6.10/6.10 WORST_CASE(?,O(n^1)) 6.10/6.10 6.10/6.10 Preprocessing Cost Relations 6.10/6.10 ===================================== 6.10/6.10 6.10/6.10 #### Computed strongly connected components 6.10/6.10 0. recursive : [f16/13,f25/13,f5/13,f7/13,f9/13] 6.10/6.10 1. non_recursive : [exit_location/1] 6.10/6.10 2. non_recursive : [f30/7] 6.10/6.10 3. non_recursive : [f5_loop_cont/8] 6.10/6.10 4. non_recursive : [f0/7] 6.10/6.10 6.10/6.10 #### Obtained direct recursion through partial evaluation 6.10/6.10 0. SCC is partially evaluated into f5/13 6.10/6.10 1. SCC is completely evaluated into other SCCs 6.10/6.10 2. SCC is completely evaluated into other SCCs 6.10/6.10 3. SCC is partially evaluated into f5_loop_cont/8 6.10/6.10 4. SCC is partially evaluated into f0/7 6.10/6.10 6.10/6.10 Control-Flow Refinement of Cost Relations 6.10/6.10 ===================================== 6.10/6.10 6.10/6.10 ### Specialization of cost equations f5/13 6.10/6.10 * CE 81 is refined into CE [84] 6.10/6.10 * CE 14 is refined into CE [85] 6.10/6.10 * CE 40 is discarded (unfeasible) 6.10/6.10 * CE 27 is discarded (unfeasible) 6.10/6.10 * CE 53 is discarded (unfeasible) 6.10/6.10 * CE 3 is refined into CE [86] 6.10/6.10 * CE 4 is discarded (unfeasible) 6.10/6.10 * CE 29 is discarded (unfeasible) 6.10/6.10 * CE 30 is discarded (unfeasible) 6.10/6.10 * CE 16 is discarded (unfeasible) 6.10/6.10 * CE 17 is discarded (unfeasible) 6.10/6.10 * CE 42 is discarded (unfeasible) 6.10/6.10 * CE 43 is discarded (unfeasible) 6.10/6.10 * CE 9 is discarded (unfeasible) 6.10/6.10 * CE 10 is refined into CE [87] 6.10/6.10 * CE 35 is discarded (unfeasible) 6.10/6.10 * CE 36 is discarded (unfeasible) 6.10/6.10 * CE 22 is discarded (unfeasible) 6.10/6.10 * CE 23 is discarded (unfeasible) 6.10/6.10 * CE 48 is discarded (unfeasible) 6.10/6.10 * CE 49 is discarded (unfeasible) 6.10/6.10 * CE 8 is refined into CE [88] 6.10/6.10 * CE 34 is discarded (unfeasible) 6.10/6.10 * CE 21 is discarded (unfeasible) 6.10/6.10 * CE 47 is discarded (unfeasible) 6.10/6.10 * CE 2 is refined into CE [89] 6.10/6.10 * CE 28 is discarded (unfeasible) 6.10/6.10 * CE 15 is discarded (unfeasible) 6.10/6.10 * CE 41 is discarded (unfeasible) 6.10/6.10 * CE 66 is refined into CE [90] 6.10/6.10 * CE 79 is discarded (unfeasible) 6.10/6.10 * CE 55 is refined into CE [91] 6.10/6.10 * CE 56 is refined into CE [92] 6.10/6.10 * CE 68 is discarded (unfeasible) 6.10/6.10 * CE 69 is discarded (unfeasible) 6.10/6.10 * CE 61 is discarded (unfeasible) 6.10/6.10 * CE 62 is refined into CE [93] 6.10/6.10 * CE 74 is discarded (unfeasible) 6.10/6.10 * CE 75 is discarded (unfeasible) 6.10/6.10 * CE 60 is refined into CE [94] 6.10/6.10 * CE 73 is discarded (unfeasible) 6.10/6.10 * CE 54 is refined into CE [95] 6.10/6.10 * CE 67 is discarded (unfeasible) 6.10/6.10 * CE 80 is refined into CE [96] 6.10/6.10 * CE 6 is refined into CE [97] 6.10/6.10 * CE 7 is discarded (unfeasible) 6.10/6.10 * CE 32 is discarded (unfeasible) 6.10/6.10 * CE 33 is discarded (unfeasible) 6.10/6.10 * CE 19 is discarded (unfeasible) 6.10/6.10 * CE 20 is discarded (unfeasible) 6.10/6.10 * CE 45 is discarded (unfeasible) 6.10/6.10 * CE 46 is discarded (unfeasible) 6.10/6.10 * CE 12 is discarded (unfeasible) 6.10/6.10 * CE 13 is refined into CE [98] 6.10/6.10 * CE 38 is discarded (unfeasible) 6.10/6.10 * CE 39 is discarded (unfeasible) 6.10/6.10 * CE 25 is discarded (unfeasible) 6.10/6.10 * CE 26 is discarded (unfeasible) 6.10/6.10 * CE 51 is discarded (unfeasible) 6.10/6.10 * CE 52 is discarded (unfeasible) 6.10/6.10 * CE 11 is refined into CE [99] 6.10/6.10 * CE 37 is discarded (unfeasible) 6.10/6.10 * CE 24 is discarded (unfeasible) 6.10/6.10 * CE 50 is discarded (unfeasible) 6.10/6.10 * CE 5 is refined into CE [100] 6.10/6.10 * CE 31 is discarded (unfeasible) 6.10/6.10 * CE 18 is discarded (unfeasible) 6.10/6.10 * CE 44 is discarded (unfeasible) 6.10/6.10 * CE 58 is refined into CE [101] 6.10/6.10 * CE 59 is refined into CE [102] 6.10/6.10 * CE 71 is discarded (unfeasible) 6.10/6.10 * CE 72 is discarded (unfeasible) 6.10/6.10 * CE 64 is discarded (unfeasible) 6.10/6.10 * CE 65 is refined into CE [103] 6.10/6.10 * CE 77 is discarded (unfeasible) 6.10/6.10 * CE 78 is discarded (unfeasible) 6.10/6.10 * CE 63 is refined into CE [104] 6.10/6.10 * CE 76 is discarded (unfeasible) 6.10/6.10 * CE 57 is refined into CE [105] 6.10/6.10 * CE 70 is discarded (unfeasible) 6.10/6.10 6.10/6.10 6.10/6.10 ### Cost equations --> "Loop" of f5/13 6.10/6.10 * CEs [97] --> Loop 84 6.10/6.10 * CEs [98] --> Loop 85 6.10/6.10 * CEs [99] --> Loop 86 6.10/6.10 * CEs [100] --> Loop 87 6.10/6.10 * CEs [103] --> Loop 88 6.10/6.10 * CEs [101] --> Loop 89 6.10/6.10 * CEs [104] --> Loop 90 6.10/6.10 * CEs [105] --> Loop 91 6.10/6.10 * CEs [102] --> Loop 92 6.10/6.10 * CEs [84] --> Loop 93 6.10/6.10 * CEs [85] --> Loop 94 6.10/6.10 * CEs [86] --> Loop 95 6.10/6.10 * CEs [87] --> Loop 96 6.10/6.10 * CEs [88] --> Loop 97 6.10/6.10 * CEs [89] --> Loop 98 6.10/6.10 * CEs [90] --> Loop 99 6.10/6.10 * CEs [93] --> Loop 100 6.10/6.10 * CEs [91] --> Loop 101 6.10/6.10 * CEs [94] --> Loop 102 6.10/6.10 * CEs [95] --> Loop 103 6.10/6.10 * CEs [92] --> Loop 104 6.10/6.10 * CEs [96] --> Loop 105 6.10/6.10 6.10/6.10 ### Ranking functions of CR f5(A,B,C,D,E,F,H,I,J,K,L,M,N) 6.10/6.10 * RF of phase [84,85,86,87]: [A-1] 6.10/6.10 * RF of phase [88]: [C/4-3/4] 6.10/6.10 * RF of phase [89]: [-C/4+63] 6.10/6.10 6.10/6.10 #### Partial ranking functions of CR f5(A,B,C,D,E,F,H,I,J,K,L,M,N) 6.10/6.10 * Partial RF of phase [84,85,86,87]: 6.10/6.10 - RF of loop [84:1,85:1,86:1,87:1]: 6.10/6.10 A-1 6.10/6.10 - RF of loop [84:1,87:1]: 6.10/6.10 -C+255 depends on loops [85:1,86:1] 6.10/6.10 - RF of loop [85:1,86:1]: 6.10/6.10 C depends on loops [84:1,87:1] 6.10/6.10 - RF of loop [86:1]: 6.10/6.10 E-1 depends on loops [85:1,87:1] 6.10/6.10 - RF of loop [87:1]: 6.10/6.10 -E+2 depends on loops [84:1,86:1] 6.10/6.10 * Partial RF of phase [88]: 6.10/6.10 - RF of loop [88:1]: 6.10/6.10 C/4-3/4 6.10/6.10 * Partial RF of phase [89]: 6.10/6.10 - RF of loop [89:1]: 6.10/6.10 -C/4+63 6.10/6.10 6.10/6.10 6.10/6.10 ### Specialization of cost equations f5_loop_cont/8 6.10/6.10 * CE 83 is refined into CE [106] 6.10/6.10 * CE 82 is refined into CE [107] 6.10/6.10 6.10/6.10 6.10/6.10 ### Cost equations --> "Loop" of f5_loop_cont/8 6.10/6.10 * CEs [106] --> Loop 106 6.10/6.10 * CEs [107] --> Loop 107 6.10/6.10 6.10/6.10 ### Ranking functions of CR f5_loop_cont(A,B,C,D,E,F,G,H) 6.10/6.10 6.10/6.10 #### Partial ranking functions of CR f5_loop_cont(A,B,C,D,E,F,G,H) 6.10/6.10 6.10/6.10 6.10/6.10 ### Specialization of cost equations f0/7 6.10/6.10 * CE 1 is refined into CE [108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139] 6.10/6.10 6.10/6.10 6.10/6.10 ### Cost equations --> "Loop" of f0/7 6.10/6.10 * CEs [133] --> Loop 108 6.10/6.10 * CEs [132] --> Loop 109 6.10/6.10 * CEs [128] --> Loop 110 6.10/6.10 * CEs [120] --> Loop 111 6.10/6.10 * CEs [129,130,131,135,136,138] --> Loop 112 6.10/6.10 * CEs [119] --> Loop 113 6.10/6.10 * CEs [117] --> Loop 114 6.10/6.10 * CEs [109] --> Loop 115 6.10/6.10 * CEs [118] --> Loop 116 6.10/6.10 * CEs [114] --> Loop 117 6.10/6.10 * CEs [134] --> Loop 118 6.10/6.10 * CEs [111,113,116,123,124,127] --> Loop 119 6.10/6.10 * CEs [122] --> Loop 120 6.10/6.10 * CEs [110,112,115,125] --> Loop 121 6.10/6.10 * CEs [121,126] --> Loop 122 6.10/6.10 * CEs [108] --> Loop 123 6.10/6.10 * CEs [137,139] --> Loop 124 6.10/6.10 6.10/6.10 ### Ranking functions of CR f0(A,B,C,D,E,F,H) 6.10/6.10 6.10/6.10 #### Partial ranking functions of CR f0(A,B,C,D,E,F,H) 6.10/6.10 6.10/6.10 6.10/6.10 Computing Bounds 6.10/6.10 ===================================== 6.10/6.10 6.10/6.10 #### Cost of chains of f5(A,B,C,D,E,F,H,I,J,K,L,M,N): 6.10/6.10 * Chain [[88],103]: 1*it(88)+0 6.10/6.10 Such that:it(88) =< C/4-K/4+3/4 6.10/6.10 6.10/6.10 with precondition: [A=4,B=0,H=2,I=3,J=1,M=2,F=N,1>=E,E>=0,K>=256,F>=D+1,L>=F+1,C>=K+1] 6.10/6.10 6.10/6.10 * Chain [[88],100]: 1*it(88)+0 6.10/6.10 Such that:it(88) =< C/4-K/4 6.10/6.10 6.10/6.10 with precondition: [A=4,B=0,H=2,I=4,J=0,M=1,F=N,1>=E,0>=K+1,E>=0,K+4>=0,F>=D+1,C>=K+8,F>=L+1] 6.10/6.10 6.10/6.10 * Chain [[88],99]: 1*it(88)+0 6.10/6.10 Such that:it(88) =< C/4-K/4 6.10/6.10 6.10/6.10 with precondition: [A=4,B=0,H=2,I=4,J=0,M=1,F=L,F=N,1>=E,E>=0,K>=0,F>=D+1,C>=K+4] 6.10/6.10 6.10/6.10 * Chain [[88],93]: 1*it(88)+0 6.10/6.10 Such that:it(88) =< C/4 6.10/6.10 6.10/6.10 with precondition: [A=4,B=0,H=3,1>=E,C>=4,E>=0,F>=D+1] 6.10/6.10 6.10/6.10 * Chain [[88],91,[84,85,86,87],105]: 4*it(84)+1*it(88)+1 6.10/6.10 Such that:aux(19) =< 3 6.10/6.10 it(88) =< C/4 6.10/6.10 it(88) =< C/4-K/4+M/2+1/2 6.10/6.10 it(84) =< aux(19) 6.10/6.10 6.10/6.10 with precondition: [A=4,B=0,H=2,I=1,J=1,F=N,1>=E,2>=M,C>=4,E>=0,M>=1,K+2>=2*M,F>=D+1,2*M+254>=K,C+2*M>=K+2] 6.10/6.10 6.10/6.10 * Chain [[88],91,[84,85,86,87],95]: 4*it(84)+1*it(88)+1 6.10/6.10 Such that:aux(14) =< 1 6.10/6.10 aux(13) =< 3 6.10/6.10 it(88) =< C/4-K/4+3/2 6.10/6.10 it(84) =< aux(13) 6.10/6.10 it(84) =< aux(14) 6.10/6.10 6.10/6.10 with precondition: [A=4,B=0,H=2,I=1,J=1,K=256,M=2,F=N,1>=E,C>=254,E>=0,F>=D+1,L>=F+1] 6.10/6.10 6.10/6.10 * Chain [[88],91,[84,85,86,87],94]: 4*it(84)+1*it(88)+1 6.10/6.10 Such that:aux(14) =< 1 6.10/6.10 aux(13) =< 3 6.10/6.10 it(88) =< C/4-K/4+M 6.10/6.10 it(84) =< aux(13) 6.10/6.10 it(84) =< aux(14) 6.10/6.10 6.10/6.10 with precondition: [A=4,B=0,H=2,I=1,J=1,F=L,F=N,1>=E,2>=M,E>=0,M>=1,K+3>=4*M,F>=D+1,4*M+249>=K,C+4*M>=K+7] 6.10/6.10 6.10/6.10 * Chain [[88],91,[84,85,86,87],93]: 4*it(84)+1*it(88)+1 6.10/6.10 Such that:aux(20) =< 3 6.10/6.10 it(88) =< C/4 6.10/6.10 it(84) =< aux(20) 6.10/6.10 6.10/6.10 with precondition: [A=4,B=0,H=3,1>=E,C>=4,E>=0,F>=D+1] 6.10/6.10 6.10/6.10 * Chain [[88],91,95]: 1*it(88)+1 6.10/6.10 Such that:it(88) =< C/4-K/4+5/4 6.10/6.10 6.10/6.10 with precondition: [A=4,B=0,H=2,I=2,J=1,M=2,F=N,1>=E,257>=K,E>=0,K>=256,F>=D+1,L>=F+1,C+1>=K] 6.10/6.10 6.10/6.10 * Chain [[88],91,94]: 1*it(88)+1 6.10/6.10 Such that:it(88) =< C/4-K/4+3/4 6.10/6.10 6.10/6.10 with precondition: [A=4,B=0,H=2,I=2,J=1,M=2,F=L,F=N,1>=E,255>=K,E>=0,K>=3,F>=D+1,C>=K+1] 6.10/6.10 6.10/6.10 * Chain [[88],91,93]: 1*it(88)+1 6.10/6.10 Such that:it(88) =< C/4 6.10/6.10 6.10/6.10 with precondition: [A=4,B=0,H=3,1>=E,C>=4,E>=0,F>=D+1] 6.10/6.10 6.10/6.10 * Chain [104]: 0 6.10/6.10 with precondition: [A=4,B=0,E=0,H=2,I=4,J=0,M=2,K=C+4,D=L,F=N,K>=256,D>=F+1] 6.10/6.10 6.10/6.10 * Chain [100]: 0 6.10/6.10 with precondition: [A=4,B=0,H=2,I=4,J=0,M=1,K+4=C,D=L,F=N,1>=E,0>=K+1,E>=0,F>=D+1] 6.10/6.10 6.10/6.10 * Chain [99]: 0 6.10/6.10 with precondition: [A=4,B=0,H=2,I=4,J=0,K=C,D=F,D=L,E=M,D=N,2>=E,E>=0] 6.10/6.10 6.10/6.10 * Chain [93]: 0 6.10/6.10 with precondition: [H=3,1>=B,B>=0,4>=A+B,E+4>=2*B+A,6>=A+B+E] 6.10/6.10 6.10/6.10 * Chain [92,[89],102]: 1*it(89)+1 6.10/6.10 Such that:it(89) =< -C/4+K/4 6.10/6.10 6.10/6.10 with precondition: [A=4,B=0,E=0,H=2,I=3,J=1,M=1,F=N,0>=K+1,K>=C+5,D>=F+1,F>=L+1] 6.10/6.10 6.10/6.10 * Chain [92,[89],101]: 1*it(89)+1 6.10/6.10 Such that:it(89) =< -C/4+62 6.10/6.10 6.10/6.10 with precondition: [A=4,B=0,E=0,H=2,I=4,J=0,M=2,F=N,259>=K,K>=256,K>=C+12,D>=F+1,L>=F+1] 6.10/6.10 6.10/6.10 * Chain [92,[89],99]: 1*it(89)+1 6.10/6.10 Such that:it(89) =< -C/4+62 6.10/6.10 it(89) =< -C/4+K/4 6.10/6.10 6.10/6.10 with precondition: [A=4,B=0,E=0,H=2,I=4,J=0,M=2,F=L,F=N,255>=K,K>=C+8,D>=F+1] 6.10/6.10 6.10/6.10 * Chain [92,[89],93]: 1*it(89)+1 6.10/6.10 Such that:it(89) =< -C/4+62 6.10/6.10 6.10/6.10 with precondition: [A=4,B=0,E=0,H=3,247>=C,D>=F+1] 6.10/6.10 6.10/6.10 * Chain [92,[89],90,[84,85,86,87],105]: 4*it(84)+1*it(89)+2 6.10/6.10 Such that:aux(19) =< 3 6.10/6.10 it(89) =< -C/4+62 6.10/6.10 it(89) =< -C/4+K/4-M/2+1 6.10/6.10 it(84) =< aux(19) 6.10/6.10 6.10/6.10 with precondition: [A=4,B=0,E=0,H=2,I=1,J=1,F=N,247>=C,2>=M,M>=1,K+5>=2*M,D>=F+1,2*M+251>=K,K>=2*M+C] 6.10/6.10 6.10/6.10 * Chain [92,[89],90,[84,85,86,87],96]: 4*it(84)+1*it(89)+2 6.10/6.10 Such that:aux(14) =< 1 6.10/6.10 aux(13) =< 3 6.10/6.10 it(89) =< -C/4+K/4+1/2 6.10/6.10 it(84) =< aux(13) 6.10/6.10 it(84) =< aux(14) 6.10/6.10 6.10/6.10 with precondition: [A=4,B=0,E=0,H=2,I=1,J=1,K+1=0,M=1,F=N,0>=C+3,D>=F+1,F>=L+1] 6.10/6.10 6.10/6.10 * Chain [92,[89],90,[84,85,86,87],94]: 4*it(84)+1*it(89)+2 6.10/6.10 Such that:aux(14) =< 1 6.10/6.10 aux(13) =< 3 6.10/6.10 it(89) =< -C/4+62 6.10/6.10 it(89) =< -C/4+K/4-M+5/4 6.10/6.10 it(84) =< aux(13) 6.10/6.10 it(84) =< aux(14) 6.10/6.10 6.10/6.10 with precondition: [A=4,B=0,E=0,H=2,I=1,J=1,F=L,F=N,2>=M,M>=1,K+6>=4*M,D>=F+1,4*M+246>=K,K+1>=4*M+C] 6.10/6.10 6.10/6.10 * Chain [92,[89],90,[84,85,86,87],93]: 4*it(84)+1*it(89)+2 6.10/6.10 Such that:aux(20) =< 3 6.10/6.10 it(89) =< -C/4+62 6.10/6.10 it(84) =< aux(20) 6.10/6.10 6.10/6.10 with precondition: [A=4,B=0,E=0,H=3,247>=C,D>=F+1] 6.10/6.10 6.10/6.10 * Chain [92,[89],90,96]: 1*it(89)+2 6.10/6.10 Such that:it(89) =< -C/4+K/4+1/4 6.10/6.10 6.10/6.10 with precondition: [A=4,B=0,E=0,H=2,I=2,J=1,M=1,F=N,0>=K+1,K+2>=0,K>=C+3,D>=F+1,F>=L+1] 6.10/6.10 6.10/6.10 * Chain [92,[89],90,94]: 1*it(89)+2 6.10/6.10 Such that:it(89) =< -C/4+62 6.10/6.10 it(89) =< -C/4+K/4 6.10/6.10 6.10/6.10 with precondition: [A=4,B=0,E=0,H=2,I=2,J=1,M=1,F=L,F=N,252>=K,K>=0,K>=C+5,D>=F+1] 6.10/6.10 6.10/6.10 * Chain [92,[89],90,93]: 1*it(89)+2 6.10/6.10 Such that:it(89) =< -C/4+62 6.10/6.10 6.10/6.10 with precondition: [A=4,B=0,E=0,H=3,247>=C,D>=F+1] 6.10/6.10 6.10/6.10 * Chain [92,102]: 1 6.10/6.10 with precondition: [A=4,B=0,E=0,H=2,I=3,J=1,M=1,K=C+1,F=N,0>=K+1,D>=F+1,F>=L+1] 6.10/6.10 6.10/6.10 * Chain [92,101]: 1 6.10/6.10 with precondition: [A=4,B=0,E=0,H=2,I=4,J=0,M=2,K=C+8,F=N,259>=K,K>=256,D>=F+1,L>=F+1] 6.10/6.10 6.10/6.10 * Chain [92,99]: 1 6.10/6.10 with precondition: [A=4,B=0,E=0,H=2,I=4,J=0,M=2,K=C+4,F=L,F=N,255>=K,D>=F+1] 6.10/6.10 6.10/6.10 * Chain [92,93]: 1 6.10/6.10 with precondition: [A=4,B=0,E=0,H=3,251>=C,D>=F+1] 6.10/6.10 6.10/6.10 * Chain [92,90,[84,85,86,87],105]: 4*it(84)+2 6.10/6.10 Such that:aux(19) =< 3 6.10/6.10 it(84) =< aux(19) 6.10/6.10 6.10/6.10 with precondition: [A=4,B=0,E=0,H=2,I=1,J=1,F=N,251>=C,2>=M,C+1>=0,M>=1,D>=F+1,K+4>=2*M+C,C+2*M>=K] 6.10/6.10 6.10/6.10 * Chain [92,90,[84,85,86,87],96]: 4*it(84)+2 6.10/6.10 Such that:aux(14) =< 1 6.10/6.10 aux(13) =< 3 6.10/6.10 it(84) =< aux(13) 6.10/6.10 it(84) =< aux(14) 6.10/6.10 6.10/6.10 with precondition: [A=4,B=0,C=1,E=0,H=2,I=1,J=1,K+1=0,M=1,F=N,D>=F+1,F>=L+1] 6.10/6.10 6.10/6.10 * Chain [92,90,[84,85,86,87],94]: 4*it(84)+2 6.10/6.10 Such that:aux(14) =< 1 6.10/6.10 aux(13) =< 3 6.10/6.10 it(84) =< aux(13) 6.10/6.10 it(84) =< aux(14) 6.10/6.10 6.10/6.10 with precondition: [A=4,B=0,E=0,H=2,I=1,J=1,F=L,F=N,C+4*M=K+5,2>=M,M>=1,K+6>=4*M,D>=F+1,4*M+246>=K] 6.10/6.10 6.10/6.10 * Chain [92,90,[84,85,86,87],93]: 4*it(84)+2 6.10/6.10 Such that:aux(20) =< 3 6.10/6.10 it(84) =< aux(20) 6.10/6.10 6.10/6.10 with precondition: [A=4,B=0,E=0,H=3,251>=C,C+1>=0,D>=F+1] 6.10/6.10 6.10/6.10 * Chain [92,90,96]: 2 6.10/6.10 with precondition: [A=4,B=0,E=0,H=2,I=2,J=1,M=1,K+1=C,F=N,0>=K+1,K+2>=0,D>=F+1,F>=L+1] 6.10/6.10 6.10/6.10 * Chain [92,90,94]: 2 6.10/6.10 with precondition: [A=4,B=0,E=0,H=2,I=2,J=1,M=1,K=C+1,F=L,F=N,252>=K,K>=0,D>=F+1] 6.10/6.10 6.10/6.10 * Chain [92,90,93]: 2 6.10/6.10 with precondition: [A=4,B=0,E=0,H=3,251>=C,C+1>=0,D>=F+1] 6.10/6.10 6.10/6.10 6.10/6.10 #### Cost of chains of f5_loop_cont(A,B,C,D,E,F,G,H): 6.10/6.10 * Chain [107]: 0 6.10/6.10 with precondition: [A=2] 6.10/6.10 6.10/6.10 * Chain [106]: 0 6.10/6.10 with precondition: [A=3] 6.10/6.10 6.10/6.10 6.10/6.10 #### Cost of chains of f0(A,B,C,D,E,F,H): 6.10/6.10 * Chain [124]: 0 6.10/6.10 with precondition: [] 6.10/6.10 6.10/6.10 * Chain [123]: 4*s(15)+2 6.10/6.10 Such that:s(13) =< 1 6.10/6.10 s(14) =< 3 6.10/6.10 s(15) =< s(14) 6.10/6.10 s(15) =< s(13) 6.10/6.10 6.10/6.10 with precondition: [C=1] 6.10/6.10 6.10/6.10 * Chain [122]: 1 6.10/6.10 with precondition: [251>=C] 6.10/6.10 6.10/6.10 * Chain [121]: 38 6.10/6.10 with precondition: [251>=C,C+1>=0] 6.10/6.10 6.10/6.10 * Chain [120]: 1 6.10/6.10 with precondition: [251>=C,C>=248] 6.10/6.10 6.10/6.10 * Chain [119]: 8*s(23)+4*s(24)+8*s(27)+2 6.10/6.10 Such that:s(21) =< 1 6.10/6.10 aux(24) =< 3 6.10/6.10 aux(25) =< -C/4+62 6.10/6.10 s(23) =< aux(25) 6.10/6.10 s(24) =< aux(24) 6.10/6.10 s(24) =< s(21) 6.10/6.10 s(27) =< aux(24) 6.10/6.10 6.10/6.10 with precondition: [247>=C] 6.10/6.10 6.10/6.11 * Chain [118]: 0 6.10/6.11 with precondition: [3>=C] 6.10/6.11 6.10/6.11 * Chain [117]: 2 6.10/6.11 with precondition: [0>=C,C+1>=0] 6.10/6.11 6.10/6.11 * Chain [116]: 1 6.10/6.11 with precondition: [0>=C+2] 6.10/6.11 6.10/6.11 * Chain [115]: 1*s(37)+4*s(38)+2 6.10/6.11 Such that:s(35) =< 1 6.10/6.11 s(36) =< 3 6.10/6.11 s(37) =< -C/4+1/4 6.10/6.11 s(38) =< s(36) 6.10/6.11 s(38) =< s(35) 6.10/6.11 6.10/6.11 with precondition: [0>=C+3] 6.10/6.11 6.10/6.11 * Chain [114]: 1*s(39)+2 6.10/6.11 Such that:s(39) =< -C/4 6.10/6.11 6.10/6.11 with precondition: [0>=C+4] 6.10/6.11 6.10/6.11 * Chain [113]: 1*s(40)+1 6.10/6.11 Such that:s(40) =< -C/4 6.10/6.11 6.10/6.11 with precondition: [0>=C+6] 6.10/6.11 6.10/6.11 * Chain [112]: 1*s(43)+4*s(44)+6*s(46)+8*s(47)+1*s(50)+1 6.10/6.11 Such that:s(41) =< 1 6.10/6.11 s(50) =< C/4+1 6.10/6.11 s(43) =< C/4+3/4 6.10/6.11 aux(26) =< 3 6.10/6.11 aux(27) =< C/4 6.10/6.11 s(46) =< aux(27) 6.10/6.11 s(44) =< aux(26) 6.10/6.11 s(44) =< s(41) 6.10/6.11 s(47) =< aux(26) 6.10/6.11 6.10/6.11 with precondition: [C>=4] 6.10/6.11 6.10/6.11 * Chain [111]: 0 6.10/6.11 with precondition: [C>=252] 6.10/6.11 6.10/6.11 * Chain [110]: 1*s(57)+4*s(58)+1 6.10/6.11 Such that:s(55) =< 1 6.10/6.11 s(56) =< 3 6.10/6.11 s(57) =< C/4 6.10/6.11 s(58) =< s(56) 6.10/6.11 s(58) =< s(55) 6.10/6.11 6.10/6.11 with precondition: [C>=254] 6.10/6.11 6.10/6.11 * Chain [109]: 1*s(59)+1 6.10/6.11 Such that:s(59) =< C/4 6.10/6.11 6.10/6.11 with precondition: [C>=255] 6.10/6.11 6.10/6.11 * Chain [108]: 1*s(60)+0 6.10/6.11 Such that:s(60) =< C/4 6.10/6.11 6.10/6.11 with precondition: [C>=257] 6.10/6.11 6.10/6.11 6.10/6.11 Closed-form bounds of f0(A,B,C,D,E,F,H): 6.10/6.11 ------------------------------------- 6.10/6.11 * Chain [124] with precondition: [] 6.10/6.11 - Upper bound: 0 6.10/6.11 - Complexity: constant 6.10/6.11 * Chain [123] with precondition: [C=1] 6.10/6.11 - Upper bound: 14 6.10/6.11 - Complexity: constant 6.10/6.11 * Chain [122] with precondition: [251>=C] 6.10/6.11 - Upper bound: 1 6.10/6.11 - Complexity: constant 6.10/6.11 * Chain [121] with precondition: [251>=C,C+1>=0] 6.10/6.11 - Upper bound: 38 6.10/6.11 - Complexity: constant 6.10/6.11 * Chain [120] with precondition: [251>=C,C>=248] 6.10/6.11 - Upper bound: 1 6.10/6.11 - Complexity: constant 6.10/6.11 * Chain [119] with precondition: [247>=C] 6.10/6.11 - Upper bound: -2*C+534 6.10/6.11 - Complexity: n 6.10/6.11 * Chain [118] with precondition: [3>=C] 6.10/6.11 - Upper bound: 0 6.10/6.11 - Complexity: constant 6.10/6.11 * Chain [117] with precondition: [0>=C,C+1>=0] 6.10/6.11 - Upper bound: 2 6.10/6.11 - Complexity: constant 6.10/6.11 * Chain [116] with precondition: [0>=C+2] 6.10/6.11 - Upper bound: 1 6.10/6.11 - Complexity: constant 6.10/6.11 * Chain [115] with precondition: [0>=C+3] 6.10/6.11 - Upper bound: -C/4+57/4 6.10/6.11 - Complexity: n 6.10/6.11 * Chain [114] with precondition: [0>=C+4] 6.10/6.11 - Upper bound: -C/4+2 6.10/6.11 - Complexity: n 6.10/6.11 * Chain [113] with precondition: [0>=C+6] 6.10/6.11 - Upper bound: -C/4+1 6.10/6.11 - Complexity: n 6.10/6.11 * Chain [112] with precondition: [C>=4] 6.10/6.11 - Upper bound: 2*C+155/4 6.10/6.11 - Complexity: n 6.10/6.11 * Chain [111] with precondition: [C>=252] 6.10/6.11 - Upper bound: 0 6.10/6.11 - Complexity: constant 6.10/6.11 * Chain [110] with precondition: [C>=254] 6.10/6.11 - Upper bound: C/4+13 6.10/6.11 - Complexity: n 6.10/6.11 * Chain [109] with precondition: [C>=255] 6.10/6.11 - Upper bound: C/4+1 6.10/6.11 - Complexity: n 6.10/6.11 * Chain [108] with precondition: [C>=257] 6.10/6.11 - Upper bound: C/4 6.10/6.11 - Complexity: n 6.10/6.11 6.10/6.11 ### Maximum cost of f0(A,B,C,D,E,F,H): max([max([max([38,nat(-C/4+1/4)+14,nat(-C/4+62)*8+38]),nat(-C/4)+2]),nat(C/4)+max([13,nat(C/4+1)+37+nat(C/4+3/4)+nat(C/4)*5])]) 6.10/6.11 Asymptotic class: n 6.10/6.11 * Total analysis performed in 5949 ms. 6.10/6.11 6.11/6.21 EOF