0.04/0.51 WORST_CASE(?,O(1)) 0.04/0.51 0.04/0.51 Preprocessing Cost Relations 0.04/0.51 ===================================== 0.04/0.51 0.04/0.51 #### Computed strongly connected components 0.04/0.51 0. recursive : [f15/5] 0.04/0.51 1. non_recursive : [exit_location/1] 0.04/0.51 2. recursive : [f25/5] 0.04/0.51 3. recursive : [f33/5] 0.04/0.51 4. recursive : [f42/5] 0.04/0.51 5. recursive : [f52/5] 0.04/0.51 6. recursive : [f60/3] 0.04/0.51 7. non_recursive : [f69/8] 0.04/0.51 8. non_recursive : [f60_loop_cont/9] 0.04/0.51 9. non_recursive : [f52_loop_cont/9] 0.04/0.51 10. non_recursive : [f42_loop_cont/9] 0.04/0.51 11. non_recursive : [f33_loop_cont/9] 0.04/0.51 12. non_recursive : [f25_loop_cont/9] 0.04/0.51 13. non_recursive : [f15_loop_cont/9] 0.04/0.51 14. non_recursive : [f0/8] 0.04/0.51 0.04/0.51 #### Obtained direct recursion through partial evaluation 0.04/0.51 0. SCC is partially evaluated into f15/5 0.04/0.51 1. SCC is completely evaluated into other SCCs 0.04/0.51 2. SCC is partially evaluated into f25/5 0.04/0.51 3. SCC is partially evaluated into f33/5 0.04/0.51 4. SCC is partially evaluated into f42/5 0.04/0.51 5. SCC is partially evaluated into f52/5 0.04/0.51 6. SCC is partially evaluated into f60/3 0.04/0.51 7. SCC is completely evaluated into other SCCs 0.04/0.51 8. SCC is partially evaluated into f60_loop_cont/9 0.04/0.51 9. SCC is partially evaluated into f52_loop_cont/9 0.04/0.51 10. SCC is partially evaluated into f42_loop_cont/9 0.04/0.51 11. SCC is partially evaluated into f33_loop_cont/9 0.04/0.51 12. SCC is partially evaluated into f25_loop_cont/9 0.04/0.51 13. SCC is partially evaluated into f15_loop_cont/9 0.04/0.51 14. SCC is partially evaluated into f0/8 0.04/0.51 0.04/0.51 Control-Flow Refinement of Cost Relations 0.04/0.51 ===================================== 0.04/0.51 0.04/0.51 ### Specialization of cost equations f15/5 0.04/0.51 * CE 3 is refined into CE [32] 0.04/0.51 * CE 4 is refined into CE [33] 0.04/0.51 * CE 2 is refined into CE [34] 0.04/0.51 0.04/0.51 0.04/0.51 ### Cost equations --> "Loop" of f15/5 0.04/0.51 * CEs [34] --> Loop 32 0.04/0.51 * CEs [32] --> Loop 33 0.04/0.51 * CEs [33] --> Loop 34 0.04/0.51 0.04/0.51 ### Ranking functions of CR f15(D,E,J,K,L) 0.04/0.51 * RF of phase [32]: [-D+50] 0.04/0.51 0.04/0.51 #### Partial ranking functions of CR f15(D,E,J,K,L) 0.04/0.51 * Partial RF of phase [32]: 0.04/0.51 - RF of loop [32:1]: 0.04/0.51 -D+50 0.04/0.51 0.04/0.51 0.04/0.51 ### Specialization of cost equations f25/5 0.04/0.51 * CE 8 is refined into CE [35] 0.04/0.51 * CE 9 is refined into CE [36] 0.04/0.51 * CE 7 is refined into CE [37] 0.04/0.51 0.04/0.51 0.04/0.51 ### Cost equations --> "Loop" of f25/5 0.04/0.51 * CEs [37] --> Loop 35 0.04/0.51 * CEs [35] --> Loop 36 0.04/0.51 * CEs [36] --> Loop 37 0.04/0.51 0.04/0.51 ### Ranking functions of CR f25(A,E,J,K,L) 0.04/0.51 * RF of phase [35]: [-E+50] 0.04/0.51 0.04/0.51 #### Partial ranking functions of CR f25(A,E,J,K,L) 0.04/0.51 * Partial RF of phase [35]: 0.04/0.51 - RF of loop [35:1]: 0.04/0.51 -E+50 0.04/0.51 0.04/0.51 0.04/0.51 ### Specialization of cost equations f33/5 0.04/0.51 * CE 13 is refined into CE [38] 0.04/0.51 * CE 14 is refined into CE [39] 0.04/0.51 * CE 12 is refined into CE [40] 0.04/0.51 0.04/0.51 0.04/0.51 ### Cost equations --> "Loop" of f33/5 0.04/0.51 * CEs [40] --> Loop 38 0.04/0.51 * CEs [38] --> Loop 39 0.04/0.51 * CEs [39] --> Loop 40 0.04/0.51 0.04/0.51 ### Ranking functions of CR f33(A,F,J,K,L) 0.04/0.51 * RF of phase [38]: [-A+50] 0.04/0.51 0.04/0.51 #### Partial ranking functions of CR f33(A,F,J,K,L) 0.04/0.51 * Partial RF of phase [38]: 0.04/0.51 - RF of loop [38:1]: 0.04/0.51 -A+50 0.04/0.51 0.04/0.51 0.04/0.51 ### Specialization of cost equations f42/5 0.04/0.51 * CE 18 is refined into CE [41] 0.04/0.51 * CE 19 is refined into CE [42] 0.04/0.51 * CE 17 is refined into CE [43] 0.04/0.51 0.04/0.51 0.04/0.51 ### Cost equations --> "Loop" of f42/5 0.04/0.51 * CEs [43] --> Loop 41 0.04/0.51 * CEs [41] --> Loop 42 0.04/0.51 * CEs [42] --> Loop 43 0.04/0.51 0.04/0.51 ### Ranking functions of CR f42(F,G,J,K,L) 0.04/0.51 * RF of phase [41]: [-F+50] 0.04/0.51 0.04/0.51 #### Partial ranking functions of CR f42(F,G,J,K,L) 0.04/0.51 * Partial RF of phase [41]: 0.04/0.51 - RF of loop [41:1]: 0.04/0.51 -F+50 0.04/0.51 0.04/0.51 0.04/0.51 ### Specialization of cost equations f52/5 0.04/0.51 * CE 23 is refined into CE [44] 0.04/0.51 * CE 24 is refined into CE [45] 0.04/0.51 * CE 22 is refined into CE [46] 0.04/0.51 0.04/0.51 0.04/0.51 ### Cost equations --> "Loop" of f52/5 0.04/0.51 * CEs [46] --> Loop 44 0.04/0.51 * CEs [44] --> Loop 45 0.04/0.51 * CEs [45] --> Loop 46 0.04/0.51 0.04/0.51 ### Ranking functions of CR f52(A,G,J,K,L) 0.04/0.51 * RF of phase [44]: [-G+50] 0.04/0.51 0.04/0.51 #### Partial ranking functions of CR f52(A,G,J,K,L) 0.04/0.51 * Partial RF of phase [44]: 0.04/0.51 - RF of loop [44:1]: 0.04/0.51 -G+50 0.04/0.51 0.04/0.51 0.04/0.51 ### Specialization of cost equations f60/3 0.04/0.51 * CE 29 is refined into CE [47] 0.04/0.51 * CE 28 is refined into CE [48] 0.04/0.51 * CE 27 is refined into CE [49] 0.04/0.51 0.04/0.51 0.04/0.51 ### Cost equations --> "Loop" of f60/3 0.04/0.51 * CEs [49] --> Loop 47 0.04/0.51 * CEs [47] --> Loop 48 0.04/0.51 * CEs [48] --> Loop 49 0.04/0.51 0.04/0.51 ### Ranking functions of CR f60(A,J,K) 0.04/0.51 * RF of phase [47]: [-A+50] 0.04/0.51 0.04/0.51 #### Partial ranking functions of CR f60(A,J,K) 0.04/0.51 * Partial RF of phase [47]: 0.04/0.51 - RF of loop [47:1]: 0.04/0.51 -A+50 0.04/0.51 0.04/0.51 0.04/0.51 ### Specialization of cost equations f60_loop_cont/9 0.04/0.51 * CE 31 is refined into CE [50] 0.04/0.51 * CE 30 is refined into CE [51] 0.04/0.51 0.04/0.51 0.04/0.51 ### Cost equations --> "Loop" of f60_loop_cont/9 0.04/0.51 * CEs [50] --> Loop 50 0.04/0.51 * CEs [51] --> Loop 51 0.04/0.51 0.04/0.51 ### Ranking functions of CR f60_loop_cont(A,B,C,D,E,F,G,H,I) 0.04/0.51 0.04/0.51 #### Partial ranking functions of CR f60_loop_cont(A,B,C,D,E,F,G,H,I) 0.04/0.51 0.04/0.51 0.04/0.51 ### Specialization of cost equations f52_loop_cont/9 0.04/0.51 * CE 26 is refined into CE [52,53,54,55] 0.04/0.51 * CE 25 is refined into CE [56] 0.04/0.51 0.04/0.51 0.04/0.51 ### Cost equations --> "Loop" of f52_loop_cont/9 0.04/0.51 * CEs [53] --> Loop 52 0.04/0.51 * CEs [52,55] --> Loop 53 0.04/0.51 * CEs [54] --> Loop 54 0.04/0.51 * CEs [56] --> Loop 55 0.04/0.51 0.04/0.51 ### Ranking functions of CR f52_loop_cont(A,B,C,D,E,F,G,H,I) 0.04/0.51 0.04/0.51 #### Partial ranking functions of CR f52_loop_cont(A,B,C,D,E,F,G,H,I) 0.04/0.51 0.04/0.51 0.04/0.51 ### Specialization of cost equations f42_loop_cont/9 0.04/0.51 * CE 21 is refined into CE [57,58,59,60,61,62] 0.04/0.51 * CE 20 is refined into CE [63] 0.04/0.51 0.04/0.51 0.04/0.51 ### Cost equations --> "Loop" of f42_loop_cont/9 0.04/0.51 * CEs [61,62] --> Loop 56 0.04/0.51 * CEs [58,59,60] --> Loop 57 0.04/0.51 * CEs [57] --> Loop 58 0.04/0.51 * CEs [63] --> Loop 59 0.04/0.51 0.04/0.51 ### Ranking functions of CR f42_loop_cont(A,B,C,D,E,F,G,H,I) 0.04/0.51 0.04/0.51 #### Partial ranking functions of CR f42_loop_cont(A,B,C,D,E,F,G,H,I) 0.04/0.51 0.04/0.51 0.04/0.51 ### Specialization of cost equations f33_loop_cont/9 0.04/0.51 * CE 16 is refined into CE [64,65,66,67,68,69] 0.04/0.51 * CE 15 is refined into CE [70] 0.04/0.51 0.04/0.51 0.04/0.51 ### Cost equations --> "Loop" of f33_loop_cont/9 0.04/0.51 * CEs [68,69] --> Loop 60 0.04/0.51 * CEs [65,66,67] --> Loop 61 0.04/0.51 * CEs [64] --> Loop 62 0.04/0.51 * CEs [70] --> Loop 63 0.04/0.51 0.04/0.51 ### Ranking functions of CR f33_loop_cont(A,B,C,D,E,F,G,H,I) 0.04/0.51 0.04/0.51 #### Partial ranking functions of CR f33_loop_cont(A,B,C,D,E,F,G,H,I) 0.04/0.51 0.04/0.51 0.04/0.51 ### Specialization of cost equations f25_loop_cont/9 0.04/0.51 * CE 11 is refined into CE [71,72,73,74,75,76] 0.04/0.51 * CE 10 is refined into CE [77] 0.04/0.51 0.04/0.51 0.04/0.51 ### Cost equations --> "Loop" of f25_loop_cont/9 0.04/0.51 * CEs [75,76] --> Loop 64 0.04/0.51 * CEs [72,73,74] --> Loop 65 0.04/0.51 * CEs [71] --> Loop 66 0.04/0.51 * CEs [77] --> Loop 67 0.04/0.51 0.04/0.51 ### Ranking functions of CR f25_loop_cont(A,B,C,D,E,F,G,H,I) 0.04/0.51 0.04/0.51 #### Partial ranking functions of CR f25_loop_cont(A,B,C,D,E,F,G,H,I) 0.04/0.51 0.04/0.51 0.04/0.51 ### Specialization of cost equations f15_loop_cont/9 0.04/0.51 * CE 6 is refined into CE [78,79,80,81,82,83] 0.04/0.51 * CE 5 is refined into CE [84] 0.04/0.51 0.04/0.51 0.04/0.51 ### Cost equations --> "Loop" of f15_loop_cont/9 0.04/0.51 * CEs [82,83] --> Loop 68 0.04/0.51 * CEs [79,80,81] --> Loop 69 0.04/0.51 * CEs [78] --> Loop 70 0.04/0.51 * CEs [84] --> Loop 71 0.04/0.51 0.04/0.51 ### Ranking functions of CR f15_loop_cont(A,B,C,D,E,F,G,H,I) 0.04/0.51 0.04/0.51 #### Partial ranking functions of CR f15_loop_cont(A,B,C,D,E,F,G,H,I) 0.04/0.51 0.04/0.51 0.04/0.51 ### Specialization of cost equations f0/8 0.04/0.51 * CE 1 is refined into CE [85,86,87,88] 0.04/0.51 0.04/0.51 0.04/0.51 ### Cost equations --> "Loop" of f0/8 0.04/0.51 * CEs [85,86,87,88] --> Loop 72 0.04/0.51 0.04/0.51 ### Ranking functions of CR f0(A,B,C,D,E,F,G,J) 0.04/0.51 0.04/0.51 #### Partial ranking functions of CR f0(A,B,C,D,E,F,G,J) 0.04/0.51 0.04/0.51 0.04/0.51 Computing Bounds 0.04/0.51 ===================================== 0.04/0.51 0.04/0.51 #### Cost of chains of f15(D,E,J,K,L): 0.04/0.51 * Chain [[32],34]: 1*it(32)+0 0.04/0.51 Such that:it(32) =< -D+50 0.04/0.51 0.04/0.51 with precondition: [J=3,49>=D,D>=0] 0.04/0.51 0.04/0.51 * Chain [[32],33]: 1*it(32)+0 0.04/0.51 Such that:it(32) =< -D+50 0.04/0.51 0.04/0.51 with precondition: [J=8,K=50,L=0,49>=D,D>=0] 0.04/0.51 0.04/0.51 * Chain [34]: 0 0.04/0.51 with precondition: [J=3,D>=0] 0.04/0.51 0.04/0.51 0.04/0.51 #### Cost of chains of f25(A,E,J,K,L): 0.04/0.51 * Chain [[35],37]: 1*it(35)+0 0.04/0.51 Such that:it(35) =< -E+50 0.04/0.51 0.04/0.51 with precondition: [A=0,J=3,49>=E] 0.04/0.51 0.04/0.51 * Chain [[35],36]: 1*it(35)+0 0.04/0.51 Such that:it(35) =< -E+50 0.04/0.51 0.04/0.51 with precondition: [A=0,J=7,K=0,L=50,49>=E] 0.04/0.51 0.04/0.51 * Chain [37]: 0 0.04/0.51 with precondition: [A=0,J=3] 0.04/0.51 0.04/0.51 * Chain [36]: 0 0.04/0.51 with precondition: [A=0,J=7,K=0,E=L,E>=50] 0.04/0.51 0.04/0.51 0.04/0.51 #### Cost of chains of f33(A,F,J,K,L): 0.04/0.51 * Chain [[38],40]: 1*it(38)+0 0.04/0.51 Such that:it(38) =< -A+50 0.04/0.51 0.04/0.51 with precondition: [J=3,49>=A] 0.04/0.51 0.04/0.51 * Chain [[38],39]: 1*it(38)+0 0.04/0.51 Such that:it(38) =< -A+50 0.04/0.51 0.04/0.51 with precondition: [J=6,K=50,L=0,49>=A] 0.04/0.51 0.04/0.51 * Chain [40]: 0 0.04/0.51 with precondition: [J=3] 0.04/0.51 0.04/0.51 * Chain [39]: 0 0.04/0.51 with precondition: [J=6,L=0,A=K,A>=50] 0.04/0.51 0.04/0.51 0.04/0.51 #### Cost of chains of f42(F,G,J,K,L): 0.04/0.52 * Chain [[41],43]: 1*it(41)+0 0.04/0.52 Such that:it(41) =< -F+50 0.04/0.52 0.04/0.52 with precondition: [J=3,49>=F] 0.04/0.52 0.04/0.52 * Chain [[41],42]: 1*it(41)+0 0.04/0.52 Such that:it(41) =< -F+50 0.04/0.52 0.04/0.52 with precondition: [J=5,K=50,L=0,49>=F] 0.04/0.52 0.04/0.52 * Chain [43]: 0 0.04/0.52 with precondition: [J=3] 0.04/0.52 0.04/0.52 * Chain [42]: 0 0.04/0.52 with precondition: [J=5,L=0,F=K,F>=50] 0.04/0.52 0.04/0.52 0.04/0.52 #### Cost of chains of f52(A,G,J,K,L): 0.04/0.52 * Chain [[44],46]: 1*it(44)+0 0.04/0.52 Such that:it(44) =< -G+50 0.04/0.52 0.04/0.52 with precondition: [J=3,49>=G] 0.04/0.52 0.04/0.52 * Chain [[44],45]: 1*it(44)+0 0.04/0.52 Such that:it(44) =< -G+50 0.04/0.52 0.04/0.52 with precondition: [J=4,K=0,L=50,49>=G] 0.04/0.52 0.04/0.52 * Chain [46]: 0 0.04/0.52 with precondition: [J=3] 0.04/0.52 0.04/0.52 * Chain [45]: 0 0.04/0.52 with precondition: [J=4,K=0,G=L,G>=50] 0.04/0.52 0.04/0.52 0.04/0.52 #### Cost of chains of f60(A,J,K): 0.04/0.52 * Chain [[47],49]: 1*it(47)+0 0.04/0.52 Such that:it(47) =< -A+50 0.04/0.52 0.04/0.52 with precondition: [J=2,K=50,49>=A] 0.04/0.52 0.04/0.52 * Chain [[47],48]: 1*it(47)+0 0.04/0.52 Such that:it(47) =< -A+50 0.04/0.52 0.04/0.52 with precondition: [J=3,49>=A] 0.04/0.52 0.04/0.52 * Chain [49]: 0 0.04/0.52 with precondition: [J=2,A=K,A>=50] 0.04/0.52 0.04/0.52 * Chain [48]: 0 0.04/0.52 with precondition: [J=3] 0.04/0.52 0.04/0.52 0.04/0.52 #### Cost of chains of f60_loop_cont(A,B,C,D,E,F,G,H,I): 0.04/0.52 * Chain [51]: 0 0.04/0.52 with precondition: [A=2] 0.04/0.52 0.04/0.52 * Chain [50]: 0 0.04/0.52 with precondition: [A=3] 0.04/0.52 0.04/0.52 0.04/0.52 #### Cost of chains of f52_loop_cont(A,B,C,D,E,F,G,H,I): 0.04/0.52 * Chain [55]: 0 0.04/0.52 with precondition: [A=3] 0.04/0.52 0.04/0.52 * Chain [54]: 0 0.04/0.52 with precondition: [A=4] 0.04/0.52 0.04/0.52 * Chain [53]: 2*s(1)+0 0.04/0.52 Such that:aux(1) =< -B+50 0.04/0.52 s(1) =< aux(1) 0.04/0.52 0.04/0.52 with precondition: [A=4,49>=B] 0.04/0.52 0.04/0.52 * Chain [52]: 0 0.04/0.52 with precondition: [A=4,B>=50] 0.04/0.52 0.04/0.52 0.04/0.52 #### Cost of chains of f42_loop_cont(A,B,C,D,E,F,G,H,I): 0.04/0.52 * Chain [59]: 0 0.04/0.52 with precondition: [A=3] 0.04/0.52 0.04/0.52 * Chain [58]: 0 0.04/0.52 with precondition: [A=5] 0.04/0.52 0.04/0.52 * Chain [57]: 3*s(3)+2*s(7)+0 0.04/0.52 Such that:s(6) =< 50 0.04/0.52 aux(2) =< -H+50 0.04/0.52 s(3) =< aux(2) 0.04/0.52 s(7) =< s(6) 0.04/0.52 0.04/0.52 with precondition: [A=5,49>=H] 0.04/0.52 0.04/0.52 * Chain [56]: 100 0.04/0.52 with precondition: [A=5,H>=50] 0.04/0.52 0.04/0.52 0.04/0.52 #### Cost of chains of f33_loop_cont(A,B,C,D,E,F,G,H,I): 0.04/0.52 * Chain [63]: 0 0.04/0.52 with precondition: [A=3] 0.04/0.52 0.04/0.52 * Chain [62]: 0 0.04/0.52 with precondition: [A=6] 0.04/0.52 0.04/0.52 * Chain [61]: 3*s(10)+5*s(15)+0 0.04/0.52 Such that:aux(3) =< 50 0.04/0.52 aux(4) =< -G+50 0.04/0.52 s(10) =< aux(4) 0.04/0.52 s(15) =< aux(3) 0.04/0.52 0.04/0.52 with precondition: [A=6,49>=G] 0.04/0.52 0.04/0.52 * Chain [60]: 250 0.04/0.52 with precondition: [A=6,G>=50] 0.04/0.52 0.04/0.52 0.04/0.52 #### Cost of chains of f25_loop_cont(A,B,C,D,E,F,G,H,I): 0.04/0.52 * Chain [67]: 0 0.04/0.52 with precondition: [A=3] 0.04/0.52 0.04/0.52 * Chain [66]: 0 0.04/0.52 with precondition: [A=7] 0.04/0.52 0.04/0.52 * Chain [65]: 3*s(21)+8*s(26)+0 0.04/0.52 Such that:aux(6) =< 50 0.04/0.52 aux(7) =< -B+50 0.04/0.52 s(21) =< aux(7) 0.04/0.52 s(26) =< aux(6) 0.04/0.52 0.04/0.52 with precondition: [A=7,49>=B] 0.04/0.52 0.04/0.52 * Chain [64]: 400 0.04/0.52 with precondition: [A=7,B>=50] 0.04/0.52 0.04/0.52 0.04/0.52 #### Cost of chains of f15_loop_cont(A,B,C,D,E,F,G,H,I): 0.04/0.52 * Chain [71]: 0 0.04/0.52 with precondition: [A=3,B=0] 0.04/0.52 0.04/0.52 * Chain [70]: 0 0.04/0.52 with precondition: [A=8,B=0] 0.04/0.52 0.04/0.52 * Chain [69]: 3*s(32)+11*s(37)+0 0.04/0.52 Such that:aux(9) =< 50 0.04/0.52 aux(10) =< -F+50 0.04/0.52 s(32) =< aux(10) 0.04/0.52 s(37) =< aux(9) 0.04/0.52 0.04/0.52 with precondition: [A=8,B=0,49>=F] 0.04/0.52 0.04/0.52 * Chain [68]: 550 0.04/0.52 with precondition: [A=8,B=0,F>=50] 0.04/0.52 0.04/0.52 0.04/0.52 #### Cost of chains of f0(A,B,C,D,E,F,G,J): 0.04/0.52 * Chain [72]: 850 0.04/0.52 with precondition: [] 0.04/0.52 0.04/0.52 0.04/0.52 Closed-form bounds of f0(A,B,C,D,E,F,G,J): 0.04/0.52 ------------------------------------- 0.04/0.52 * Chain [72] with precondition: [] 0.04/0.52 - Upper bound: 850 0.04/0.52 - Complexity: constant 0.04/0.52 0.04/0.52 ### Maximum cost of f0(A,B,C,D,E,F,G,J): 850 0.04/0.52 Asymptotic class: constant 0.04/0.52 * Total analysis performed in 425 ms. 0.04/0.52 0.52/0.62 EOF