0.03/0.47 WORST_CASE(?,O(1)) 0.03/0.47 0.03/0.47 Preprocessing Cost Relations 0.03/0.47 ===================================== 0.03/0.47 0.03/0.47 #### Computed strongly connected components 0.03/0.47 0. recursive : [f13/5] 0.03/0.47 1. recursive : [f10/5,f13_loop_cont/6] 0.03/0.47 2. non_recursive : [exit_location/1] 0.03/0.47 3. recursive : [f27/5] 0.03/0.47 4. recursive : [f24/7,f27_loop_cont/8] 0.03/0.47 5. recursive : [f21/7,f24_loop_cont/8] 0.03/0.47 6. non_recursive : [f39/4] 0.03/0.47 7. non_recursive : [f21_loop_cont/5] 0.03/0.47 8. non_recursive : [f10_loop_cont/5] 0.03/0.47 9. non_recursive : [f0/4] 0.03/0.47 0.03/0.47 #### Obtained direct recursion through partial evaluation 0.03/0.47 0. SCC is partially evaluated into f13/5 0.03/0.47 1. SCC is partially evaluated into f10/5 0.03/0.47 2. SCC is completely evaluated into other SCCs 0.03/0.47 3. SCC is partially evaluated into f27/5 0.03/0.47 4. SCC is partially evaluated into f24/7 0.03/0.47 5. SCC is partially evaluated into f21/7 0.03/0.47 6. SCC is completely evaluated into other SCCs 0.03/0.47 7. SCC is partially evaluated into f21_loop_cont/5 0.03/0.47 8. SCC is partially evaluated into f10_loop_cont/5 0.03/0.47 9. SCC is partially evaluated into f0/4 0.03/0.47 0.03/0.47 Control-Flow Refinement of Cost Relations 0.03/0.47 ===================================== 0.03/0.47 0.03/0.47 ### Specialization of cost equations f13/5 0.03/0.47 * CE 9 is refined into CE [24] 0.03/0.47 * CE 10 is refined into CE [25] 0.03/0.47 * CE 8 is refined into CE [26] 0.03/0.47 0.03/0.47 0.03/0.47 ### Cost equations --> "Loop" of f13/5 0.03/0.47 * CEs [26] --> Loop 24 0.03/0.47 * CEs [24] --> Loop 25 0.03/0.47 * CEs [25] --> Loop 26 0.03/0.47 0.03/0.47 ### Ranking functions of CR f13(A,B,D,E,F) 0.03/0.47 * RF of phase [24]: [-B+6] 0.03/0.47 0.03/0.47 #### Partial ranking functions of CR f13(A,B,D,E,F) 0.03/0.47 * Partial RF of phase [24]: 0.03/0.47 - RF of loop [24:1]: 0.03/0.47 -B+6 0.03/0.47 0.03/0.47 0.03/0.47 ### Specialization of cost equations f10/5 0.03/0.47 * CE 4 is refined into CE [27] 0.03/0.47 * CE 2 is refined into CE [28,29] 0.03/0.47 * CE 5 is refined into CE [30] 0.03/0.47 * CE 3 is refined into CE [31] 0.03/0.47 0.03/0.47 0.03/0.47 ### Cost equations --> "Loop" of f10/5 0.03/0.47 * CEs [31] --> Loop 27 0.03/0.47 * CEs [27] --> Loop 28 0.03/0.47 * CEs [28,29] --> Loop 29 0.03/0.47 * CEs [30] --> Loop 30 0.03/0.47 0.03/0.47 ### Ranking functions of CR f10(A,B,D,E,F) 0.03/0.47 * RF of phase [27]: [-A+6] 0.03/0.47 0.03/0.47 #### Partial ranking functions of CR f10(A,B,D,E,F) 0.03/0.47 * Partial RF of phase [27]: 0.03/0.47 - RF of loop [27:1]: 0.03/0.47 -A+6 0.03/0.47 0.03/0.47 0.03/0.47 ### Specialization of cost equations f27/5 0.03/0.47 * CE 23 is refined into CE [32] 0.03/0.47 * CE 22 is refined into CE [33] 0.03/0.47 * CE 21 is refined into CE [34] 0.03/0.47 0.03/0.47 0.03/0.47 ### Cost equations --> "Loop" of f27/5 0.03/0.47 * CEs [34] --> Loop 31 0.03/0.47 * CEs [32] --> Loop 32 0.03/0.47 * CEs [33] --> Loop 33 0.03/0.47 0.03/0.47 ### Ranking functions of CR f27(B,C,D,E,F) 0.03/0.47 * RF of phase [31]: [-C+6] 0.03/0.47 0.03/0.47 #### Partial ranking functions of CR f27(B,C,D,E,F) 0.03/0.47 * Partial RF of phase [31]: 0.03/0.47 - RF of loop [31:1]: 0.03/0.47 -C+6 0.03/0.47 0.03/0.47 0.03/0.47 ### Specialization of cost equations f24/7 0.03/0.47 * CE 19 is refined into CE [35] 0.03/0.47 * CE 17 is refined into CE [36,37] 0.03/0.47 * CE 20 is refined into CE [38] 0.03/0.47 * CE 18 is refined into CE [39] 0.03/0.47 0.03/0.47 0.03/0.47 ### Cost equations --> "Loop" of f24/7 0.03/0.47 * CEs [39] --> Loop 34 0.03/0.47 * CEs [35] --> Loop 35 0.03/0.47 * CEs [36,37] --> Loop 36 0.03/0.47 * CEs [38] --> Loop 37 0.03/0.47 0.03/0.47 ### Ranking functions of CR f24(A,B,C,D,E,F,G) 0.03/0.47 * RF of phase [34]: [-B+6] 0.03/0.47 0.03/0.47 #### Partial ranking functions of CR f24(A,B,C,D,E,F,G) 0.03/0.47 * Partial RF of phase [34]: 0.03/0.47 - RF of loop [34:1]: 0.03/0.47 -B+6 0.03/0.47 0.03/0.47 0.03/0.47 ### Specialization of cost equations f21/7 0.03/0.47 * CE 13 is refined into CE [40] 0.03/0.47 * CE 11 is refined into CE [41,42,43] 0.03/0.47 * CE 14 is refined into CE [44] 0.03/0.47 * CE 12 is refined into CE [45] 0.03/0.47 0.03/0.47 0.03/0.47 ### Cost equations --> "Loop" of f21/7 0.03/0.47 * CEs [45] --> Loop 38 0.03/0.47 * CEs [40] --> Loop 39 0.03/0.47 * CEs [41,42,43] --> Loop 40 0.03/0.47 * CEs [44] --> Loop 41 0.03/0.47 0.03/0.47 ### Ranking functions of CR f21(A,B,C,D,E,F,G) 0.03/0.47 * RF of phase [38]: [-A+6] 0.03/0.47 0.03/0.47 #### Partial ranking functions of CR f21(A,B,C,D,E,F,G) 0.03/0.47 * Partial RF of phase [38]: 0.03/0.47 - RF of loop [38:1]: 0.03/0.47 -A+6 0.03/0.47 0.03/0.47 0.03/0.47 ### Specialization of cost equations f21_loop_cont/5 0.03/0.47 * CE 15 is refined into CE [46] 0.03/0.47 * CE 16 is refined into CE [47] 0.03/0.47 0.03/0.47 0.03/0.47 ### Cost equations --> "Loop" of f21_loop_cont/5 0.03/0.47 * CEs [46] --> Loop 42 0.03/0.47 * CEs [47] --> Loop 43 0.03/0.47 0.03/0.47 ### Ranking functions of CR f21_loop_cont(A,B,C,D,E) 0.03/0.47 0.03/0.47 #### Partial ranking functions of CR f21_loop_cont(A,B,C,D,E) 0.03/0.47 0.03/0.47 0.03/0.47 ### Specialization of cost equations f10_loop_cont/5 0.03/0.47 * CE 7 is refined into CE [48,49,50,51,52] 0.03/0.47 * CE 6 is refined into CE [53] 0.03/0.47 0.03/0.47 0.03/0.47 ### Cost equations --> "Loop" of f10_loop_cont/5 0.03/0.47 * CEs [52] --> Loop 44 0.03/0.47 * CEs [50] --> Loop 45 0.03/0.47 * CEs [49,51] --> Loop 46 0.03/0.47 * CEs [48] --> Loop 47 0.03/0.47 * CEs [53] --> Loop 48 0.03/0.47 0.03/0.47 ### Ranking functions of CR f10_loop_cont(A,B,C,D,E) 0.03/0.47 0.03/0.47 #### Partial ranking functions of CR f10_loop_cont(A,B,C,D,E) 0.03/0.47 0.03/0.47 0.03/0.47 ### Specialization of cost equations f0/4 0.03/0.47 * CE 1 is refined into CE [54,55,56,57,58,59] 0.03/0.47 0.03/0.47 0.03/0.47 ### Cost equations --> "Loop" of f0/4 0.03/0.47 * CEs [54,55,56,57,58,59] --> Loop 49 0.03/0.47 0.03/0.47 ### Ranking functions of CR f0(A,B,C,D) 0.03/0.47 0.03/0.47 #### Partial ranking functions of CR f0(A,B,C,D) 0.03/0.47 0.03/0.47 0.03/0.47 Computing Bounds 0.03/0.47 ===================================== 0.03/0.47 0.03/0.47 #### Cost of chains of f13(A,B,D,E,F): 0.03/0.47 * Chain [[24],26]: 1*it(24)+0 0.03/0.47 Such that:it(24) =< -B+6 0.03/0.47 0.03/0.47 with precondition: [D=3,5>=A,5>=B,B>=1] 0.03/0.47 0.03/0.47 * Chain [[24],25]: 1*it(24)+0 0.03/0.47 Such that:it(24) =< -B+6 0.03/0.47 0.03/0.47 with precondition: [D=5,F=6,A+1=E,5>=A,5>=B,B>=1] 0.03/0.47 0.03/0.47 * Chain [26]: 0 0.03/0.47 with precondition: [D=3,5>=A,B>=1] 0.03/0.47 0.03/0.47 0.03/0.47 #### Cost of chains of f10(A,B,D,E,F): 0.03/0.47 * Chain [[27],30]: 1*it(27)+1*s(3)+0 0.03/0.47 Such that:aux(4) =< -A+6 0.03/0.47 it(27) =< aux(4) 0.03/0.47 s(3) =< aux(4)*5 0.03/0.47 0.03/0.47 with precondition: [D=3,5>=A,A>=1] 0.03/0.47 0.03/0.47 * Chain [[27],29]: 1*it(27)+1*s(3)+5 0.03/0.47 Such that:aux(3) =< -A+5 0.03/0.47 aux(2) =< -A+6 0.03/0.47 aux(1) =< aux(2) 0.03/0.47 it(27) =< aux(2) 0.03/0.47 aux(1) =< aux(3) 0.03/0.47 it(27) =< aux(3) 0.03/0.47 s(3) =< aux(1)*5 0.03/0.47 0.03/0.47 with precondition: [D=3,4>=A,A>=1] 0.03/0.47 0.03/0.47 * Chain [[27],28]: 1*it(27)+1*s(3)+0 0.03/0.47 Such that:aux(5) =< -A+6 0.03/0.47 it(27) =< aux(5) 0.03/0.47 s(3) =< aux(5)*5 0.03/0.47 0.03/0.47 with precondition: [D=4,E=1,F=6,5>=A] 0.03/0.47 0.03/0.47 * Chain [30]: 0 0.03/0.47 with precondition: [D=3,A>=1] 0.03/0.47 0.03/0.47 * Chain [29]: 5 0.03/0.47 with precondition: [D=3,5>=A,A>=1] 0.03/0.47 0.03/0.47 0.03/0.47 #### Cost of chains of f27(B,C,D,E,F): 0.03/0.47 * Chain [[31],33]: 1*it(31)+0 0.03/0.47 Such that:it(31) =< -C+6 0.03/0.47 0.03/0.47 with precondition: [D=2,F=6,B+1=E,5>=B,5>=C,C>=1] 0.03/0.47 0.03/0.47 * Chain [[31],32]: 1*it(31)+0 0.03/0.47 Such that:it(31) =< -C+6 0.03/0.47 0.03/0.47 with precondition: [D=3,5>=B,5>=C,C>=1] 0.03/0.47 0.03/0.47 * Chain [32]: 0 0.03/0.47 with precondition: [D=3,5>=B,C>=1] 0.03/0.47 0.03/0.47 0.03/0.47 #### Cost of chains of f24(A,B,C,D,E,F,G): 0.03/0.47 * Chain [[34],37]: 1*it(34)+1*s(10)+0 0.03/0.47 Such that:aux(9) =< -B+6 0.03/0.47 it(34) =< aux(9) 0.03/0.47 s(10) =< aux(9)*5 0.03/0.47 0.03/0.47 with precondition: [D=3,5>=A,5>=B,B>=1] 0.03/0.47 0.03/0.47 * Chain [[34],36]: 1*it(34)+1*s(10)+5 0.03/0.47 Such that:aux(8) =< -B+5 0.03/0.47 aux(7) =< -B+6 0.03/0.47 aux(6) =< aux(7) 0.03/0.47 it(34) =< aux(7) 0.03/0.47 aux(6) =< aux(8) 0.03/0.47 it(34) =< aux(8) 0.03/0.47 s(10) =< aux(6)*5 0.03/0.47 0.03/0.47 with precondition: [D=3,5>=A,4>=B,B>=1] 0.03/0.47 0.03/0.47 * Chain [[34],35]: 1*it(34)+1*s(10)+0 0.03/0.47 Such that:aux(10) =< -B+6 0.03/0.47 it(34) =< aux(10) 0.03/0.47 s(10) =< aux(10)*5 0.03/0.47 0.03/0.47 with precondition: [D=4,F=6,G=6,A+1=E,5>=A,5>=B] 0.03/0.47 0.03/0.47 * Chain [37]: 0 0.03/0.47 with precondition: [D=3,5>=A,B>=1] 0.03/0.47 0.03/0.47 * Chain [36]: 5 0.03/0.47 with precondition: [D=3,5>=A,5>=B,B>=1] 0.03/0.47 0.03/0.47 0.03/0.47 #### Cost of chains of f21(A,B,C,D,E,F,G): 0.03/0.47 * Chain [[38],41]: 1*it(38)+1*s(21)+1*s(22)+0 0.03/0.47 Such that:aux(14) =< -A+6 0.03/0.47 it(38) =< aux(14) 0.03/0.47 s(23) =< aux(14)*5 0.03/0.47 s(21) =< s(23) 0.03/0.47 s(22) =< s(23)*5 0.03/0.47 0.03/0.47 with precondition: [D=3,5>=A] 0.03/0.47 0.03/0.47 * Chain [[38],40]: 1*it(38)+1*s(21)+1*s(22)+65 0.03/0.47 Such that:aux(13) =< -A+5 0.03/0.47 aux(12) =< -A+6 0.03/0.47 aux(11) =< aux(12) 0.03/0.47 it(38) =< aux(12) 0.03/0.47 aux(11) =< aux(13) 0.03/0.47 it(38) =< aux(13) 0.03/0.47 s(23) =< aux(11)*5 0.03/0.47 s(21) =< s(23) 0.03/0.47 s(22) =< s(23)*5 0.03/0.47 0.03/0.47 with precondition: [D=3,4>=A] 0.03/0.47 0.03/0.47 * Chain [[38],39]: 1*it(38)+1*s(21)+1*s(22)+0 0.03/0.47 Such that:aux(16) =< -A+6 0.03/0.47 it(38) =< aux(16) 0.03/0.47 s(23) =< aux(16)*5 0.03/0.47 s(21) =< s(23) 0.03/0.47 s(22) =< s(23)*5 0.03/0.47 0.03/0.47 with precondition: [D=6,E=6,F=6,G=6,5>=A] 0.03/0.47 0.03/0.47 * Chain [41]: 0 0.03/0.47 with precondition: [D=3] 0.03/0.47 0.03/0.47 * Chain [40]: 65 0.03/0.47 with precondition: [D=3,5>=A] 0.03/0.47 0.03/0.47 * Chain [39]: 0 0.03/0.47 with precondition: [D=6,F=B,G=C,A=E,A>=6] 0.03/0.47 0.03/0.47 0.03/0.47 #### Cost of chains of f21_loop_cont(A,B,C,D,E): 0.03/0.47 * Chain [43]: 0 0.03/0.47 with precondition: [A=3] 0.03/0.47 0.03/0.47 * Chain [42]: 0 0.03/0.47 with precondition: [A=6] 0.03/0.47 0.03/0.47 0.03/0.47 #### Cost of chains of f10_loop_cont(A,B,C,D,E): 0.03/0.47 * Chain [48]: 0 0.03/0.47 with precondition: [A=3] 0.03/0.47 0.03/0.47 * Chain [47]: 0 0.03/0.47 with precondition: [A=4] 0.03/0.47 0.03/0.47 * Chain [46]: 2*s(38)+2*s(40)+2*s(41)+65 0.03/0.47 Such that:aux(17) =< -B+6 0.03/0.47 s(38) =< aux(17) 0.03/0.47 s(39) =< aux(17)*5 0.03/0.47 s(40) =< s(39) 0.03/0.47 s(41) =< s(39)*5 0.03/0.47 0.03/0.47 with precondition: [A=4,5>=B] 0.03/0.47 0.03/0.47 * Chain [45]: 1*s(50)+1*s(52)+1*s(53)+65 0.03/0.47 Such that:s(47) =< -B+5 0.03/0.47 s(48) =< -B+6 0.03/0.47 s(49) =< s(48) 0.03/0.47 s(50) =< s(48) 0.03/0.47 s(49) =< s(47) 0.03/0.47 s(50) =< s(47) 0.03/0.47 s(51) =< s(49)*5 0.03/0.47 s(52) =< s(51) 0.03/0.47 s(53) =< s(51)*5 0.03/0.47 0.03/0.47 with precondition: [A=4,4>=B] 0.03/0.47 0.03/0.47 * Chain [44]: 0 0.03/0.47 with precondition: [A=4,B>=6] 0.03/0.47 0.03/0.47 0.03/0.47 #### Cost of chains of f0(A,B,C,D): 0.03/0.47 * Chain [49]: 680 0.03/0.47 with precondition: [] 0.03/0.47 0.03/0.47 0.03/0.47 Closed-form bounds of f0(A,B,C,D): 0.03/0.47 ------------------------------------- 0.03/0.47 * Chain [49] with precondition: [] 0.03/0.47 - Upper bound: 680 0.03/0.47 - Complexity: constant 0.03/0.47 0.03/0.47 ### Maximum cost of f0(A,B,C,D): 680 0.03/0.47 Asymptotic class: constant 0.03/0.47 * Total analysis performed in 390 ms. 0.03/0.47 0.46/0.57 EOF