3.25/3.31 WORST_CASE(?,O(1)) 3.25/3.31 3.25/3.31 Preprocessing Cost Relations 3.25/3.31 ===================================== 3.25/3.31 3.25/3.31 #### Computed strongly connected components 3.25/3.31 0. recursive : [f23/4] 3.25/3.31 1. non_recursive : [exit_location/1] 3.25/3.31 2. recursive : [f33/14] 3.25/3.31 3. recursive : [f29/14,f33_loop_cont/15,f44/14] 3.25/3.31 4. recursive : [f52/12,f55/12] 3.25/3.31 5. non_recursive : [f71/13] 3.25/3.31 6. non_recursive : [f63/13] 3.25/3.31 7. non_recursive : [f52_loop_cont/14] 3.25/3.31 8. non_recursive : [f29_loop_cont/14] 3.25/3.31 9. non_recursive : [f23_loop_cont/14] 3.25/3.31 10. non_recursive : [f0/13] 3.25/3.31 3.25/3.31 #### Obtained direct recursion through partial evaluation 3.25/3.31 0. SCC is partially evaluated into f23/4 3.25/3.31 1. SCC is completely evaluated into other SCCs 3.25/3.31 2. SCC is partially evaluated into f33/14 3.25/3.31 3. SCC is partially evaluated into f29/14 3.25/3.31 4. SCC is partially evaluated into f52/12 3.25/3.31 5. SCC is completely evaluated into other SCCs 3.25/3.31 6. SCC is partially evaluated into f63/13 3.25/3.31 7. SCC is partially evaluated into f52_loop_cont/14 3.25/3.31 8. SCC is partially evaluated into f29_loop_cont/14 3.25/3.31 9. SCC is partially evaluated into f23_loop_cont/14 3.25/3.31 10. SCC is partially evaluated into f0/13 3.25/3.31 3.25/3.31 Control-Flow Refinement of Cost Relations 3.25/3.31 ===================================== 3.25/3.31 3.25/3.31 ### Specialization of cost equations f23/4 3.25/3.31 * CE 4 is refined into CE [39] 3.25/3.31 * CE 3 is refined into CE [40] 3.25/3.31 * CE 2 is refined into CE [41] 3.25/3.31 3.25/3.31 3.25/3.31 ### Cost equations --> "Loop" of f23/4 3.25/3.31 * CEs [41] --> Loop 39 3.25/3.31 * CEs [39] --> Loop 40 3.25/3.31 * CEs [40] --> Loop 41 3.25/3.31 3.25/3.31 ### Ranking functions of CR f23(C,F,O,P) 3.25/3.31 * RF of phase [39]: [-F+10] 3.25/3.31 3.25/3.31 #### Partial ranking functions of CR f23(C,F,O,P) 3.25/3.31 * Partial RF of phase [39]: 3.25/3.31 - RF of loop [39:1]: 3.25/3.31 -F+10 3.25/3.31 3.25/3.31 3.25/3.31 ### Specialization of cost equations f33/14 3.25/3.31 * CE 23 is refined into CE [42] 3.25/3.31 * CE 21 is refined into CE [43] 3.25/3.31 * CE 20 is refined into CE [44] 3.25/3.31 * CE 22 is refined into CE [45] 3.25/3.31 * CE 17 is refined into CE [46] 3.25/3.31 * CE 16 is discarded (unfeasible) 3.25/3.31 * CE 18 is refined into CE [47] 3.25/3.31 * CE 19 is refined into CE [48] 3.25/3.31 3.25/3.31 3.25/3.31 ### Cost equations --> "Loop" of f33/14 3.25/3.31 * CEs [46] --> Loop 42 3.25/3.31 * CEs [47] --> Loop 43 3.25/3.31 * CEs [48] --> Loop 44 3.25/3.31 * CEs [42] --> Loop 45 3.25/3.31 * CEs [43] --> Loop 46 3.25/3.31 * CEs [44] --> Loop 47 3.25/3.31 * CEs [45] --> Loop 48 3.25/3.31 3.25/3.31 ### Ranking functions of CR f33(A,C,F,G,H,I,J,O,P,Q,R,S,T,U) 3.25/3.31 * RF of phase [42]: [-H+10] 3.25/3.31 * RF of phase [44]: [-H+10] 3.25/3.31 3.25/3.31 #### Partial ranking functions of CR f33(A,C,F,G,H,I,J,O,P,Q,R,S,T,U) 3.25/3.31 * Partial RF of phase [42]: 3.25/3.31 - RF of loop [42:1]: 3.25/3.31 -H+10 3.25/3.31 * Partial RF of phase [44]: 3.25/3.31 - RF of loop [44:1]: 3.25/3.31 -H+10 3.25/3.31 3.25/3.31 3.25/3.31 ### Specialization of cost equations f29/14 3.25/3.31 * CE 12 is refined into CE [49] 3.25/3.31 * CE 10 is refined into CE [50,51,52,53] 3.25/3.31 * CE 13 is refined into CE [54] 3.25/3.31 * CE 11 is refined into CE [55,56,57] 3.25/3.31 * CE 8 is refined into CE [58,59,60,61] 3.25/3.31 * CE 9 is discarded (unfeasible) 3.25/3.31 * CE 7 is refined into CE [62,63] 3.25/3.31 3.25/3.31 3.25/3.31 ### Cost equations --> "Loop" of f29/14 3.25/3.31 * CEs [60,61] --> Loop 49 3.25/3.31 * CEs [58,59] --> Loop 50 3.25/3.31 * CEs [63] --> Loop 51 3.25/3.31 * CEs [62] --> Loop 52 3.25/3.31 * CEs [56,57] --> Loop 53 3.25/3.31 * CEs [55] --> Loop 54 3.25/3.31 * CEs [49] --> Loop 55 3.25/3.31 * CEs [50,51,52,53] --> Loop 56 3.25/3.31 * CEs [54] --> Loop 57 3.25/3.31 3.25/3.31 ### Ranking functions of CR f29(A,C,F,G,H,I,J,O,P,Q,R,S,T,U) 3.25/3.31 * RF of phase [49]: [-F+10] 3.25/3.31 * RF of phase [53,54]: [-F+10] 3.25/3.31 3.25/3.31 #### Partial ranking functions of CR f29(A,C,F,G,H,I,J,O,P,Q,R,S,T,U) 3.25/3.31 * Partial RF of phase [49]: 3.25/3.31 - RF of loop [49:1]: 3.25/3.31 -F+10 3.25/3.31 * Partial RF of phase [53,54]: 3.25/3.31 - RF of loop [53:1,54:1]: 3.25/3.31 -F+10 3.25/3.31 3.25/3.31 3.25/3.31 ### Specialization of cost equations f52/12 3.25/3.31 * CE 30 is refined into CE [64] 3.25/3.31 * CE 29 is refined into CE [65] 3.25/3.31 * CE 32 is refined into CE [66] 3.25/3.31 * CE 31 is refined into CE [67] 3.25/3.31 * CE 26 is refined into CE [68] 3.25/3.31 * CE 27 is discarded (unfeasible) 3.25/3.31 * CE 24 is refined into CE [69] 3.25/3.31 * CE 25 is discarded (unfeasible) 3.25/3.31 * CE 28 is refined into CE [70] 3.25/3.31 3.25/3.31 3.25/3.31 ### Cost equations --> "Loop" of f52/12 3.25/3.31 * CEs [68] --> Loop 58 3.25/3.31 * CEs [69] --> Loop 59 3.25/3.31 * CEs [70] --> Loop 60 3.25/3.31 * CEs [64] --> Loop 61 3.25/3.31 * CEs [65] --> Loop 62 3.25/3.31 * CEs [66] --> Loop 63 3.25/3.31 * CEs [67] --> Loop 64 3.25/3.31 3.25/3.31 ### Ranking functions of CR f52(A,B,C,F,K,L,O,P,Q,R,S,T) 3.25/3.31 * RF of phase [58]: [-F+9] 3.25/3.31 * RF of phase [60]: [-F+9] 3.25/3.31 3.25/3.31 #### Partial ranking functions of CR f52(A,B,C,F,K,L,O,P,Q,R,S,T) 3.25/3.31 * Partial RF of phase [58]: 3.25/3.31 - RF of loop [58:1]: 3.25/3.31 -F+9 3.25/3.31 * Partial RF of phase [60]: 3.25/3.31 - RF of loop [60:1]: 3.25/3.31 -F+9 3.25/3.31 3.25/3.31 3.25/3.31 ### Specialization of cost equations f63/13 3.25/3.31 * CE 37 is refined into CE [71] 3.25/3.31 * CE 36 is refined into CE [72] 3.25/3.31 * CE 38 is refined into CE [73] 3.25/3.31 3.25/3.31 3.25/3.31 ### Cost equations --> "Loop" of f63/13 3.25/3.31 * CEs [71] --> Loop 65 3.25/3.31 * CEs [72] --> Loop 66 3.25/3.31 * CEs [73] --> Loop 67 3.25/3.31 3.25/3.31 ### Ranking functions of CR f63(A,B,C,D,E,F,G,H,I,J,K,L,O) 3.25/3.31 3.25/3.31 #### Partial ranking functions of CR f63(A,B,C,D,E,F,G,H,I,J,K,L,O) 3.25/3.31 3.25/3.31 3.25/3.31 ### Specialization of cost equations f52_loop_cont/14 3.25/3.31 * CE 34 is refined into CE [74] 3.25/3.31 * CE 33 is refined into CE [75,76,77] 3.25/3.31 * CE 35 is refined into CE [78] 3.25/3.31 3.25/3.31 3.25/3.31 ### Cost equations --> "Loop" of f52_loop_cont/14 3.25/3.31 * CEs [74] --> Loop 68 3.25/3.31 * CEs [77] --> Loop 69 3.25/3.31 * CEs [76] --> Loop 70 3.25/3.31 * CEs [75] --> Loop 71 3.25/3.31 * CEs [78] --> Loop 72 3.25/3.31 3.25/3.31 ### Ranking functions of CR f52_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N) 3.25/3.31 3.25/3.31 #### Partial ranking functions of CR f52_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N) 3.25/3.31 3.25/3.31 3.25/3.31 ### Specialization of cost equations f29_loop_cont/14 3.25/3.31 * CE 15 is refined into CE [79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97] 3.25/3.31 * CE 14 is refined into CE [98] 3.25/3.31 3.25/3.31 3.25/3.31 ### Cost equations --> "Loop" of f29_loop_cont/14 3.25/3.31 * CEs [97] --> Loop 73 3.25/3.31 * CEs [92] --> Loop 74 3.25/3.31 * CEs [88] --> Loop 75 3.25/3.31 * CEs [91] --> Loop 76 3.25/3.31 * CEs [87] --> Loop 77 3.25/3.31 * CEs [94] --> Loop 78 3.25/3.31 * CEs [86] --> Loop 79 3.25/3.31 * CEs [96] --> Loop 80 3.25/3.31 * CEs [90] --> Loop 81 3.25/3.31 * CEs [89] --> Loop 82 3.25/3.31 * CEs [93] --> Loop 83 3.25/3.31 * CEs [85] --> Loop 84 3.25/3.31 * CEs [84] --> Loop 85 3.25/3.31 * CEs [95] --> Loop 86 3.25/3.31 * CEs [83] --> Loop 87 3.25/3.31 * CEs [81] --> Loop 88 3.25/3.31 * CEs [80] --> Loop 89 3.25/3.31 * CEs [82] --> Loop 90 3.25/3.31 * CEs [79] --> Loop 91 3.25/3.31 * CEs [98] --> Loop 92 3.25/3.31 3.25/3.31 ### Ranking functions of CR f29_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N) 3.25/3.31 3.25/3.31 #### Partial ranking functions of CR f29_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N) 3.25/3.31 3.25/3.31 3.25/3.31 ### Specialization of cost equations f23_loop_cont/14 3.25/3.31 * CE 5 is refined into CE [99] 3.25/3.31 * CE 6 is refined into CE [100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147] 3.25/3.31 3.25/3.31 3.25/3.31 ### Cost equations --> "Loop" of f23_loop_cont/14 3.25/3.31 * CEs [99] --> Loop 93 3.25/3.31 * CEs [141,142,143,144,145,146,147] --> Loop 94 3.25/3.31 * CEs [110] --> Loop 95 3.25/3.31 * CEs [109,125,126,127,128,129,130,131] --> Loop 96 3.25/3.31 * CEs [108,111,112,113,114,115,116,117,118,119,120,121,122,123,124] --> Loop 97 3.25/3.31 * CEs [107,132,133,134,135,136,137,138,139] --> Loop 98 3.25/3.31 * CEs [100,101,102,103,104,105,106] --> Loop 99 3.25/3.31 * CEs [140] --> Loop 100 3.25/3.31 3.25/3.31 ### Ranking functions of CR f23_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N) 3.25/3.31 3.25/3.31 #### Partial ranking functions of CR f23_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N) 3.25/3.31 3.25/3.31 3.25/3.31 ### Specialization of cost equations f0/13 3.25/3.31 * CE 1 is refined into CE [148,149,150,151,152,153,154] 3.25/3.31 3.25/3.31 3.25/3.31 ### Cost equations --> "Loop" of f0/13 3.25/3.31 * CEs [148,149,150,151,152,153,154] --> Loop 101 3.25/3.31 3.25/3.31 ### Ranking functions of CR f0(A,B,C,D,E,F,G,H,I,J,K,L,O) 3.25/3.31 3.25/3.31 #### Partial ranking functions of CR f0(A,B,C,D,E,F,G,H,I,J,K,L,O) 3.25/3.31 3.25/3.31 3.25/3.31 Computing Bounds 3.25/3.31 ===================================== 3.25/3.31 3.25/3.31 #### Cost of chains of f23(C,F,O,P): 3.25/3.31 * Chain [[39],41]: 1*it(39)+0 3.25/3.31 Such that:it(39) =< -F+10 3.25/3.31 3.25/3.31 with precondition: [C=10,O=3,P=0,9>=F,F>=0] 3.25/3.31 3.25/3.31 * Chain [[39],40]: 1*it(39)+0 3.25/3.31 Such that:it(39) =< -F+10 3.25/3.31 3.25/3.31 with precondition: [C=10,O=4,9>=F,F>=0] 3.25/3.31 3.25/3.31 * Chain [40]: 0 3.25/3.31 with precondition: [C=10,O=4,F>=0] 3.25/3.31 3.25/3.31 3.25/3.31 #### Cost of chains of f33(A,C,F,G,H,I,J,O,P,Q,R,S,T,U): 3.25/3.31 * Chain [[44],48]: 1*it(44)+0 3.25/3.31 Such that:it(44) =< -H+10 3.25/3.31 3.25/3.31 with precondition: [A=0,C=10,G=0,O=3,P=0,R=0,S=10,T=0,U=0,F+1=Q,9>=F,9>=H,H>=0] 3.25/3.31 3.25/3.31 * Chain [[44],47]: 1*it(44)+0 3.25/3.31 Such that:it(44) =< -H+10 3.25/3.31 3.25/3.31 with precondition: [C=10,G=0,O=2,R=0,S=10,T=0,A=P,F=Q,J=U,0>=A+1,9>=F,9>=H,H>=0] 3.25/3.31 3.25/3.31 * Chain [[44],46]: 1*it(44)+0 3.25/3.31 Such that:it(44) =< -H+10 3.25/3.31 3.25/3.31 with precondition: [C=10,G=0,O=2,R=0,S=10,T=0,A=P,F=Q,J=U,9>=F,9>=H,A>=1,H>=0] 3.25/3.31 3.25/3.31 * Chain [[44],45]: 1*it(44)+0 3.25/3.31 Such that:it(44) =< -H+10 3.25/3.31 3.25/3.31 with precondition: [C=10,G=0,O=4,9>=F,9>=H,H>=0] 3.25/3.31 3.25/3.31 * Chain [[44],43,[42],48]: 2*it(42)+1 3.25/3.31 Such that:aux(1) =< -H+8 3.25/3.31 aux(2) =< -H+9 3.25/3.31 it(42) =< aux(1) 3.25/3.31 it(42) =< aux(2) 3.25/3.31 3.25/3.31 with precondition: [A=0,C=10,G=0,O=3,P=0,R=1,S=10,T=1,U=0,F+1=Q,9>=F,7>=H,H>=0] 3.25/3.31 3.25/3.31 * Chain [[44],43,[42],47]: 2*it(42)+1 3.25/3.31 Such that:aux(3) =< -H+8 3.25/3.31 aux(4) =< -H+9 3.25/3.31 it(42) =< aux(3) 3.25/3.31 it(42) =< aux(4) 3.25/3.31 3.25/3.31 with precondition: [C=10,G=0,O=2,R=1,S=10,T=1,A=P,F=Q,J=U,0>=A+1,9>=F,7>=H,H>=0] 3.25/3.31 3.25/3.31 * Chain [[44],43,[42],46]: 2*it(42)+1 3.25/3.31 Such that:aux(5) =< -H+8 3.25/3.31 aux(6) =< -H+9 3.25/3.31 it(42) =< aux(5) 3.25/3.31 it(42) =< aux(6) 3.25/3.31 3.25/3.31 with precondition: [C=10,G=0,O=2,R=1,S=10,T=1,A=P,F=Q,J=U,9>=F,7>=H,A>=1,H>=0] 3.25/3.31 3.25/3.31 * Chain [[44],43,[42],45]: 2*it(42)+1 3.25/3.31 Such that:aux(7) =< -H+8 3.25/3.31 aux(8) =< -H+9 3.25/3.31 it(42) =< aux(7) 3.25/3.31 it(42) =< aux(8) 3.25/3.31 3.25/3.31 with precondition: [C=10,G=0,O=4,9>=F,7>=H,H>=0] 3.25/3.31 3.25/3.31 * Chain [[44],43,48]: 1*it(44)+1 3.25/3.31 Such that:it(44) =< -H+9 3.25/3.31 3.25/3.31 with precondition: [A=0,C=10,G=0,O=3,P=0,R=1,S=10,T=1,U=0,F+1=Q,9>=F,8>=H,H>=0] 3.25/3.31 3.25/3.31 * Chain [[44],43,47]: 1*it(44)+1 3.25/3.31 Such that:it(44) =< -H+9 3.25/3.31 3.25/3.31 with precondition: [C=10,G=0,O=2,R=1,S=10,T=1,A=P,F=Q,J=U,0>=A+1,9>=F,8>=H,H>=0] 3.25/3.31 3.25/3.31 * Chain [[44],43,46]: 1*it(44)+1 3.25/3.31 Such that:it(44) =< -H+9 3.25/3.31 3.25/3.31 with precondition: [C=10,G=0,O=2,R=1,S=10,T=1,A=P,F=Q,J=U,9>=F,8>=H,A>=1,H>=0] 3.25/3.31 3.25/3.31 * Chain [[44],43,45]: 1*it(44)+1 3.25/3.31 Such that:it(44) =< -H+9 3.25/3.31 3.25/3.31 with precondition: [C=10,G=0,O=4,9>=F,8>=H,H>=0] 3.25/3.31 3.25/3.31 * Chain [45]: 0 3.25/3.31 with precondition: [C=10,O=4,9>=F,1>=G,G>=0,H>=G] 3.25/3.31 3.25/3.31 * Chain [43,[42],48]: 1*it(42)+1 3.25/3.31 Such that:it(42) =< -H+9 3.25/3.31 3.25/3.31 with precondition: [A=0,C=10,G=0,O=3,P=0,R=1,S=10,T=1,U=0,F+1=Q,9>=F,8>=H,H>=0] 3.25/3.31 3.25/3.31 * Chain [43,[42],47]: 1*it(42)+1 3.25/3.31 Such that:it(42) =< -H+9 3.25/3.31 3.25/3.31 with precondition: [C=10,G=0,O=2,R=1,S=10,T=1,A=P,F=Q,J=U,0>=A+1,9>=F,8>=H,H>=0] 3.25/3.31 3.25/3.31 * Chain [43,[42],46]: 1*it(42)+1 3.25/3.31 Such that:it(42) =< -H+9 3.25/3.31 3.25/3.31 with precondition: [C=10,G=0,O=2,R=1,S=10,T=1,A=P,F=Q,J=U,9>=F,8>=H,A>=1,H>=0] 3.25/3.31 3.25/3.31 * Chain [43,[42],45]: 1*it(42)+1 3.25/3.31 Such that:it(42) =< -H+9 3.25/3.31 3.25/3.31 with precondition: [C=10,G=0,O=4,9>=F,8>=H,H>=0] 3.25/3.31 3.25/3.31 * Chain [43,45]: 1 3.25/3.31 with precondition: [C=10,G=0,O=4,9>=F,9>=H,H>=0] 3.25/3.31 3.25/3.31 3.25/3.31 #### Cost of chains of f29(A,C,F,G,H,I,J,O,P,Q,R,S,T,U): 3.25/3.31 * Chain [[49],57]: 36*it(49)+0 3.25/3.31 Such that:it(49) =< -F+10 3.25/3.31 3.25/3.31 with precondition: [A=1,C=10,O=4,9>=F] 3.25/3.31 3.25/3.31 * Chain [[49],56]: 36*it(49)+45 3.25/3.31 Such that:it(49) =< -F+9 3.25/3.31 3.25/3.31 with precondition: [A=1,C=10,O=4,8>=F] 3.25/3.31 3.25/3.31 * Chain [[49],55]: 36*it(49)+0 3.25/3.31 Such that:it(49) =< -F+10 3.25/3.31 3.25/3.31 with precondition: [A=1,C=10,O=7,P=1,Q=0,R=1,S=10,T=1,U=1,9>=F] 3.25/3.31 3.25/3.31 * Chain [[49],51,[53,54],57]: 36*it(49)+37*it(53)+1*s(28)+1*s(29)+1 3.25/3.31 Such that:s(29) =< 10 3.25/3.31 aux(20) =< -F+8 3.25/3.31 aux(21) =< -F+9 3.25/3.31 aux(19) =< aux(20) 3.25/3.31 it(49) =< aux(20) 3.25/3.31 aux(19) =< aux(21) 3.25/3.31 it(49) =< aux(21) 3.25/3.31 it(53) =< aux(19) 3.25/3.31 s(28) =< aux(19)*10 3.25/3.31 3.25/3.31 with precondition: [A=1,C=10,O=4,7>=F] 3.25/3.31 3.25/3.31 * Chain [[49],51,[53,54],56]: 36*it(49)+37*it(53)+1*s(28)+1*s(29)+46 3.25/3.31 Such that:s(29) =< 10 3.25/3.31 aux(18) =< -F+7 3.25/3.31 aux(22) =< -F+8 3.25/3.31 aux(23) =< -F+9 3.25/3.31 aux(17) =< aux(22) 3.25/3.31 aux(18) =< aux(22) 3.25/3.31 it(49) =< aux(22) 3.25/3.31 aux(17) =< aux(23) 3.25/3.31 it(49) =< aux(23) 3.25/3.31 aux(16) =< aux(17) 3.25/3.31 it(53) =< aux(17) 3.25/3.31 aux(16) =< aux(18) 3.25/3.31 it(53) =< aux(18) 3.25/3.31 s(28) =< aux(16)*10 3.25/3.31 3.25/3.31 with precondition: [A=1,C=10,O=4,6>=F] 3.25/3.31 3.25/3.31 * Chain [[49],51,[53,54],55]: 36*it(49)+37*it(53)+1*s(28)+1*s(29)+1 3.25/3.31 Such that:s(29) =< 10 3.25/3.31 aux(25) =< -F+8 3.25/3.31 aux(26) =< -F+9 3.25/3.31 aux(24) =< aux(25) 3.25/3.31 it(49) =< aux(25) 3.25/3.31 aux(24) =< aux(26) 3.25/3.31 it(49) =< aux(26) 3.25/3.31 it(53) =< aux(24) 3.25/3.31 s(28) =< aux(24)*10 3.25/3.31 3.25/3.31 with precondition: [A=1,C=10,O=7,P=0,Q=0,S=10,U=0,R=T,7>=F,1>=R,R>=0] 3.25/3.31 3.25/3.31 * Chain [[49],51,57]: 36*it(49)+1*s(29)+1 3.25/3.31 Such that:s(29) =< 10 3.25/3.31 it(49) =< -F+9 3.25/3.31 3.25/3.31 with precondition: [A=1,C=10,O=4,8>=F] 3.25/3.31 3.25/3.31 * Chain [[49],51,56]: 36*it(49)+1*s(29)+46 3.25/3.31 Such that:s(29) =< 10 3.25/3.31 it(49) =< -F+8 3.25/3.31 3.25/3.31 with precondition: [A=1,C=10,O=4,7>=F] 3.25/3.31 3.25/3.31 * Chain [[49],51,55]: 36*it(49)+1*s(29)+1 3.25/3.31 Such that:s(29) =< 10 3.25/3.31 it(49) =< -F+9 3.25/3.31 3.25/3.31 with precondition: [A=1,C=10,O=7,P=0,Q=0,R=0,S=10,T=0,U=0,8>=F] 3.25/3.31 3.25/3.31 * Chain [57]: 0 3.25/3.31 with precondition: [C=10,O=4,1>=A,A>=0] 3.25/3.31 3.25/3.31 * Chain [56]: 45 3.25/3.31 with precondition: [C=10,O=4,1>=A,9>=F,A>=0] 3.25/3.31 3.25/3.31 * Chain [55]: 0 3.25/3.31 with precondition: [C=10,O=7,Q=0,R=G,S=H,T=I,U=J,A=P,1>=A,A>=0,F>=10] 3.25/3.31 3.25/3.31 * Chain [51,[53,54],57]: 37*it(53)+1*s(28)+1*s(29)+1 3.25/3.31 Such that:s(29) =< 10 3.25/3.31 aux(19) =< -F+9 3.25/3.31 it(53) =< aux(19) 3.25/3.31 s(28) =< aux(19)*10 3.25/3.31 3.25/3.31 with precondition: [A=1,C=10,O=4,8>=F] 3.25/3.31 3.25/3.31 * Chain [51,[53,54],56]: 37*it(53)+1*s(28)+1*s(29)+46 3.25/3.31 Such that:s(29) =< 10 3.25/3.31 aux(18) =< -F+8 3.25/3.31 aux(17) =< -F+9 3.25/3.31 aux(16) =< aux(17) 3.25/3.31 it(53) =< aux(17) 3.25/3.31 aux(16) =< aux(18) 3.25/3.31 it(53) =< aux(18) 3.25/3.31 s(28) =< aux(16)*10 3.25/3.31 3.25/3.31 with precondition: [A=1,C=10,O=4,7>=F] 3.25/3.31 3.25/3.31 * Chain [51,[53,54],55]: 37*it(53)+1*s(28)+1*s(29)+1 3.25/3.31 Such that:s(29) =< 10 3.25/3.31 aux(24) =< -F+9 3.25/3.31 it(53) =< aux(24) 3.25/3.31 s(28) =< aux(24)*10 3.25/3.31 3.25/3.31 with precondition: [A=1,C=10,O=7,P=0,Q=0,S=10,U=0,R=T,8>=F,1>=R,R>=0] 3.25/3.31 3.25/3.31 * Chain [51,57]: 1*s(29)+1 3.25/3.31 Such that:s(29) =< 10 3.25/3.31 3.25/3.31 with precondition: [A=1,C=10,O=4,9>=F] 3.25/3.31 3.25/3.31 * Chain [51,56]: 1*s(29)+46 3.25/3.31 Such that:s(29) =< 10 3.25/3.31 3.25/3.31 with precondition: [A=1,C=10,O=4,8>=F] 3.25/3.31 3.25/3.31 * Chain [51,55]: 1*s(29)+1 3.25/3.31 Such that:s(29) =< 10 3.25/3.31 3.25/3.31 with precondition: [A=1,C=10,F=9,O=7,P=0,Q=0,R=0,S=10,T=0,U=0] 3.25/3.31 3.25/3.31 3.25/3.31 #### Cost of chains of f52(A,B,C,F,K,L,O,P,Q,R,S,T): 3.25/3.31 * Chain [[58],64]: 1*it(58)+0 3.25/3.31 Such that:it(58) =< -F+9 3.25/3.31 3.25/3.31 with precondition: [A=0,B=1,C=10,O=6,P=0,Q=1,R=9,S=1,T=1,8>=F] 3.25/3.31 3.25/3.31 * Chain [[58],63]: 1*it(58)+0 3.25/3.31 Such that:it(58) =< -F+9 3.25/3.31 3.25/3.31 with precondition: [B=1,C=10,O=4,8>=F] 3.25/3.31 3.25/3.31 * Chain [[58],62]: 1*it(58)+0 3.25/3.31 Such that:it(58) =< -F+9 3.25/3.31 3.25/3.31 with precondition: [B=1,C=10,O=5,Q=1,R=9,S=1,A=P,L=T,0>=A+1,8>=F] 3.25/3.31 3.25/3.31 * Chain [[58],61]: 1*it(58)+0 3.25/3.31 Such that:it(58) =< -F+9 3.25/3.31 3.25/3.31 with precondition: [B=1,C=10,O=5,Q=1,R=9,S=1,A=P,L=T,8>=F,A>=1] 3.25/3.31 3.25/3.31 * Chain [[58],59,[60],64]: 2*it(58)+1 3.25/3.31 Such that:aux(32) =< -F+7 3.25/3.31 aux(33) =< -F+8 3.25/3.31 it(58) =< aux(32) 3.25/3.31 it(58) =< aux(33) 3.25/3.31 3.25/3.31 with precondition: [A=0,B=1,C=10,O=6,P=0,Q=0,R=9,S=0,T=1,6>=F] 3.25/3.31 3.25/3.31 * Chain [[58],59,[60],63]: 2*it(58)+1 3.25/3.31 Such that:aux(34) =< -F+7 3.25/3.31 aux(35) =< -F+8 3.25/3.31 it(58) =< aux(34) 3.25/3.31 it(58) =< aux(35) 3.25/3.31 3.25/3.31 with precondition: [B=1,C=10,O=4,6>=F] 3.25/3.31 3.25/3.31 * Chain [[58],59,[60],62]: 2*it(58)+1 3.25/3.31 Such that:aux(36) =< -F+7 3.25/3.31 aux(37) =< -F+8 3.25/3.31 it(58) =< aux(36) 3.25/3.31 it(58) =< aux(37) 3.25/3.31 3.25/3.31 with precondition: [B=1,C=10,O=5,Q=0,R=9,S=0,A=P,L=T,0>=A+1,6>=F] 3.25/3.31 3.25/3.31 * Chain [[58],59,[60],61]: 2*it(58)+1 3.25/3.31 Such that:aux(38) =< -F+7 3.25/3.31 aux(39) =< -F+8 3.25/3.31 it(58) =< aux(38) 3.25/3.31 it(58) =< aux(39) 3.25/3.31 3.25/3.31 with precondition: [B=1,C=10,O=5,Q=0,R=9,S=0,A=P,L=T,6>=F,A>=1] 3.25/3.31 3.25/3.31 * Chain [[58],59,64]: 1*it(58)+1 3.25/3.31 Such that:it(58) =< -F+8 3.25/3.31 3.25/3.31 with precondition: [A=0,B=1,C=10,O=6,P=0,Q=0,R=9,S=0,T=1,7>=F] 3.25/3.31 3.25/3.31 * Chain [[58],59,63]: 1*it(58)+1 3.25/3.31 Such that:it(58) =< -F+8 3.25/3.31 3.25/3.31 with precondition: [B=1,C=10,O=4,7>=F] 3.25/3.31 3.25/3.31 * Chain [[58],59,62]: 1*it(58)+1 3.25/3.31 Such that:it(58) =< -F+8 3.25/3.31 3.25/3.31 with precondition: [B=1,C=10,O=5,Q=0,R=9,S=0,A=P,L=T,0>=A+1,7>=F] 3.25/3.31 3.25/3.31 * Chain [[58],59,61]: 1*it(58)+1 3.25/3.31 Such that:it(58) =< -F+8 3.25/3.31 3.25/3.31 with precondition: [B=1,C=10,O=5,Q=0,R=9,S=0,A=P,L=T,7>=F,A>=1] 3.25/3.31 3.25/3.31 * Chain [64]: 0 3.25/3.31 with precondition: [A=0,C=10,O=6,P=0,T=1,S=K,B=Q,F=R,1>=B,B>=0,F>=9] 3.25/3.31 3.25/3.31 * Chain [63]: 0 3.25/3.31 with precondition: [C=10,O=4,1>=B,B>=0] 3.25/3.31 3.25/3.31 * Chain [62]: 0 3.25/3.31 with precondition: [C=10,O=5,S=K,T=L,A=P,B=Q,F=R,0>=A+1,1>=B,B>=0,F>=9] 3.25/3.31 3.25/3.31 * Chain [61]: 0 3.25/3.31 with precondition: [C=10,O=5,S=K,T=L,A=P,B=Q,F=R,1>=B,A>=1,B>=0,F>=9] 3.25/3.31 3.25/3.31 * Chain [59,[60],64]: 1*it(60)+1 3.25/3.31 Such that:it(60) =< -F+8 3.25/3.31 3.25/3.31 with precondition: [A=0,B=1,C=10,O=6,P=0,Q=0,R=9,S=0,T=1,7>=F] 3.25/3.31 3.25/3.31 * Chain [59,[60],63]: 1*it(60)+1 3.25/3.31 Such that:it(60) =< -F+8 3.25/3.31 3.25/3.31 with precondition: [B=1,C=10,O=4,7>=F] 3.25/3.31 3.25/3.31 * Chain [59,[60],62]: 1*it(60)+1 3.25/3.31 Such that:it(60) =< -F+8 3.25/3.31 3.25/3.31 with precondition: [B=1,C=10,O=5,Q=0,R=9,S=0,A=P,L=T,0>=A+1,7>=F] 3.25/3.31 3.25/3.31 * Chain [59,[60],61]: 1*it(60)+1 3.25/3.31 Such that:it(60) =< -F+8 3.25/3.31 3.25/3.31 with precondition: [B=1,C=10,O=5,Q=0,R=9,S=0,A=P,L=T,7>=F,A>=1] 3.25/3.31 3.25/3.31 * Chain [59,64]: 1 3.25/3.31 with precondition: [A=0,B=1,C=10,F=8,O=6,P=0,Q=0,R=9,S=0,T=1] 3.25/3.31 3.25/3.31 * Chain [59,63]: 1 3.25/3.31 with precondition: [B=1,C=10,O=4,8>=F] 3.25/3.31 3.25/3.31 * Chain [59,62]: 1 3.25/3.31 with precondition: [B=1,C=10,F=8,O=5,Q=0,R=9,S=0,A=P,L=T,0>=A+1] 3.25/3.31 3.25/3.31 * Chain [59,61]: 1 3.25/3.31 with precondition: [B=1,C=10,F=8,O=5,Q=0,R=9,S=0,A=P,L=T,A>=1] 3.25/3.31 3.25/3.31 3.25/3.31 #### Cost of chains of f63(A,B,C,D,E,F,G,H,I,J,K,L,O): 3.25/3.31 * Chain [67]: 0 3.25/3.31 with precondition: [B=0,C=10] 3.25/3.31 3.25/3.31 * Chain [66]: 0 3.25/3.31 with precondition: [C=10,0>=B+1] 3.25/3.31 3.25/3.31 * Chain [65]: 0 3.25/3.31 with precondition: [C=10,B>=1] 3.25/3.31 3.25/3.31 3.25/3.31 #### Cost of chains of f52_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N): 3.25/3.31 * Chain [72]: 0 3.25/3.31 with precondition: [A=4,D=10] 3.25/3.31 3.25/3.31 * Chain [71]: 0 3.25/3.31 with precondition: [A=5,C=0,D=10] 3.25/3.31 3.25/3.31 * Chain [70]: 0 3.25/3.31 with precondition: [A=5,D=10,0>=C+1] 3.25/3.31 3.25/3.31 * Chain [69]: 0 3.25/3.31 with precondition: [A=5,D=10,C>=1] 3.25/3.31 3.25/3.31 * Chain [68]: 0 3.25/3.31 with precondition: [A=6,D=10] 3.25/3.31 3.25/3.31 3.25/3.31 #### Cost of chains of f29_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N): 3.25/3.31 * Chain [92]: 0 3.25/3.31 with precondition: [A=4,C=1,D=10] 3.25/3.31 3.25/3.31 * Chain [91]: 1 3.25/3.31 with precondition: [A=7,B=0,C=1,D=10,G=8] 3.25/3.31 3.25/3.31 * Chain [90]: 1*s(64)+0 3.25/3.31 Such that:s(64) =< -G+9 3.25/3.31 3.25/3.31 with precondition: [A=7,B=0,C=1,D=10,8>=G] 3.25/3.31 3.25/3.31 * Chain [89]: 2*s(66)+1 3.25/3.31 Such that:s(65) =< -G+8 3.25/3.31 s(66) =< s(65) 3.25/3.31 3.25/3.31 with precondition: [A=7,B=0,C=1,D=10,7>=G] 3.25/3.31 3.25/3.31 * Chain [88]: 2*s(69)+1 3.25/3.31 Such that:s(67) =< -G+7 3.25/3.31 s(68) =< -G+8 3.25/3.31 s(69) =< s(67) 3.25/3.31 s(69) =< s(68) 3.25/3.31 3.25/3.31 with precondition: [A=7,B=0,C=1,D=10,6>=G] 3.25/3.31 3.25/3.31 * Chain [87]: 0 3.25/3.31 with precondition: [A=7,B=0,C=1,D=10,G>=9] 3.25/3.31 3.25/3.31 * Chain [86]: 0 3.25/3.31 with precondition: [A=7,C=1,D=10] 3.25/3.31 3.25/3.31 * Chain [85]: 1 3.25/3.31 with precondition: [A=7,C=1,D=10,G=8,0>=B+1] 3.25/3.31 3.25/3.31 * Chain [84]: 1 3.25/3.31 with precondition: [A=7,C=1,D=10,G=8,B>=1] 3.25/3.31 3.25/3.31 * Chain [83]: 1*s(70)+0 3.25/3.31 Such that:s(70) =< -G+9 3.25/3.31 3.25/3.31 with precondition: [A=7,C=1,D=10,0>=B+1,8>=G] 3.25/3.31 3.25/3.31 * Chain [82]: 2*s(72)+1 3.25/3.31 Such that:s(71) =< -G+8 3.25/3.31 s(72) =< s(71) 3.25/3.31 3.25/3.31 with precondition: [A=7,C=1,D=10,0>=B+1,7>=G] 3.25/3.31 3.25/3.31 * Chain [81]: 2*s(75)+1 3.25/3.31 Such that:s(73) =< -G+7 3.25/3.31 s(74) =< -G+8 3.25/3.31 s(75) =< s(73) 3.25/3.31 s(75) =< s(74) 3.25/3.31 3.25/3.31 with precondition: [A=7,C=1,D=10,0>=B+1,6>=G] 3.25/3.31 3.25/3.31 * Chain [80]: 0 3.25/3.31 with precondition: [A=7,C=1,D=10,0>=B+1,G>=9] 3.25/3.31 3.25/3.31 * Chain [79]: 1*s(76)+1 3.25/3.31 Such that:s(76) =< -G+9 3.25/3.31 3.25/3.31 with precondition: [A=7,C=1,D=10,8>=G] 3.25/3.31 3.25/3.31 * Chain [78]: 1*s(77)+0 3.25/3.31 Such that:s(77) =< -G+9 3.25/3.31 3.25/3.31 with precondition: [A=7,C=1,D=10,8>=G,B>=1] 3.25/3.31 3.25/3.31 * Chain [77]: 2*s(79)+1 3.25/3.31 Such that:s(78) =< -G+8 3.25/3.31 s(79) =< s(78) 3.25/3.31 3.25/3.31 with precondition: [A=7,C=1,D=10,7>=G] 3.25/3.31 3.25/3.31 * Chain [76]: 2*s(81)+1 3.25/3.31 Such that:s(80) =< -G+8 3.25/3.31 s(81) =< s(80) 3.25/3.31 3.25/3.31 with precondition: [A=7,C=1,D=10,7>=G,B>=1] 3.25/3.31 3.25/3.31 * Chain [75]: 2*s(84)+1 3.25/3.31 Such that:s(82) =< -G+7 3.25/3.31 s(83) =< -G+8 3.25/3.31 s(84) =< s(82) 3.25/3.31 s(84) =< s(83) 3.25/3.31 3.25/3.31 with precondition: [A=7,C=1,D=10,6>=G] 3.25/3.31 3.25/3.31 * Chain [74]: 2*s(87)+1 3.25/3.31 Such that:s(85) =< -G+7 3.25/3.31 s(86) =< -G+8 3.25/3.31 s(87) =< s(85) 3.25/3.31 s(87) =< s(86) 3.25/3.31 3.25/3.31 with precondition: [A=7,C=1,D=10,6>=G,B>=1] 3.25/3.31 3.25/3.31 * Chain [73]: 0 3.25/3.31 with precondition: [A=7,C=1,D=10,B>=1,G>=9] 3.25/3.31 3.25/3.31 3.25/3.31 #### Cost of chains of f23_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N): 3.25/3.31 * Chain [100]: 0 3.25/3.31 with precondition: [A=3,B=1,C=1,D=10] 3.25/3.31 3.25/3.31 * Chain [99]: 150 3.25/3.31 with precondition: [A=3,B=1,C=1,D=10,G=9] 3.25/3.31 3.25/3.31 * Chain [98]: 1*s(107)+288*s(108)+2*s(111)+4*s(116)+4*s(123)+45 3.25/3.31 Such that:s(107) =< 10 3.25/3.31 aux(48) =< 7 3.25/3.31 aux(49) =< 8 3.25/3.31 aux(50) =< 9 3.25/3.31 aux(51) =< -G+10 3.25/3.31 s(111) =< aux(50) 3.25/3.31 s(108) =< aux(51) 3.25/3.31 s(123) =< aux(48) 3.25/3.31 s(123) =< aux(49) 3.25/3.31 s(116) =< aux(49) 3.25/3.31 3.25/3.31 with precondition: [A=3,B=1,C=1,D=10,9>=G] 3.25/3.31 3.25/3.31 * Chain [97]: 17*s(130)+620*s(131)+8*s(132)+4*s(135)+8*s(139)+8*s(144)+46 3.25/3.31 Such that:aux(52) =< 7 3.25/3.31 aux(53) =< 8 3.25/3.31 aux(54) =< 9 3.25/3.31 aux(55) =< 10 3.25/3.31 aux(56) =< -G+9 3.25/3.31 s(135) =< aux(54) 3.25/3.31 s(130) =< aux(55) 3.25/3.31 s(131) =< aux(56) 3.25/3.31 s(144) =< aux(52) 3.25/3.31 s(144) =< aux(53) 3.25/3.31 s(132) =< aux(56)*10 3.25/3.31 s(139) =< aux(53) 3.25/3.31 3.25/3.31 with precondition: [A=3,B=1,C=1,D=10,8>=G] 3.25/3.31 3.25/3.31 * Chain [96]: 10*s(202)+36*s(203)+325*s(205)+9*s(206)+296*s(207)+2*s(215)+4*s(224)+4*s(234)+46 3.25/3.31 Such that:aux(57) =< 7 3.25/3.31 aux(58) =< 8 3.25/3.31 aux(59) =< 9 3.25/3.31 aux(60) =< 10 3.25/3.31 aux(61) =< -G+8 3.25/3.31 aux(62) =< -G+9 3.25/3.31 s(215) =< aux(59) 3.25/3.31 s(202) =< aux(60) 3.25/3.31 s(234) =< aux(57) 3.25/3.31 s(234) =< aux(58) 3.25/3.31 s(204) =< aux(61) 3.25/3.31 s(205) =< aux(61) 3.25/3.31 s(204) =< aux(62) 3.25/3.31 s(205) =< aux(62) 3.25/3.31 s(207) =< s(204) 3.25/3.31 s(206) =< s(204)*10 3.25/3.31 s(224) =< aux(58) 3.25/3.31 s(203) =< aux(61) 3.25/3.31 3.25/3.31 with precondition: [A=3,B=1,C=1,D=10,7>=G] 3.25/3.31 3.25/3.31 * Chain [95]: 1*s(269)+36*s(274)+37*s(276)+1*s(277)+46 3.25/3.31 Such that:s(269) =< 10 3.25/3.31 s(270) =< -G+7 3.25/3.31 s(271) =< -G+8 3.25/3.31 s(272) =< -G+9 3.25/3.31 s(273) =< s(271) 3.25/3.31 s(270) =< s(271) 3.25/3.31 s(274) =< s(271) 3.25/3.31 s(273) =< s(272) 3.25/3.31 s(274) =< s(272) 3.25/3.31 s(275) =< s(273) 3.25/3.31 s(276) =< s(273) 3.25/3.31 s(275) =< s(270) 3.25/3.31 s(276) =< s(270) 3.25/3.31 s(277) =< s(275)*10 3.25/3.31 3.25/3.31 with precondition: [A=3,B=1,C=1,D=10,6>=G] 3.25/3.31 3.25/3.31 * Chain [94]: 79 3.25/3.31 with precondition: [A=3,B=1,C=1,D=10,G>=10] 3.25/3.31 3.25/3.31 * Chain [93]: 0 3.25/3.31 with precondition: [A=4,B=1,C=1,D=10] 3.25/3.31 3.25/3.31 3.25/3.31 #### Cost of chains of f0(A,B,C,D,E,F,G,H,I,J,K,L,O): 3.25/3.31 * Chain [101]: 16528 3.25/3.31 with precondition: [] 3.25/3.31 3.25/3.31 3.25/3.31 Closed-form bounds of f0(A,B,C,D,E,F,G,H,I,J,K,L,O): 3.25/3.31 ------------------------------------- 3.25/3.31 * Chain [101] with precondition: [] 3.25/3.31 - Upper bound: 16528 3.25/3.31 - Complexity: constant 3.25/3.31 3.25/3.31 ### Maximum cost of f0(A,B,C,D,E,F,G,H,I,J,K,L,O): 16528 3.25/3.31 Asymptotic class: constant 3.25/3.31 * Total analysis performed in 3108 ms. 3.25/3.31 3.31/3.41 EOF