 Such that:it(26) =< 1 4.14/4.85 it(21) =< A/3+D/3-2/3*E 4.14/4.85 4.14/4.85 with precondition: [H=2,2*A+3*B+10=4*D+4*E,3>=A,3>=B,A>=0,B>=0,E>=0,B+2*A+2>=4*E,B+2*A+4*E>=2] 4.14/4.85 4.14/4.85 * Chain [[21],[25],27]: 1*it(21)+1*it(25)+0 4.14/4.85 Such that:it(25) =< A/2+3/4*B-D-E+3/2 4.14/4.85 it(21) =< -B/2+D 4.14/4.85 4.14/4.85 with precondition: [H=2,3>=A,3>=B,E>=0,2*D>=B+4,B+2>=D,2*A+3*B+4>=4*D+4*E] 4.14/4.85 4.14/4.85 * Chain [[21],[24],27]: 1*it(21)+1*it(24)+0 4.14/4.85 Such that:it(24) =< 1 4.14/4.85 it(21) =< -B/2+D 4.14/4.85 4.14/4.85 with precondition: [H=2,2*A+3*B+13=4*D+4*E,3>=A,3>=B,A>=0,B>=0,E>=0,B+2*A+3>=4*E,3*B+4*E+6*A>=3] 4.14/4.85 4.14/4.85 * Chain [[21],[23],27]: 1*it(21)+1*it(23)+0 4.14/4.85 Such that:it(23) =< A/2+3/4*B-D-E+9/4 4.14/4.85 it(21) =< -B/2+D 4.14/4.85 4.14/4.85 with precondition: [H=2,3>=A,3>=B,E>=0,3*B+5>=2*D,2*D>=B+5,2*A+3*B+7>=4*D+4*E] 4.14/4.85 4.14/4.85 * Chain [[21],[19,22],[26],27]: 1*it(19)+1*it(21)+1*it(22)+1*s(1)+0 4.14/4.85 Such that:aux(32) =< -A/2-B/2+D+E 4.14/4.85 aux(32) =< -A/2+D+E 4.14/4.85 it(21) =< A/3+D/3-2/3*E 4.14/4.85 aux(35) =< -3/4*B+D+E 4.14/4.85 aux(35) =< -B/4+D+E 4.14/4.85 aux(40) =< -A/2-3/4*B+D+E 4.14/4.85 aux(41) =< -A/2-B/4+D+E 4.14/4.85 aux(42) =< -B/2+D+E 4.14/4.85 aux(43) =< D+E 4.14/4.85 aux(31) =< aux(40) 4.14/4.85 aux(33) =< aux(40) 4.14/4.85 aux(31) =< aux(41) 4.14/4.85 aux(37) =< aux(41) 4.14/4.85 aux(33) =< aux(42) 4.14/4.85 it(22) =< aux(42) 4.14/4.85 aux(37) =< aux(43) 4.14/4.85 it(22) =< aux(43) 4.14/4.85 it(22) =< aux(31) 4.14/4.85 s(1) =< aux(31) 4.14/4.85 it(22) =< aux(32) 4.14/4.85 s(1) =< aux(32) 4.14/4.85 it(19) =< aux(33) 4.14/4.85 it(22) =< aux(33) 4.14/4.85 it(22) =< aux(35) 4.14/4.85 it(19) =< aux(37) 4.14/4.85 it(22) =< aux(37) 4.14/4.85 4.14/4.85 with precondition: [H=2,3>=A,3>=B,A>=0,B>=0,E>=0,2*D>=B+6,A+D>=2*E+1,2*D+4*E>=B+8,4*D+4*E>=3*B+2*A+14] 4.14/4.85 4.14/4.85 * Chain [[21],[19,22],[24],27]: 1*it(19)+1*it(21)+1*it(22)+1*s(2)+0 4.14/4.85 Such that:aux(56) =< -A/2-3/4*B+D+E 4.14/4.85 aux(56) =< -A/2-B/4+D+E 4.14/4.85 it(21) =< A/3+D/3-2/3*E 4.14/4.85 aux(64) =< -A/2-B/2+D+E 4.14/4.85 aux(65) =< -A/2+D+E 4.14/4.85 aux(66) =< -3/4*B+D+E 4.14/4.85 aux(67) =< -B/4+D+E 4.14/4.85 aux(57) =< aux(64) 4.14/4.85 aux(58) =< aux(64) 4.14/4.85 aux(57) =< aux(65) 4.14/4.85 aux(61) =< aux(65) 4.14/4.85 aux(58) =< aux(66) 4.14/4.85 it(22) =< aux(66) 4.14/4.85 aux(61) =< aux(67) 4.14/4.85 it(22) =< aux(67) 4.14/4.85 it(22) =< aux(56) 4.14/4.85 s(2) =< aux(56) 4.14/4.85 it(22) =< aux(57) 4.14/4.85 s(2) =< aux(57) 4.14/4.85 it(19) =< aux(58) 4.14/4.85 it(22) =< aux(58) 4.14/4.85 it(19) =< aux(61) 4.14/4.85 it(22) =< aux(61) 4.14/4.85 4.14/4.85 with precondition: [H=2,3>=A,3>=B,A>=0,B>=0,E>=0,2*D>=B+7,6*D+8*E>=3*B+27,A+D>=2*E+1,4*D+4*E>=3*B+2*A+17] 4.14/4.85 4.14/4.85 * Chain [[21],[19,22],27]: 1*it(19)+1*it(21)+1*it(22)+0 4.14/4.85 Such that:aux(68) =< -A/3-B/2+2/3*D+2/3*E 4.14/4.85 aux(11) =< -A/3+2/3*D+2/3*E 4.14/4.85 it(21) =< A/3+D/3-2/3*E 4.14/4.85 aux(69) =< -A/2-3/4*B+D+E 4.14/4.85 aux(70) =< -A/2-B/4+D+E 4.14/4.85 aux(68) =< aux(69) 4.14/4.85 it(22) =< aux(69) 4.14/4.85 aux(11) =< aux(70) 4.14/4.85 it(22) =< aux(70) 4.14/4.85 it(22) =< aux(68) 4.14/4.85 it(19) =< aux(68) 4.14/4.85 it(19) =< aux(11) 4.14/4.85 it(22) =< aux(11) 4.14/4.85 4.14/4.85 with precondition: [H=2,3>=A,3>=B,A>=0,B>=0,E>=0,2*D>=B+6,A+D>=2*E+1,2*D+4*E>=B+8,4*D+4*E>=3*B+2*A+14] 4.14/4.85 4.14/4.85 * Chain [[21],27]: 1*it(21)+0 4.14/4.85 Such that:it(21) =< A/3+D/3-2/3*E 4.14/4.85 it(21) =< -B/2+D 4.14/4.85 4.14/4.85 with precondition: [H=2,3>=A,3>=B,A>=0,B>=0,E>=0,2*D>=B+4,A+D>=2*E+1] 4.14/4.85 4.14/4.85 * Chain [[21],20,[19,22],[26],27]: 1*it(19)+1*it(21)+1*it(22)+1*s(1)+1 4.14/4.85 Such that:aux(33) =< -A/3-B/2+2/3*D+2/3*E 4.14/4.85 aux(37) =< -A/3+2/3*D+2/3*E 4.14/4.85 aux(31) =< -A/6-B/4+D/3+E/3 4.14/4.85 aux(32) =< -A/6+D/3+E/3 4.14/4.85 aux(35) =< A/3-B/4+D/3+E/3 4.14/4.85 it(21) =< A/3+D/3-2/3*E 4.14/4.85 it(22) =< A/3+D/3+E/3 4.14/4.85 it(22) =< aux(31) 4.14/4.85 s(1) =< aux(31) 4.14/4.85 it(22) =< aux(32) 4.14/4.85 s(1) =< aux(32) 4.14/4.85 it(19) =< aux(33) 4.14/4.85 it(22) =< aux(33) 4.14/4.85 it(22) =< aux(35) 4.14/4.85 it(19) =< aux(37) 4.14/4.85 it(22) =< aux(37) 4.14/4.85 4.14/4.85 with precondition: [H=2,3>=A,3>=B,A>=0,B>=0,E>=0,A+D>=2*E+3,A+D+4*E>=6,4*D+4*E>=3*B+2*A+18] 4.14/4.85 4.14/4.85 * Chain [[21],20,[19,22],[24],27]: 1*it(19)+1*it(21)+1*it(22)+1*s(2)+1 4.14/4.85 Such that:aux(58) =< -A/3-B/2+2/3*D+2/3*E 4.14/4.85 aux(61) =< -A/3+2/3*D+2/3*E 4.14/4.85 aux(56) =< -A/6-B/4+D/3+E/3 4.14/4.85 aux(57) =< -A/6+D/3+E/3 4.14/4.85 it(22) =< A/3-B/4+D/3+E/3 4.14/4.85 it(21) =< A/3+D/3-2/3*E 4.14/4.85 it(22) =< aux(56) 4.14/4.85 s(2) =< aux(56) 4.14/4.85 it(22) =< aux(57) 4.14/4.85 s(2) =< aux(57) 4.14/4.85 it(19) =< aux(58) 4.14/4.85 it(22) =< aux(58) 4.14/4.85 it(19) =< aux(61) 4.14/4.85 it(22) =< aux(61) 4.14/4.85 4.14/4.85 with precondition: [H=2,3>=A,3>=B,A>=0,B>=0,E>=0,A+D>=2*E+3,A+D+2*E>=6,4*D+4*E>=3*B+2*A+21] 4.14/4.85 4.14/4.85 * Chain [[21],20,[19,22],27]: 1*it(19)+1*it(21)+1*it(22)+1 4.14/4.85 Such that:aux(68) =< -A/3-B/2+2/3*D+2/3*E 4.14/4.85 aux(11) =< -A/3+2/3*D+2/3*E 4.14/4.85 it(22) =< -A/6-B/4+D/3+E/3 4.14/4.85 it(21) =< A/3+D/3-2/3*E 4.14/4.85 it(22) =< aux(68) 4.14/4.85 it(19) =< aux(68) 4.14/4.85 it(19) =< aux(11) 4.14/4.85 it(22) =< aux(11) 4.14/4.85 4.14/4.85 with precondition: [H=2,3>=A,3>=B,A>=0,B>=0,E>=0,A+D>=2*E+3,A+D+4*E>=6,4*D+4*E>=3*B+2*A+18] 4.14/4.85 4.14/4.85 * Chain [[21],20,27]: 1*it(21)+1 4.14/4.85 Such that:it(21) =< A/3+D/3-2/3*E 4.14/4.85 4.14/4.85 with precondition: [H=2,3>=A,3>=B,A>=0,B>=0,E>=0,A+D>=2*E+3,4*D+4*E>=3*B+2*A+12,A+D+2*E>=B+3] 4.14/4.85 4.14/4.85 * Chain [[19,22],[26],27]: 1*it(19)+1*it(22)+1*s(1)+0 4.14/4.85 Such that:it(22) =< E 4.14/4.85 aux(31) =< -A/2-B/4+E 4.14/4.85 aux(32) =< -A/2+E 4.14/4.85 aux(33) =< -B/2+D 4.14/4.85 aux(35) =< -B/4+E 4.14/4.85 aux(37) =< D 4.14/4.85 it(22) =< aux(31) 4.14/4.85 s(1) =< aux(31) 4.14/4.85 it(22) =< aux(32) 4.14/4.85 s(1) =< aux(32) 4.14/4.85 it(19) =< aux(33) 4.14/4.85 it(22) =< aux(33) 4.14/4.85 it(22) =< aux(35) 4.14/4.85 it(19) =< aux(37) 4.14/4.85 it(22) =< aux(37) 4.14/4.85 4.14/4.85 with precondition: [H=2,3>=A,3>=B,A>=0,B>=0,2*D>=B+4,2*E>=A+D+1] 4.14/4.85 4.14/4.85 * Chain [[19,22],[24],27]: 1*it(19)+1*it(22)+1*s(2)+0 4.14/4.85 Such that:it(22) =< -B/4+E 4.14/4.85 it(22) =< E 4.14/4.85 aux(56) =< -A/2-B/4+E 4.14/4.85 aux(57) =< -A/2+E 4.14/4.85 aux(58) =< -B/2+D 4.14/4.85 aux(61) =< D 4.14/4.85 it(22) =< aux(56) 4.14/4.85 s(2) =< aux(56) 4.14/4.85 it(22) =< aux(57) 4.14/4.85 s(2) =< aux(57) 4.14/4.85 it(19) =< aux(58) 4.14/4.85 it(22) =< aux(58) 4.14/4.85 it(19) =< aux(61) 4.14/4.85 it(22) =< aux(61) 4.14/4.85 4.14/4.85 with precondition: [H=2,3>=A,3>=B,A>=0,B>=0,2*D>=B+5,2*E>=A+D+1] 4.14/4.85 4.14/4.85 * Chain [[19,22],27]: 1*it(19)+1*it(22)+0 4.14/4.85 Such that:it(22) =< -A-B/2+2*E 4.14/4.85 it(22) =< -A/2-B/4+E 4.14/4.85 aux(11) =< D 4.14/4.85 aux(68) =< -B/2+D 4.14/4.85 it(22) =< aux(68) 4.14/4.85 it(19) =< aux(68) 4.14/4.85 it(19) =< aux(11) 4.14/4.85 it(22) =< aux(11) 4.14/4.85 4.14/4.85 with precondition: [H=2,3>=A,3>=B,A>=0,B>=0,2*D>=B+4,2*E>=A+D+1] 4.14/4.85 4.14/4.85 * Chain [[18],[26],27]: 1*it(18)+1*it(26)+0 4.14/4.85 Such that:it(26) =< -A/2-3/4*B+D+E 4.14/4.85 it(18) =< B/2-D+1 4.14/4.85 4.14/4.85 with precondition: [H=2,B=2*D,3>=E,A>=0,B>=0,4*E>=2*A+B+10] 4.14/4.85 4.14/4.85 * Chain [[18],[25],27]: 1*it(18)+1*it(25)+0 4.14/4.85 Such that:it(25) =< 1/2 4.14/4.85 it(18) =< B/2-D+2/3 4.14/4.85 4.14/4.85 with precondition: [H=2,4*D+4*E=3*B+2*A+4,3>=B,3>=E,D>=0,B+10>=4*E,B>=2*D,4*D+4*E>=3*B+4] 4.14/4.85 4.14/4.85 * Chain [[18],[24],27]: 1*it(18)+1*it(24)+0 4.14/4.85 Such that:it(24) =< -A/2-3/4*B+D+E 4.14/4.85 it(18) =< B/2-D+1 4.14/4.85 4.14/4.85 with precondition: [H=2,B+1=2*D,3>=E,A>=0,B>=0,4*E>=2*A+B+11] 4.14/4.85 4.14/4.85 * Chain [[18],[23],27]: 1*it(18)+1*it(23)+0 4.14/4.85 Such that:it(23) =< 1/2 4.14/4.85 it(18) =< -A/3-D/3+2/3*E 4.14/4.85 4.14/4.85 with precondition: [H=2,4*D+4*E=3*B+2*A+7,3>=B,3>=E,D>=0,B+11>=4*E,B+1>=2*D,B+2*D>=1,4*D+4*E>=3*B+7] 4.14/4.85 4.14/4.85 * Chain [[18],[16,17],[25],27]: 1*it(16)+1*it(17)+1*it(18)+1*it(25)+0 4.14/4.85 Such that:it(18) =< -A/3-D/3+2/3*E 4.14/4.85 it(25) =< A/2+1/2 4.14/4.85 aux(83) =< B/2-D 4.14/4.85 aux(81) =< -D+2 4.14/4.85 aux(84) =< A/2+B/4-D-E+3 4.14/4.85 aux(85) =< A/2+3/4*B-D-E+1 4.14/4.85 aux(81) =< aux(84) 4.14/4.85 it(17) =< aux(84) 4.14/4.85 aux(83) =< aux(85) 4.14/4.85 it(17) =< aux(85) 4.14/4.85 it(17) =< aux(83) 4.14/4.85 it(16) =< aux(83) 4.14/4.85 it(16) =< aux(81) 4.14/4.85 it(17) =< aux(81) 4.14/4.85 4.14/4.85 with precondition: [H=2,3>=A,3>=B,3>=E,D>=0,B>=2*D+2,A+D+3>=2*E,2*E>=A+D+2,4*E+6*A>=B+4] 4.14/4.85 4.14/4.85 * Chain [[18],[16,17],[23],27]: 1*it(16)+1*it(17)+1*it(18)+1*it(23)+0 4.14/4.85 Such that:it(18) =< -A/3-D/3+2/3*E 4.14/4.85 it(23) =< A/2+1/2 4.14/4.85 aux(81) =< A/2+B/4-D-E+13/4 4.14/4.85 it(17) =< A/6+B/3+5/4 4.14/4.85 it(17) =< 2/3*A+B/3 4.14/4.85 aux(79) =< B/2-D 4.14/4.85 aux(86) =< B/2-D+1/2 4.14/4.85 it(17) =< B/4-E+5/2 4.14/4.85 it(17) =< 3/4*B-D-E+2 4.14/4.85 aux(81) =< -D+2 4.14/4.85 aux(87) =< A/2+3/4*B-D-E+5/4 4.14/4.85 aux(88) =< A/2+3/4*B-D-E+7/4 4.14/4.85 aux(79) =< aux(87) 4.14/4.85 it(17) =< aux(87) 4.14/4.85 aux(86) =< aux(88) 4.14/4.85 it(17) =< aux(88) 4.14/4.85 it(17) =< aux(86) 4.14/4.85 it(16) =< aux(79) 4.14/4.85 it(17) =< aux(79) 4.14/4.85 it(16) =< aux(86) 4.14/4.85 it(16) =< aux(81) 4.14/4.85 it(17) =< aux(81) 4.14/4.85 4.14/4.85 with precondition: [H=2,3>=A,3>=B,3>=E,A>=0,D>=0,B>=2*D+1,2*E>=A+D+2,B+2*A+12*E>=15,2*A+3*B+3>=4*D+4*E] 4.14/4.85 4.14/4.85 * Chain [[18],[16,17],27]: 1*it(16)+1*it(17)+1*it(18)+0 4.14/4.85 Such that:it(17) =< -A/2+B/4-E+4 4.14/4.85 it(18) =< -A/3-D/3+2/3*E 4.14/4.85 it(17) =< A/2+3/4*B-D-E+1/2 4.14/4.85 aux(81) =< A/2-D-E+4 4.14/4.85 aux(89) =< B+1 4.14/4.85 aux(79) =< B/2-D 4.14/4.85 aux(90) =< B/2-D+1/2 4.14/4.85 it(17) =< B/4-E+5/2 4.14/4.85 it(17) =< 3/4*B-D-E+2 4.14/4.85 aux(81) =< -D+2 4.14/4.85 aux(91) =< A/2+B/2-D-E+2 4.14/4.85 aux(92) =< A/2+B/2-D-E+5/2 4.14/4.85 aux(79) =< aux(91) 4.14/4.85 it(17) =< aux(91) 4.14/4.85 aux(90) =< aux(92) 4.14/4.85 it(17) =< aux(92) 4.14/4.85 aux(80) =< aux(89) 4.14/4.85 it(17) =< aux(89) 4.14/4.85 aux(80) =< aux(90) 4.14/4.85 it(16) =< aux(79) 4.14/4.85 it(17) =< aux(79) 4.14/4.85 it(16) =< aux(80) 4.14/4.85 it(17) =< aux(80) 4.14/4.85 it(16) =< aux(81) 4.14/4.85 it(17) =< aux(81) 4.14/4.85 4.14/4.85 with precondition: [H=2,3>=A,3>=B,3>=E,A>=0,D>=0,B>=2*D+1,2*E>=A+D+2,2*A+3*B+3>=4*D+4*E] 4.14/4.85 4.14/4.85 * Chain [[18],27]: 1*it(18)+0 4.14/4.85 Such that:it(18) =< -A/3-D/3+2/3*E 4.14/4.85 it(18) =< B/2-D+1 4.14/4.85 4.14/4.85 with precondition: [H=2,3>=A,3>=B,3>=E,A>=0,B>=0,D>=0,B+1>=2*D,2*E>=A+D+2] 4.14/4.85 4.14/4.85 * Chain [[18],15,[16,17],[23],27]: 1*it(16)+1*it(18)+1*it(23)+1 4.14/4.85 Such that:aux(79) =< 1/2 4.14/4.85 it(23) =< A/2+1/2 4.14/4.85 aux(93) =< 1 4.14/4.85 it(18) =< aux(93) 4.14/4.85 it(16) =< aux(79) 4.14/4.85 it(16) =< aux(93) 4.14/4.85 4.14/4.85 with precondition: [B=3,D=0,H=2,2*E=A+4,3>=E,E>=2] 4.14/4.85 4.14/4.85 * Chain [[18],15,[16,17],27]: 1*it(16)+1*it(18)+1 4.14/4.85 Such that:aux(89) =< 4 4.14/4.85 aux(79) =< 1/2 4.14/4.85 aux(94) =< 1 4.14/4.85 it(18) =< aux(94) 4.14/4.85 aux(80) =< aux(89) 4.14/4.85 aux(80) =< aux(94) 4.14/4.85 it(16) =< aux(79) 4.14/4.85 it(16) =< aux(80) 4.14/4.85 it(16) =< aux(94) 4.14/4.85 4.14/4.85 with precondition: [B=3,D=0,H=2,2*E=A+4,3>=E,E>=2] 4.14/4.85 4.14/4.85 * Chain [[18],15,27]: 1*it(18)+1 4.14/4.85 Such that:it(18) =< -A/3-D/3+2/3*E 4.14/4.85 4.14/4.85 with precondition: [H=2,2*E=A+D+4,3>=B,3>=E,D>=0,B>=2*D+1,2*E>=D+4] 4.14/4.85 4.14/4.85 * Chain [[16,17],[25],27]: 1*it(16)+1*it(17)+1*it(25)+0 4.14/4.85 Such that:it(25) =< A/2+1/2 4.14/4.85 it(17) =< A/2+B/4-E 4.14/4.85 aux(81) =< -D+3 4.14/4.85 aux(83) =< B/2-D+1 4.14/4.85 it(17) =< aux(83) 4.14/4.85 it(16) =< aux(83) 4.14/4.85 it(16) =< aux(81) 4.14/4.85 it(17) =< aux(81) 4.14/4.85 4.14/4.85 with precondition: [H=2,3>=A,3>=B,D>=0,E>=0,B>=2*D,A+D>=2*E,4*E+6*A>=B] 4.14/4.85 4.14/4.85 * Chain [[16,17],[23],27]: 1*it(16)+1*it(17)+1*it(23)+0 4.14/4.85 Such that:it(23) =< A/2+1/2 4.14/4.85 it(17) =< A/2+B/4-E 4.14/4.85 it(17) =< A/2+B/4-E+1/4 4.14/4.85 it(23) =< A/2+B/4+3*E 4.14/4.85 it(17) =< A/2-E+1 4.14/4.85 aux(79) =< B/2-D+1 4.14/4.85 it(17) =< B/4-E+3/2 4.14/4.85 aux(81) =< -D+3 4.14/4.85 aux(86) =< B/2-D+3/2 4.14/4.85 it(17) =< aux(86) 4.14/4.85 it(16) =< aux(79) 4.14/4.85 it(17) =< aux(79) 4.14/4.85 it(16) =< aux(86) 4.14/4.85 it(16) =< aux(81) 4.14/4.85 it(17) =< aux(81) 4.14/4.85 4.14/4.85 with precondition: [H=2,3>=A,3>=B,A>=0,D>=0,E>=0,B+1>=2*D,B+2*D>=1,A+D>=2*E,B+2*A+12*E>=3] 4.14/4.85 4.14/4.85 * Chain [[16,17],27]: 1*it(16)+1*it(17)+0 4.14/4.85 Such that:it(17) =< 2*A+B 4.14/4.85 it(17) =< A/2+B/4-E 4.14/4.85 it(17) =< A/2-E+1 4.14/4.85 aux(79) =< B/2-D+1 4.14/4.85 it(17) =< B/4-E+3/2 4.14/4.85 aux(81) =< -D+3 4.14/4.85 aux(89) =< B+1 4.14/4.85 aux(90) =< B/2-D+3/2 4.14/4.85 aux(80) =< aux(89) 4.14/4.85 it(17) =< aux(89) 4.14/4.85 aux(80) =< aux(90) 4.14/4.85 it(16) =< aux(79) 4.14/4.85 it(17) =< aux(79) 4.14/4.85 it(16) =< aux(80) 4.14/4.85 it(17) =< aux(80) 4.14/4.85 it(16) =< aux(81) 4.14/4.85 it(17) =< aux(81) 4.14/4.85 4.14/4.85 with precondition: [H=2,3>=A,3>=B,A>=0,B>=0,D>=0,E>=0,B+1>=2*D,A+D>=2*E,A+B+2*E>=D] 4.14/4.85 4.14/4.85 * Chain [27]: 0 4.14/4.85 with precondition: [H=2,3>=A,3>=B,A>=0,B>=0,D>=0,E>=0] 4.14/4.85 4.14/4.85 * Chain [20,[19,22],[26],27]: 1*it(19)+1*it(22)+1*s(1)+1 4.14/4.85 Such that:aux(33) =< -A-B/2+2*E 4.14/4.85 aux(37) =< -A+2*E 4.14/4.85 aux(31) =< -A/2-B/4+E 4.14/4.85 aux(32) =< -A/2+E 4.14/4.85 aux(35) =< -B/4+E 4.14/4.85 it(22) =< E 4.14/4.85 it(22) =< aux(31) 4.14/4.85 s(1) =< aux(31) 4.14/4.85 it(22) =< aux(32) 4.14/4.85 s(1) =< aux(32) 4.14/4.85 it(19) =< aux(33) 4.14/4.85 it(22) =< aux(33) 4.14/4.85 it(22) =< aux(35) 4.14/4.85 it(19) =< aux(37) 4.14/4.85 it(22) =< aux(37) 4.14/4.85 4.14/4.85 with precondition: [H=2,A+D=2*E,3>=B,B>=0,D+3>=2*E,2*D>=B+6,2*E>=D] 4.14/4.85 4.14/4.85 * Chain [20,[19,22],[24],27]: 1*it(19)+1*it(22)+1*s(2)+1 4.14/4.85 Such that:aux(58) =< -A-B/2+2*E 4.14/4.85 aux(61) =< -A+2*E 4.14/4.85 aux(56) =< -A/2-B/4+E 4.14/4.85 aux(57) =< -A/2+E 4.14/4.85 it(22) =< -B/4+E 4.14/4.85 it(22) =< aux(56) 4.14/4.85 s(2) =< aux(56) 4.14/4.85 it(22) =< aux(57) 4.14/4.85 s(2) =< aux(57) 4.14/4.85 it(19) =< aux(58) 4.14/4.85 it(22) =< aux(58) 4.14/4.85 it(19) =< aux(61) 4.14/4.85 it(22) =< aux(61) 4.14/4.85 4.14/4.85 with precondition: [H=2,A+D=2*E,3>=B,B>=0,D+3>=2*E,2*D>=B+7,2*E>=D] 4.14/4.85 4.14/4.85 * Chain [20,[19,22],27]: 1*it(19)+1*it(22)+1 4.14/4.85 Such that:aux(68) =< -A-B/2+2*E 4.14/4.85 aux(11) =< -A+2*E 4.14/4.85 it(22) =< -A/2-B/4+E 4.14/4.85 it(22) =< aux(68) 4.14/4.85 it(19) =< aux(68) 4.14/4.85 it(19) =< aux(11) 4.14/4.85 it(22) =< aux(11) 4.14/4.85 4.14/4.85 with precondition: [H=2,A+D=2*E,3>=B,B>=0,D+3>=2*E,2*D>=B+6,2*E>=D] 4.14/4.85 4.14/4.85 * Chain [20,27]: 1 4.14/4.85 with precondition: [H=2,A+D=2*E,3>=B,B>=0,D+3>=2*E,2*D>=B+4,2*E>=D] 4.14/4.85 4.14/4.85 * Chain [15,[16,17],[25],27]: 1*it(16)+1*it(17)+1*it(25)+1 4.14/4.85 Such that:it(25) =< A/2+1/2 4.14/4.85 aux(83) =< B/2-D 4.14/4.85 it(17) =< B/4-D/2 4.14/4.85 aux(81) =< -D+2 4.14/4.85 it(17) =< aux(83) 4.14/4.85 it(16) =< aux(83) 4.14/4.85 it(16) =< aux(81) 4.14/4.85 it(17) =< aux(81) 4.14/4.85 4.14/4.85 with precondition: [H=2,A+D+1=2*E,3>=B,D>=0,B>=2*D+2,D+4>=2*E,16*E>=6*D+B+6] 4.14/4.85 4.14/4.85 * Chain [15,[16,17],[23],27]: 1*it(16)+1*it(17)+1*it(23)+1 4.14/4.85 Such that:it(17) =< -A/2+B/4-D/2+1 4.14/4.85 it(23) =< A/2+1/2 4.14/4.85 aux(79) =< B/2-D 4.14/4.85 aux(86) =< B/2-D+1/2 4.14/4.85 it(17) =< B/4-D/2 4.14/4.85 it(17) =< B/4-E+3/2 4.14/4.85 aux(81) =< -D+2 4.14/4.85 it(17) =< -D/2+1/4 4.14/4.85 it(17) =< aux(86) 4.14/4.85 it(16) =< aux(79) 4.14/4.85 it(17) =< aux(79) 4.14/4.85 it(16) =< aux(86) 4.14/4.85 it(16) =< aux(81) 4.14/4.85 it(17) =< aux(81) 4.14/4.85 4.14/4.85 with precondition: [H=2,A+D+1=2*E,3>=B,D>=0,B>=2*D+1,D+4>=2*E,2*E>=D+1] 4.14/4.85 4.14/4.85 * Chain [15,[16,17],27]: 1*it(16)+1*it(17)+1 4.14/4.85 Such that:it(17) =< -A/2+B/4-D/2+1 4.14/4.85 aux(89) =< B+1 4.14/4.85 aux(79) =< B/2-D 4.14/4.85 aux(90) =< B/2-D+1/2 4.14/4.85 it(17) =< B/4-D/2 4.14/4.85 it(17) =< B/4-E+3/2 4.14/4.85 aux(81) =< -D+2 4.14/4.85 it(17) =< -D/2+1/2 4.14/4.85 it(17) =< -D/2+1/4 4.14/4.85 aux(80) =< aux(89) 4.14/4.85 it(17) =< aux(89) 4.14/4.85 aux(80) =< aux(90) 4.14/4.85 it(16) =< aux(79) 4.14/4.85 it(17) =< aux(79) 4.14/4.85 it(16) =< aux(80) 4.14/4.85 it(17) =< aux(80) 4.14/4.85 it(16) =< aux(81) 4.14/4.85 it(17) =< aux(81) 4.14/4.85 4.14/4.85 with precondition: [H=2,A+D+1=2*E,3>=B,D>=0,B>=2*D+1,D+4>=2*E,2*E>=D+1] 4.14/4.85 4.14/4.85 * Chain [15,27]: 1 4.14/4.85 with precondition: [H=2,A+D+1=2*E,3>=B,B>=0,D>=0,B+1>=2*D,D+4>=2*E,2*E>=D+1] 4.14/4.85 4.14/4.85 4.14/4.85 #### Cost of chains of f0(A,B,C,D,E,F,G,H): 4.14/4.85 * Chain [63]: 1*s(86)+2*s(89)+1*s(91)+1*s(92)+1 4.14/4.85 Such that:s(87) =< 1 4.14/4.85 s(85) =< 4 4.14/4.85 s(88) =< 1/2 4.14/4.85 s(86) =< E 4.14/4.85 s(89) =< s(87) 4.14/4.85 s(90) =< s(85) 4.14/4.85 s(90) =< s(87) 4.14/4.85 s(91) =< s(88) 4.14/4.85 s(91) =< s(90) 4.14/4.85 s(91) =< s(87) 4.14/4.85 s(92) =< s(88) 4.14/4.85 s(92) =< s(87) 4.14/4.85 4.14/4.85 with precondition: [B=3,D=0,2*E=A+4,3>=C,3>=E,E>=2] 4.14/4.85 4.14/4.85 * Chain [62]: 1*s(93)+0 4.14/4.85 Such that:s(93) =< A/2+D/2-E 4.14/4.85 4.14/4.85 with precondition: [B+2=2*D,3>=A,3>=B,3>=C,A>=0,B>=0,E>=0,B+2*A>=4*E] 4.14/4.85 4.14/4.85 * Chain [61]: 1*s(94)+1*s(95)+0 4.14/4.85 Such that:s(95) =< 1 4.14/4.85 s(94) =< -A/2-B/4+E 4.14/4.85 4.14/4.85 with precondition: [2*D=B,3>=C,3>=E,A>=0,D>=0,2*E>=A+D+5] 4.14/4.85 4.14/4.85 * Chain [60]: 1*s(96)+1*s(97)+0 4.14/4.85 Such that:s(97) =< 1/2 4.14/4.85 s(96) =< -A/2-B/4+E+1/2 4.14/4.85 4.14/4.85 with precondition: [2*D=B+1,3>=C,3>=E,A>=0,2*D>=1,2*E>=A+D+5] 4.14/4.85 4.14/4.85 * Chain [59]: 1*s(98)+0 4.14/4.85 Such that:s(98) =< -A/2-D/2+E 4.14/4.85 4.14/4.85 with precondition: [2*D=B+2,5>=2*D,3>=C,3>=E,A>=0,D>=1,2*E>=A+D+2] 4.14/4.85 4.14/4.85 * Chain [58]: 1*s(99)+0 4.14/4.85 Such that:s(99) =< A/2+D/2-E 4.14/4.85 4.14/4.85 with precondition: [2*D=B+3,3>=A,3>=C,3>=D,A>=0,E>=0,2*D>=3,A+D>=2*E+1] 4.14/4.85 4.14/4.85 * Chain [57]: 1*s(100)+0 4.14/4.85 Such that:s(100) =< -A/2-D/2+E 4.14/4.85 4.14/4.85 with precondition: [2*D=B+3,3>=C,3>=D,3>=E,A>=0,2*D>=3,2*E>=A+D+2] 4.14/4.85 4.14/4.85 * Chain [56]: 1 4.14/4.85 with precondition: [2*E=A+D+1,3>=B,3>=C,B>=0,D>=0,B+1>=2*D,D+4>=2*E,2*E>=D+1] 4.14/4.85 4.14/4.85 * Chain [55]: 1*s(101)+1*s(103)+1*s(111)+1*s(113)+1*s(114)+1 4.14/4.85 Such that:s(110) =< A/2-E+3/4 4.14/4.85 s(102) =< B+1 4.14/4.85 s(105) =< B/2-D 4.14/4.85 s(106) =< B/2-D+1/2 4.14/4.85 s(107) =< B/4-D/2 4.14/4.85 s(109) =< -D+2 4.14/4.85 s(103) =< -D/2+1/2 4.14/4.85 s(110) =< -D/2+1/4 4.14/4.85 s(101) =< -D/2+E 4.14/4.85 aux(117) =< -A/2+B/4-D/2+1 4.14/4.85 aux(118) =< B/4-E+3/2 4.14/4.85 s(104) =< aux(117) 4.14/4.85 s(104) =< aux(118) 4.14/4.85 s(103) =< s(104) 4.14/4.85 s(111) =< s(104) 4.14/4.85 s(103) =< s(107) 4.14/4.85 s(111) =< s(107) 4.14/4.85 s(103) =< s(110) 4.14/4.85 s(111) =< s(110) 4.14/4.85 s(112) =< s(102) 4.14/4.85 s(103) =< s(102) 4.14/4.85 s(112) =< s(106) 4.14/4.85 s(113) =< s(105) 4.14/4.85 s(103) =< s(105) 4.14/4.85 s(113) =< s(112) 4.14/4.85 s(103) =< s(112) 4.14/4.85 s(113) =< s(109) 4.14/4.85 s(103) =< s(109) 4.14/4.85 s(111) =< s(106) 4.14/4.85 s(114) =< s(105) 4.14/4.85 s(111) =< s(105) 4.14/4.85 s(114) =< s(106) 4.14/4.85 s(114) =< s(109) 4.14/4.85 s(111) =< s(109) 4.14/4.85 4.14/4.85 with precondition: [2*E=A+D+1,3>=B,3>=C,D>=0,B>=2*D+1,D+4>=2*E,2*E>=D+1] 4.14/4.85 4.14/4.85 * Chain [54]: 1*s(115)+1*s(117)+1*s(119)+1 4.14/4.85 Such that:s(115) =< A/2+1/2 4.14/4.85 s(116) =< B/2-D 4.14/4.85 s(117) =< B/4-D/2 4.14/4.85 s(118) =< -D+2 4.14/4.85 s(117) =< s(116) 4.14/4.85 s(119) =< s(116) 4.14/4.85 s(119) =< s(118) 4.14/4.85 s(117) =< s(118) 4.14/4.85 4.14/4.85 with precondition: [2*E=A+D+1,3>=B,3>=C,D>=0,B>=2*D+2,D+4>=2*E,16*E>=6*D+B+6] 4.14/4.85 4.14/4.85 * Chain [53]: 1 4.14/4.85 with precondition: [2*E=A+D,3>=B,3>=C,3>=E,B>=0,D+3>=2*E,2*D>=B+4,2*E>=D] 4.14/4.85 4.14/4.85 * Chain [52]: 1*s(122)+1*s(126)+2*s(127)+1*s(128)+1 4.14/4.85 Such that:s(123) =< -A-B/2+2*E 4.14/4.85 s(124) =< -A+2*E 4.14/4.85 s(125) =< -A/2-B/4+E 4.14/4.85 s(120) =< -A/2+E 4.14/4.85 s(121) =< -B/4+E 4.14/4.85 s(122) =< E 4.14/4.85 s(126) =< s(125) 4.14/4.85 s(126) =< s(123) 4.14/4.85 s(127) =< s(123) 4.14/4.85 s(127) =< s(124) 4.14/4.85 s(126) =< s(124) 4.14/4.85 s(122) =< s(125) 4.14/4.85 s(128) =< s(125) 4.14/4.85 s(122) =< s(120) 4.14/4.85 s(128) =< s(120) 4.14/4.85 s(122) =< s(123) 4.14/4.85 s(122) =< s(121) 4.14/4.85 s(122) =< s(124) 4.14/4.85 4.14/4.85 with precondition: [2*E=A+D,3>=B,3>=C,3>=E,B>=0,2*D>=B+6,2*E>=D] 4.14/4.85 4.14/4.85 * Chain [51]: 1*s(133)+1*s(134)+1*s(135)+1 4.14/4.85 Such that:s(129) =< -A-B/2+2*E 4.14/4.85 s(130) =< -A+2*E 4.14/4.85 s(131) =< -A/2-B/4+E 4.14/4.85 s(132) =< -A/2+E 4.14/4.85 s(133) =< -B/4+E 4.14/4.85 s(133) =< s(131) 4.14/4.85 s(134) =< s(131) 4.14/4.85 s(133) =< s(132) 4.14/4.85 s(134) =< s(132) 4.14/4.85 s(135) =< s(129) 4.14/4.85 s(133) =< s(129) 4.14/4.85 s(135) =< s(130) 4.14/4.85 s(133) =< s(130) 4.14/4.85 4.14/4.85 with precondition: [2*E=A+D,3>=B,3>=C,3>=E,B>=0,2*D>=B+7,2*E>=D] 4.14/4.85 4.14/4.85 * Chain [50]: 1*s(136)+1 4.14/4.85 Such that:s(136) =< 4/3 4.14/4.85 4.14/4.85 with precondition: [A+D+4=2*E,3>=B,3>=C,3>=E,D>=0,B>=2*D+1,2*E>=D+4] 4.14/4.85 4.14/4.85 * Chain [49]: 1*s(137)+1*s(138)+0 4.14/4.85 Such that:s(137) =< 1 4.14/4.85 s(138) =< -B/2+D 4.14/4.85 4.14/4.85 with precondition: [4*D+4*E=3*B+2*A+13,3>=B,3>=C,B>=0,E>=0,2*D>=B+5,3*B+19>=4*D+4*E,4*D+4*E>=3*B+13,6*D+8*E>=3*B+21] 4.14/4.85 4.14/4.85 * Chain [48]: 1*s(139)+1*s(140)+0 4.14/4.85 Such that:s(139) =< 1 4.14/4.85 s(140) =< -B/2+D 4.14/4.85 4.14/4.85 with precondition: [4*D+4*E=3*B+2*A+10,3>=B,3>=C,B>=0,E>=0,2*D>=B+4,3*B+16>=4*D+4*E,4*D+4*E>=3*B+10,2*D+4*E>=B+6] 4.14/4.85 4.14/4.85 * Chain [47]: 1*s(141)+1*s(142)+0 4.14/4.85 Such that:s(141) =< 1/2 4.14/4.85 s(142) =< B/2-D+7/6 4.14/4.85 4.14/4.85 with precondition: [4*D+4*E=3*B+2*A+7,3>=B,3>=C,3>=E,D>=0,B+11>=4*E,B+1>=2*D,B+2*D>=1,4*D+4*E>=3*B+7] 4.14/4.85 4.14/4.85 * Chain [46]: 1*s(143)+1*s(144)+0 4.14/4.85 Such that:s(143) =< 1/2 4.14/4.85 s(144) =< B/2-D+2/3 4.14/4.85 4.14/4.85 with precondition: [4*D+4*E=3*B+2*A+4,3>=B,3>=C,3>=E,D>=0,B+10>=4*E,B>=2*D,4*D+4*E>=3*B+4] 4.14/4.85 4.14/4.85 * Chain [45]: 0 4.14/4.85 with precondition: [3>=A,3>=B,3>=C,3>=E,A>=0,B>=0,D>=0,E>=0] 4.14/4.85 4.14/4.85 * Chain [44]: 1*s(145)+0 4.14/4.85 Such that:s(145) =< -A/3-D/3+2/3*E 4.14/4.85 s(145) =< B/2-D+1 4.14/4.85 4.14/4.85 with precondition: [3>=A,3>=B,3>=C,3>=E,A>=0,B>=0,D>=0,B+1>=2*D,2*E>=A+D+2] 4.14/4.85 4.14/4.85 * Chain [43]: 1*s(146)+0 4.14/4.85 Such that:s(146) =< A/3+D/3-2/3*E 4.14/4.85 s(146) =< -B/2+D 4.14/4.85 4.14/4.85 with precondition: [3>=A,3>=B,3>=C,3>=E,A>=0,B>=0,E>=0,2*D>=B+4,A+D>=2*E+1] 4.14/4.85 4.14/4.85 * Chain [42]: 2*s(156)+1*s(160)+1*s(161)+1*s(162)+1*s(163)+1*s(164)+0 4.14/4.85 Such that:s(153) =< -A/2-3/4*B+D+E 4.14/4.85 s(147) =< -A/2-B/2+D+E 4.14/4.85 s(154) =< -A/2-B/4+D+E 4.14/4.85 s(148) =< -A/3-B/2+2/3*D+2/3*E 4.14/4.85 s(149) =< -A/3+2/3*D+2/3*E 4.14/4.85 s(155) =< A/3+D/3-2/3*E 4.14/4.85 s(150) =< -3/4*B+D+E 4.14/4.85 s(151) =< -B/2+D+E 4.14/4.85 s(152) =< D+E 4.14/4.85 s(156) =< s(155) 4.14/4.85 s(157) =< s(153) 4.14/4.85 s(158) =< s(153) 4.14/4.85 s(157) =< s(154) 4.14/4.85 s(159) =< s(154) 4.14/4.85 s(158) =< s(151) 4.14/4.85 s(160) =< s(151) 4.14/4.85 s(159) =< s(152) 4.14/4.85 s(160) =< s(152) 4.14/4.85 s(160) =< s(157) 4.14/4.85 s(161) =< s(157) 4.14/4.85 s(160) =< s(147) 4.14/4.85 s(161) =< s(147) 4.14/4.85 s(162) =< s(158) 4.14/4.85 s(160) =< s(158) 4.14/4.85 s(160) =< s(150) 4.14/4.85 s(162) =< s(159) 4.14/4.85 s(160) =< s(159) 4.14/4.85 s(148) =< s(153) 4.14/4.85 s(163) =< s(153) 4.14/4.85 s(149) =< s(154) 4.14/4.85 s(163) =< s(154) 4.14/4.85 s(163) =< s(148) 4.14/4.85 s(164) =< s(148) 4.14/4.85 s(164) =< s(149) 4.14/4.85 s(163) =< s(149) 4.14/4.85 4.14/4.85 with precondition: [3>=A,3>=B,3>=C,3>=E,A>=0,B>=0,E>=0,2*D>=B+6,A+D>=2*E+1,2*D+4*E>=B+8,4*D+4*E>=3*B+2*A+14] 4.14/4.85 4.14/4.85 * Chain [41]: 1*s(166)+1*s(174)+1*s(175)+1*s(176)+0 4.14/4.85 Such that:s(165) =< -A/2-3/4*B+D+E 4.14/4.85 s(167) =< -A/2-B/2+D+E 4.14/4.85 s(168) =< -A/2+D+E 4.14/4.85 s(166) =< A/3+D/3-2/3*E 4.14/4.85 s(169) =< -3/4*B+D+E 4.14/4.85 s(170) =< -B/4+D+E 4.14/4.85 s(171) =< s(167) 4.14/4.85 s(172) =< s(167) 4.14/4.85 s(171) =< s(168) 4.14/4.85 s(173) =< s(168) 4.14/4.85 s(172) =< s(169) 4.14/4.85 s(174) =< s(169) 4.14/4.85 s(173) =< s(170) 4.14/4.85 s(174) =< s(170) 4.14/4.85 s(174) =< s(165) 4.14/4.85 s(175) =< s(165) 4.14/4.85 s(174) =< s(171) 4.14/4.85 s(175) =< s(171) 4.14/4.85 s(176) =< s(172) 4.14/4.85 s(174) =< s(172) 4.14/4.85 s(176) =< s(173) 4.14/4.85 s(174) =< s(173) 4.14/4.85 4.14/4.85 with precondition: [3>=A,3>=B,3>=C,3>=E,A>=0,B>=0,E>=0,2*D>=B+7,6*D+8*E>=3*B+27,A+D>=2*E+1,4*D+4*E>=3*B+2*A+17] 4.14/4.85 4.14/4.85 * Chain [40]: 1*s(181)+1*s(182)+1*s(183)+1*s(184)+1 4.14/4.85 Such that:s(177) =< -A/3-B/2+2/3*D+2/3*E 4.14/4.85 s(178) =< -A/3+2/3*D+2/3*E 4.14/4.86 s(179) =< -A/6-B/4+D/3+E/3 4.14/4.86 s(180) =< -A/6+D/3+E/3 4.14/4.86 s(181) =< A/3-B/4+D/3+E/3 4.14/4.86 s(182) =< A/3+D/3-2/3*E 4.14/4.86 s(181) =< s(179) 4.14/4.86 s(183) =< s(179) 4.14/4.86 s(181) =< s(180) 4.14/4.86 s(183) =< s(180) 4.14/4.86 s(184) =< s(177) 4.14/4.86 s(181) =< s(177) 4.14/4.86 s(184) =< s(178) 4.14/4.86 s(181) =< s(178) 4.14/4.86 4.14/4.86 with precondition: [3>=A,3>=B,3>=C,3>=E,A>=0,B>=0,E>=0,A+D>=2*E+3,A+D+2*E>=6,4*D+4*E>=3*B+2*A+21] 4.14/4.86 4.14/4.86 * Chain [39]: 1*s(187)+1*s(192)+2*s(193)+2*s(194)+1*s(195)+1 4.14/4.86 Such that:s(188) =< -A/3-B/2+2/3*D+2/3*E 4.14/4.86 s(189) =< -A/3+2/3*D+2/3*E 4.14/4.86 s(190) =< -A/6-B/4+D/3+E/3 4.14/4.86 s(185) =< -A/6+D/3+E/3 4.14/4.86 s(186) =< A/3-B/4+D/3+E/3 4.14/4.86 s(191) =< A/3+D/3-2/3*E 4.14/4.86 s(187) =< A/3+D/3+E/3 4.14/4.86 s(192) =< s(190) 4.14/4.86 s(193) =< s(191) 4.14/4.86 s(192) =< s(188) 4.14/4.86 s(194) =< s(188) 4.14/4.86 s(194) =< s(189) 4.14/4.86 s(192) =< s(189) 4.14/4.86 s(187) =< s(190) 4.14/4.86 s(195) =< s(190) 4.14/4.86 s(187) =< s(185) 4.14/4.86 s(195) =< s(185) 4.14/4.86 s(187) =< s(188) 4.14/4.86 s(187) =< s(186) 4.14/4.86 s(187) =< s(189) 4.14/4.86 4.14/4.86 with precondition: [3>=A,3>=B,3>=C,3>=E,A>=0,B>=0,E>=0,A+D>=2*E+3,A+D+4*E>=6,4*D+4*E>=3*B+2*A+18] 4.14/4.86 4.14/4.86 * Chain [38]: 1*s(196)+1 4.14/4.86 Such that:s(196) =< A/3+D/3-2/3*E 4.14/4.86 4.14/4.86 with precondition: [3>=A,3>=B,3>=C,3>=E,A>=0,B>=0,E>=0,A+D>=2*E+3,4*D+4*E>=3*B+2*A+12,A+D+2*E>=B+3] 4.14/4.86 4.14/4.86 * Chain [37]: 1*s(197)+1*s(198)+1*s(200)+1*s(205)+0 4.14/4.86 Such that:s(197) =< -A/3-D/3+2/3*E 4.14/4.86 s(198) =< A/2+1/2 4.14/4.86 s(199) =< A/2+B/4-D-E+13/4 4.14/4.86 s(203) =< A/2+3/4*B-D-E+5/4 4.14/4.86 s(204) =< A/2+3/4*B-D-E+7/4 4.14/4.86 s(200) =< A/6+B/3+5/4 4.14/4.86 s(200) =< 2/3*A+B/3 4.14/4.86 s(201) =< B/2-D 4.14/4.86 s(202) =< B/2-D+1/2 4.14/4.86 s(200) =< B/4-E+5/2 4.14/4.86 s(200) =< 3/4*B-D-E+2 4.14/4.86 s(199) =< -D+2 4.14/4.86 s(200) =< -D-E+17/4 4.14/4.86 s(200) =< -E+13/4 4.14/4.86 s(201) =< s(203) 4.14/4.86 s(200) =< s(203) 4.14/4.86 s(202) =< s(204) 4.14/4.86 s(200) =< s(204) 4.14/4.86 s(200) =< s(202) 4.14/4.86 s(205) =< s(201) 4.14/4.86 s(200) =< s(201) 4.14/4.86 s(205) =< s(202) 4.14/4.86 s(205) =< s(199) 4.14/4.86 s(200) =< s(199) 4.14/4.86 4.14/4.86 with precondition: [3>=A,3>=B,3>=C,3>=E,A>=0,D>=0,B>=2*D+1,2*E>=A+D+2,B+2*A+12*E>=15,2*A+3*B+3>=4*D+4*E] 4.14/4.86 4.14/4.86 * Chain [36]: 1*s(206)+1*s(207)+1*s(215)+0 4.14/4.86 Such that:s(206) =< -A/2+B/4-E+4 4.14/4.86 s(207) =< -A/3-D/3+2/3*E 4.14/4.86 s(212) =< A/2+B/2-D-E+2 4.14/4.86 s(213) =< A/2+B/2-D-E+5/2 4.14/4.86 s(206) =< A/2+3/4*B-D-E+1/2 4.14/4.86 s(208) =< A/2-D-E+4 4.14/4.86 s(209) =< B+1 4.14/4.86 s(210) =< B/2-D 4.14/4.86 s(211) =< B/2-D+1/2 4.14/4.86 s(206) =< B/4-E+4 4.14/4.86 s(206) =< B/4-E+5/2 4.14/4.86 s(206) =< 3/4*B-D-E+2 4.14/4.86 s(206) =< 3/4*B-3/2*D 4.14/4.86 s(208) =< -D+2 4.14/4.86 s(206) =< -D-E+17/4 4.14/4.86 s(206) =< -E+13/4 4.14/4.86 s(210) =< s(212) 4.14/4.86 s(206) =< s(212) 4.14/4.86 s(211) =< s(213) 4.14/4.86 s(206) =< s(213) 4.14/4.86 s(214) =< s(209) 4.14/4.86 s(206) =< s(209) 4.14/4.86 s(214) =< s(211) 4.14/4.86 s(215) =< s(210) 4.14/4.86 s(206) =< s(210) 4.14/4.86 s(215) =< s(214) 4.14/4.86 s(206) =< s(214) 4.14/4.86 s(215) =< s(208) 4.14/4.86 s(206) =< s(208) 4.14/4.86 4.14/4.86 with precondition: [3>=A,3>=B,3>=C,3>=E,A>=0,D>=0,B>=2*D+1,2*E>=A+D+2,2*A+3*B+3>=4*D+4*E] 4.14/4.86 4.14/4.86 * Chain [35]: 1*s(216)+1*s(217)+1*s(222)+1*s(223)+0 4.14/4.86 Such that:s(216) =< -A/3-D/3+2/3*E 4.14/4.86 s(217) =< A/2+1/2 4.14/4.86 s(220) =< A/2+B/4-D-E+3 4.14/4.86 s(221) =< A/2+3/4*B-D-E+1 4.14/4.86 s(218) =< B/2-D 4.14/4.86 s(219) =< -D+2 4.14/4.86 s(219) =< s(220) 4.14/4.86 s(222) =< s(220) 4.14/4.86 s(218) =< s(221) 4.14/4.86 s(222) =< s(221) 4.14/4.86 s(222) =< s(218) 4.14/4.86 s(223) =< s(218) 4.14/4.86 s(223) =< s(219) 4.14/4.86 s(222) =< s(219) 4.14/4.86 4.14/4.86 with precondition: [3>=A,3>=B,3>=C,3>=E,D>=0,B>=2*D+2,A+D+3>=2*E,2*E>=A+D+2,4*E+6*A>=B+4] 4.14/4.86 4.14/4.86 * Chain [34]: 1*s(224)+1*s(230)+0 4.14/4.86 Such that:s(224) =< 2*A+B 4.14/4.86 s(224) =< A/2+B/4-E 4.14/4.86 s(224) =< A/2-E+1 4.14/4.86 s(227) =< B+1 4.14/4.86 s(225) =< B/2-D+1 4.14/4.86 s(228) =< B/2-D+3/2 4.14/4.86 s(224) =< B/4-E+3/2 4.14/4.86 s(226) =< -D+3 4.14/4.86 s(224) =< -E+9/4 4.14/4.86 s(229) =< s(227) 4.14/4.86 s(224) =< s(227) 4.14/4.86 s(229) =< s(228) 4.14/4.86 s(230) =< s(225) 4.14/4.86 s(224) =< s(225) 4.14/4.86 s(230) =< s(229) 4.14/4.86 s(224) =< s(229) 4.14/4.86 s(230) =< s(226) 4.14/4.86 s(224) =< s(226) 4.14/4.86 4.14/4.86 with precondition: [3>=A,3>=B,3>=C,A>=0,B>=0,D>=0,E>=0,B+1>=2*D,A+D>=2*E,A+B+2*E>=D] 4.14/4.86 4.14/4.86 * Chain [33]: 1*s(231)+1*s(232)+1*s(236)+0 4.14/4.86 Such that:s(231) =< A/2+1/2 4.14/4.86 s(232) =< A/2+B/4-E 4.14/4.86 s(232) =< A/2+B/4-E+1/4 4.14/4.86 s(231) =< A/2+B/4+3*E 4.14/4.86 s(233) =< B/2-D+1 4.14/4.86 s(235) =< B/2-D+3/2 4.14/4.86 s(232) =< B/4-E+3/2 4.14/4.86 s(234) =< -D+3 4.14/4.86 s(232) =< -E+9/4 4.14/4.86 s(232) =< s(235) 4.14/4.86 s(236) =< s(233) 4.14/4.86 s(232) =< s(233) 4.14/4.86 s(236) =< s(235) 4.14/4.86 s(236) =< s(234) 4.14/4.86 s(232) =< s(234) 4.14/4.86 4.14/4.86 with precondition: [3>=A,3>=B,3>=C,A>=0,D>=0,E>=0,B+1>=2*D,B+2*D>=1,A+D>=2*E,B+2*A+12*E>=3] 4.14/4.86 4.14/4.86 * Chain [32]: 1*s(237)+1*s(238)+1*s(241)+0 4.14/4.86 Such that:s(237) =< A/2+1/2 4.14/4.86 s(238) =< A/2+B/4-E 4.14/4.86 s(240) =< B/2-D+1 4.14/4.86 s(239) =< -D+3 4.14/4.86 s(238) =< s(240) 4.14/4.86 s(241) =< s(240) 4.14/4.86 s(241) =< s(239) 4.14/4.86 s(238) =< s(239) 4.14/4.86 4.14/4.86 with precondition: [3>=A,3>=B,3>=C,D>=0,E>=0,B>=2*D,A+D>=2*E,4*E+6*A>=B] 4.14/4.86 4.14/4.86 * Chain [31]: 1*s(242)+1*s(243)+0 4.14/4.86 Such that:s(242) =< A/2+3/4*B-D-E+9/4 4.14/4.86 s(243) =< -B/2+D 4.14/4.86 4.14/4.86 with precondition: [3>=A,3>=B,3>=C,E>=0,3*B+5>=2*D,2*D>=B+5,2*A+3*B+7>=4*D+4*E] 4.14/4.86 4.14/4.86 * Chain [30]: 1*s(244)+1*s(245)+0 4.14/4.86 Such that:s(244) =< A/2+3/4*B-D-E+3/2 4.14/4.86 s(245) =< -B/2+D 4.14/4.86 4.14/4.86 with precondition: [3>=A,3>=B,3>=C,E>=0,2*D>=B+4,B+2>=D,2*A+3*B+4>=4*D+4*E] 4.14/4.86 4.14/4.86 * Chain [29]: 1*s(246)+1*s(249)+2*s(253)+1*s(254)+0 4.14/4.86 Such that:s(246) =< -A-B/2+2*E 4.14/4.86 s(250) =< -A/2-B/4+E 4.14/4.86 s(247) =< -A/2+E 4.14/4.86 s(251) =< -B/2+D 4.14/4.86 s(248) =< -B/4+E 4.14/4.86 s(252) =< D 4.14/4.86 s(249) =< E 4.14/4.86 s(246) =< s(250) 4.14/4.86 s(246) =< s(251) 4.14/4.86 s(253) =< s(251) 4.14/4.86 s(253) =< s(252) 4.14/4.86 s(246) =< s(252) 4.14/4.86 s(249) =< s(250) 4.14/4.86 s(254) =< s(250) 4.14/4.86 s(249) =< s(247) 4.14/4.86 s(254) =< s(247) 4.14/4.86 s(249) =< s(251) 4.14/4.86 s(249) =< s(248) 4.14/4.86 s(249) =< s(252) 4.14/4.86 4.14/4.86 with precondition: [3>=B,3>=C,3>=E,A>=0,B>=0,2*D>=B+4,2*E>=A+D+1] 4.14/4.86 4.14/4.86 * Chain [28]: 1*s(255)+1*s(260)+1*s(261)+0 4.14/4.86 Such that:s(256) =< -A/2-B/4+E 4.14/4.86 s(257) =< -A/2+E 4.14/4.86 s(258) =< -B/2+D 4.14/4.86 s(255) =< -B/4+E 4.14/4.86 s(259) =< D 4.14/4.86 s(255) =< s(256) 4.14/4.86 s(260) =< s(256) 4.14/4.86 s(255) =< s(257) 4.14/4.86 s(260) =< s(257) 4.14/4.86 s(261) =< s(258) 4.14/4.86 s(255) =< s(258) 4.14/4.86 s(261) =< s(259) 4.14/4.86 s(255) =< s(259) 4.14/4.86 4.14/4.86 with precondition: [3>=B,3>=C,3>=E,A>=0,B>=0,2*D>=B+5,2*E>=A+D+1] 4.14/4.86 4.14/4.86 4.14/4.86 Closed-form bounds of f0(A,B,C,D,E,F,G,H): 4.14/4.86 ------------------------------------- 4.14/4.86 * Chain [63] with precondition: [B=3,D=0,2*E=A+4,3>=C,3>=E,E>=2] 4.14/4.86 - Upper bound: E+4 4.14/4.86 - Complexity: n 4.14/4.86 * Chain [62] with precondition: [B+2=2*D,3>=A,3>=B,3>=C,A>=0,B>=0,E>=0,B+2*A>=4*E] 4.14/4.86 - Upper bound: A/2+D/2-E 4.14/4.86 - Complexity: n 4.14/4.86 * Chain [61] with precondition: [2*D=B,3>=C,3>=E,A>=0,D>=0,2*E>=A+D+5] 4.14/4.86 - Upper bound: -A/2-B/4+E+1 4.14/4.86 - Complexity: n 4.14/4.86 * Chain [60] with precondition: [2*D=B+1,3>=C,3>=E,A>=0,2*D>=1,2*E>=A+D+5] 4.14/4.86 - Upper bound: -A/2-B/4+E+1 4.14/4.86 - Complexity: n 4.14/4.86 * Chain [59] with precondition: [2*D=B+2,5>=2*D,3>=C,3>=E,A>=0,D>=1,2*E>=A+D+2] 4.14/4.86 - Upper bound: -A/2-D/2+E 4.14/4.86 - Complexity: n 4.14/4.86 * Chain [58] with precondition: [2*D=B+3,3>=A,3>=C,3>=D,A>=0,E>=0,2*D>=3,A+D>=2*E+1] 4.14/4.86 - Upper bound: A/2+D/2-E 4.14/4.86 - Complexity: n 4.14/4.86 * Chain [57] with precondition: [2*D=B+3,3>=C,3>=D,3>=E,A>=0,2*D>=3,2*E>=A+D+2] 4.14/4.86 - Upper bound: -A/2-D/2+E 4.14/4.86 - Complexity: n 4.14/4.86 * Chain [56] with precondition: [2*E=A+D+1,3>=B,3>=C,B>=0,D>=0,B+1>=2*D,D+4>=2*E,2*E>=D+1] 4.14/4.86 - Upper bound: 1 4.14/4.86 - Complexity: constant 4.14/4.86 * Chain [55] with precondition: [2*E=A+D+1,3>=B,3>=C,D>=0,B>=2*D+1,D+4>=2*E,2*E>=D+1] 4.14/4.86 - Upper bound: B-2*D+(-D/2+1/2+(-D/2+E+(nat(-A/2+B/4-D/2+1)+1))) 4.14/4.86 - Complexity: n 4.14/4.86 * Chain [54] with precondition: [2*E=A+D+1,3>=B,3>=C,D>=0,B>=2*D+2,D+4>=2*E,16*E>=6*D+B+6] 4.14/4.86 - Upper bound: A/2+3/4*B-3/2*D+3/2 4.14/4.86 - Complexity: n 4.14/4.86 * Chain [53] with precondition: [2*E=A+D,3>=B,3>=C,3>=E,B>=0,D+3>=2*E,2*D>=B+4,2*E>=D] 4.14/4.86 - Upper bound: 1 4.14/4.86 - Complexity: constant 4.14/4.86 * Chain [52] with precondition: [2*E=A+D,3>=B,3>=C,3>=E,B>=0,2*D>=B+6,2*E>=D] 4.14/4.86 - Upper bound: -3*A-3/2*B+7*E+1 4.14/4.86 - Complexity: n 4.14/4.86 * Chain [51] with precondition: [2*E=A+D,3>=B,3>=C,3>=E,B>=0,2*D>=B+7,2*E>=D] 4.14/4.86 - Upper bound: -3/2*A-B+4*E+1 4.14/4.86 - Complexity: n 4.14/4.86 * Chain [50] with precondition: [A+D+4=2*E,3>=B,3>=C,3>=E,D>=0,B>=2*D+1,2*E>=D+4] 4.14/4.86 - Upper bound: 7/3 4.14/4.86 - Complexity: constant 4.14/4.86 * Chain [49] with precondition: [4*D+4*E=3*B+2*A+13,3>=B,3>=C,B>=0,E>=0,2*D>=B+5,3*B+19>=4*D+4*E,4*D+4*E>=3*B+13,6*D+8*E>=3*B+21] 4.14/4.86 - Upper bound: -B/2+D+1 4.14/4.86 - Complexity: n 4.14/4.86 * Chain [48] with precondition: [4*D+4*E=3*B+2*A+10,3>=B,3>=C,B>=0,E>=0,2*D>=B+4,3*B+16>=4*D+4*E,4*D+4*E>=3*B+10,2*D+4*E>=B+6] 4.14/4.86 - Upper bound: -B/2+D+1 4.14/4.86 - Complexity: n 4.14/4.86 * Chain [47] with precondition: [4*D+4*E=3*B+2*A+7,3>=B,3>=C,3>=E,D>=0,B+11>=4*E,B+1>=2*D,B+2*D>=1,4*D+4*E>=3*B+7] 4.14/4.86 - Upper bound: B/2-D+5/3 4.14/4.86 - Complexity: n 4.14/4.86 * Chain [46] with precondition: [4*D+4*E=3*B+2*A+4,3>=B,3>=C,3>=E,D>=0,B+10>=4*E,B>=2*D,4*D+4*E>=3*B+4] 4.14/4.86 - Upper bound: B/2-D+7/6 4.14/4.86 - Complexity: n 4.14/4.86 * Chain [45] with precondition: [3>=A,3>=B,3>=C,3>=E,A>=0,B>=0,D>=0,E>=0] 4.14/4.86 - Upper bound: 0 4.14/4.86 - Complexity: constant 4.14/4.86 * Chain [44] with precondition: [3>=A,3>=B,3>=C,3>=E,A>=0,B>=0,D>=0,B+1>=2*D,2*E>=A+D+2] 4.14/4.86 - Upper bound: -A/3-D/3+2/3*E 4.14/4.86 - Complexity: n 4.14/4.86 * Chain [43] with precondition: [3>=A,3>=B,3>=C,3>=E,A>=0,B>=0,E>=0,2*D>=B+4,A+D>=2*E+1] 4.14/4.86 - Upper bound: A/3+D/3-2/3*E 4.14/4.86 - Complexity: n 4.14/4.86 * Chain [42] with precondition: [3>=A,3>=B,3>=C,3>=E,A>=0,B>=0,E>=0,2*D>=B+6,A+D>=2*E+1,2*D+4*E>=B+8,4*D+4*E>=3*B+2*A+14] 4.14/4.86 - Upper bound: -7/6*A-13/4*B+16/3*D+10/3*E 4.14/4.86 - Complexity: n 4.14/4.86 * Chain [41] with precondition: [3>=A,3>=B,3>=C,3>=E,A>=0,B>=0,E>=0,2*D>=B+7,6*D+8*E>=3*B+27,A+D>=2*E+1,4*D+4*E>=3*B+2*A+17] 4.14/4.86 - Upper bound: -2/3*A-2*B+10/3*D+7/3*E 4.14/4.86 - Complexity: n 4.14/4.86 * Chain [40] with precondition: [3>=A,3>=B,3>=C,3>=E,A>=0,B>=0,E>=0,A+D>=2*E+3,A+D+2*E>=6,4*D+4*E>=3*B+2*A+21] 4.14/4.86 - Upper bound: A/6-B+5/3*D+2/3*E+1 4.14/4.86 - Complexity: n 4.14/4.86 * Chain [39] with precondition: [3>=A,3>=B,3>=C,3>=E,A>=0,B>=0,E>=0,A+D>=2*E+3,A+D+4*E>=6,4*D+4*E>=3*B+2*A+18] 4.14/4.86 - Upper bound: -3/2*B+3*D+E+1 4.14/4.86 - Complexity: n 4.14/4.86 * Chain [38] with precondition: [3>=A,3>=B,3>=C,3>=E,A>=0,B>=0,E>=0,A+D>=2*E+3,4*D+4*E>=3*B+2*A+12,A+D+2*E>=B+3] 4.14/4.86 - Upper bound: A/3+D/3-2/3*E+1 4.14/4.86 - Complexity: n 4.14/4.86 * Chain [37] with precondition: [3>=A,3>=B,3>=C,3>=E,A>=0,D>=0,B>=2*D+1,2*E>=A+D+2,B+2*A+12*E>=15,2*A+3*B+3>=4*D+4*E] 4.14/4.86 - Upper bound: A/3+5/6*B-4/3*D+2/3*E+7/4 4.14/4.86 - Complexity: n 4.14/4.86 * Chain [36] with precondition: [3>=A,3>=B,3>=C,3>=E,A>=0,D>=0,B>=2*D+1,2*E>=A+D+2,2*A+3*B+3>=4*D+4*E] 4.14/4.86 - Upper bound: B/2-D+(-A/3-D/3+2/3*E+nat(-A/2+B/4-E+4)) 4.14/4.86 - Complexity: n 4.14/4.86 * Chain [35] with precondition: [3>=A,3>=B,3>=C,3>=E,D>=0,B>=2*D+2,A+D+3>=2*E,2*E>=A+D+2,4*E+6*A>=B+4] 4.14/4.86 - Upper bound: 2/3*A+3/4*B-7/3*D-E/3+7/2 4.14/4.86 - Complexity: n 4.14/4.86 * Chain [34] with precondition: [3>=A,3>=B,3>=C,A>=0,B>=0,D>=0,E>=0,B+1>=2*D,A+D>=2*E,A+B+2*E>=D] 4.14/4.86 - Upper bound: 2*A+3/2*B-D+1 4.14/4.86 - Complexity: n 4.14/4.86 * Chain [33] with precondition: [3>=A,3>=B,3>=C,A>=0,D>=0,E>=0,B+1>=2*D,B+2*D>=1,A+D>=2*E,B+2*A+12*E>=3] 4.14/4.86 - Upper bound: A/2+B/2-D+3/2+nat(A/2+B/4-E) 4.14/4.86 - Complexity: n 4.14/4.86 * Chain [32] with precondition: [3>=A,3>=B,3>=C,D>=0,E>=0,B>=2*D,A+D>=2*E,4*E+6*A>=B] 4.14/4.86 - Upper bound: A+3/4*B-D-E+3/2 4.14/4.86 - Complexity: n 4.14/4.86 * Chain [31] with precondition: [3>=A,3>=B,3>=C,E>=0,3*B+5>=2*D,2*D>=B+5,2*A+3*B+7>=4*D+4*E] 4.14/4.86 - Upper bound: A/2+B/4-E+9/4 4.14/4.86 - Complexity: n 4.14/4.86 * Chain [30] with precondition: [3>=A,3>=B,3>=C,E>=0,2*D>=B+4,B+2>=D,2*A+3*B+4>=4*D+4*E] 4.14/4.86 - Upper bound: A/2+B/4-E+3/2 4.14/4.86 - Complexity: n 4.14/4.86 * Chain [29] with precondition: [3>=B,3>=C,3>=E,A>=0,B>=0,2*D>=B+4,2*E>=A+D+1] 4.14/4.86 - Upper bound: -3/2*A-7/4*B+2*D+4*E 4.14/4.86 - Complexity: n 4.14/4.86 * Chain [28] with precondition: [3>=B,3>=C,3>=E,A>=0,B>=0,2*D>=B+5,2*E>=A+D+1] 4.14/4.86 - Upper bound: -A/2-B+D+2*E 4.14/4.86 - Complexity: n 4.14/4.86 4.14/4.86 ### Maximum cost of f0(A,B,C,D,E,F,G,H): max([max([max([max([max([max([E+4,nat(-A/2-D/2+E),nat(-A/3-D/3+2/3*E),nat(A/2+D/2-E),1/2+nat(-A/2-B/4+E+1/2),1/2+nat(B/2-D+2/3),1/2+nat(B/2-D+7/6)]),nat(B/2-D+1)+max([2*A+B,A/2+1/2+nat(A/2+B/4-E)])]),nat(-B/2+D)+max([1,nat(A/2+3/4*B-D-E+3/2),nat(A/2+3/4*B-D-E+9/4)])]),nat(B/2-D)+max([max([nat(-D/2+E)+nat(-A/2+B/4-D/2+1)+nat(-D/2+1/2)+nat(B/2-D),A/2+1/2+nat(B/4-D/2)])+1,nat(-A/3-D/3+2/3*E)+max([nat(-A/2+B/4-E+4),A/2+1/2+max([A/6+B/3+5/4,nat(A/2+B/4-D-E+3)])])])]),nat(-A/2-B/4+E)+max([max([1,nat(-B/4+E)+nat(-B/2+D)]),nat(-A-B/2+2*E)+max([max([nat(-B/2+D)*2,nat(-A-B/2+2*E)+1+nat(-A/2-B/4+E)])+E,nat(-B/4+E)+1])])]),nat(A/3+D/3-2/3*E)+max([max([1,nat(-A/2-3/4*B+D+E)+nat(-3/4*B+D+E)+nat(-A/2-B/2+D+E)]),nat(-A/3-B/2+2/3*D+2/3*E)+max([nat(-A/6-B/4+D/3+E/3)+1+max([nat(A/3-B/4+D/3+E/3),A/3+D/3+E/3+(nat(-A/6-B/4+D/3+E/3)+nat(-A/3-B/2+2/3*D+2/3*E))+nat(A/3+D/3-2/3*E)]),nat(-A/2-3/4*B+D+E)*3+nat(-B/2+D+E)+nat(A/3+D/3-2/3*E)])])]) 4.14/4.86 Asymptotic class: n 4.14/4.86 * Total analysis performed in 3979 ms. 4.14/4.86 4.14/4.86 EOF