0.03/0.40 WORST_CASE(?,O(n^1)) 0.03/0.40 0.03/0.40 Preprocessing Cost Relations 0.03/0.40 ===================================== 0.03/0.40 0.03/0.40 #### Computed strongly connected components 0.03/0.40 0. recursive : [f1/6] 0.03/0.40 1. non_recursive : [exit_location/1] 0.03/0.40 2. recursive : [f2/5] 0.03/0.40 3. recursive : [f3/6] 0.03/0.40 4. recursive : [f4/2] 0.03/0.40 5. non_recursive : [f4_loop_cont/2] 0.03/0.40 6. non_recursive : [f3_loop_cont/7] 0.03/0.40 7. non_recursive : [f2_loop_cont/7] 0.03/0.40 8. non_recursive : [f1_loop_cont/7] 0.03/0.40 9. non_recursive : [f0/6] 0.03/0.40 0.03/0.40 #### Obtained direct recursion through partial evaluation 0.03/0.40 0. SCC is partially evaluated into f1/6 0.03/0.40 1. SCC is completely evaluated into other SCCs 0.03/0.40 2. SCC is partially evaluated into f2/5 0.03/0.40 3. SCC is partially evaluated into f3/6 0.03/0.40 4. SCC is partially evaluated into f4/2 0.03/0.40 5. SCC is completely evaluated into other SCCs 0.03/0.40 6. SCC is partially evaluated into f3_loop_cont/7 0.03/0.40 7. SCC is partially evaluated into f2_loop_cont/7 0.03/0.40 8. SCC is partially evaluated into f1_loop_cont/7 0.03/0.40 9. SCC is partially evaluated into f0/6 0.03/0.40 0.03/0.40 Control-Flow Refinement of Cost Relations 0.03/0.40 ===================================== 0.03/0.40 0.03/0.40 ### Specialization of cost equations f1/6 0.03/0.40 * CE 3 is refined into CE [19] 0.03/0.40 * CE 4 is refined into CE [20] 0.03/0.40 * CE 2 is refined into CE [21] 0.03/0.40 0.03/0.40 0.03/0.40 ### Cost equations --> "Loop" of f1/6 0.03/0.40 * CEs [21] --> Loop 19 0.03/0.40 * CEs [19] --> Loop 20 0.03/0.40 * CEs [20] --> Loop 21 0.03/0.40 0.03/0.40 ### Ranking functions of CR f1(A,B,C,F,G,H) 0.03/0.40 * RF of phase [19]: [A-B] 0.03/0.40 0.03/0.40 #### Partial ranking functions of CR f1(A,B,C,F,G,H) 0.03/0.40 * Partial RF of phase [19]: 0.03/0.40 - RF of loop [19:1]: 0.03/0.40 A-B 0.03/0.40 0.03/0.40 0.03/0.40 ### Specialization of cost equations f2/5 0.03/0.40 * CE 8 is refined into CE [22] 0.03/0.40 * CE 9 is refined into CE [23] 0.03/0.40 * CE 7 is refined into CE [24] 0.03/0.40 0.03/0.40 0.03/0.40 ### Cost equations --> "Loop" of f2/5 0.03/0.40 * CEs [24] --> Loop 22 0.03/0.40 * CEs [22] --> Loop 23 0.03/0.40 * CEs [23] --> Loop 24 0.03/0.40 0.03/0.40 ### Ranking functions of CR f2(C,D,F,G,H) 0.03/0.40 * RF of phase [22]: [C] 0.03/0.40 0.03/0.40 #### Partial ranking functions of CR f2(C,D,F,G,H) 0.03/0.40 * Partial RF of phase [22]: 0.03/0.40 - RF of loop [22:1]: 0.03/0.40 C 0.03/0.40 0.03/0.40 0.03/0.40 ### Specialization of cost equations f3/6 0.03/0.40 * CE 13 is refined into CE [25] 0.03/0.40 * CE 14 is refined into CE [26] 0.03/0.40 * CE 12 is refined into CE [27] 0.03/0.40 0.03/0.40 0.03/0.40 ### Cost equations --> "Loop" of f3/6 0.03/0.40 * CEs [27] --> Loop 25 0.03/0.40 * CEs [25] --> Loop 26 0.03/0.40 * CEs [26] --> Loop 27 0.03/0.40 0.03/0.40 ### Ranking functions of CR f3(A,D,E,F,G,H) 0.03/0.40 * RF of phase [25]: [A-D] 0.03/0.40 0.03/0.40 #### Partial ranking functions of CR f3(A,D,E,F,G,H) 0.03/0.40 * Partial RF of phase [25]: 0.03/0.40 - RF of loop [25:1]: 0.03/0.40 A-D 0.03/0.40 0.03/0.40 0.03/0.40 ### Specialization of cost equations f4/2 0.03/0.40 * CE 18 is refined into CE [28] 0.03/0.40 * CE 17 is refined into CE [29] 0.03/0.40 0.03/0.40 0.03/0.40 ### Cost equations --> "Loop" of f4/2 0.03/0.40 * CEs [29] --> Loop 28 0.03/0.40 * CEs [28] --> Loop 29 0.03/0.40 0.03/0.40 ### Ranking functions of CR f4(E,F) 0.03/0.40 * RF of phase [28]: [E] 0.03/0.40 0.03/0.40 #### Partial ranking functions of CR f4(E,F) 0.03/0.40 * Partial RF of phase [28]: 0.03/0.40 - RF of loop [28:1]: 0.03/0.40 E 0.03/0.40 0.03/0.40 0.03/0.40 ### Specialization of cost equations f3_loop_cont/7 0.03/0.40 * CE 16 is refined into CE [30,31] 0.03/0.40 * CE 15 is refined into CE [32] 0.03/0.40 0.03/0.40 0.03/0.40 ### Cost equations --> "Loop" of f3_loop_cont/7 0.03/0.40 * CEs [31] --> Loop 30 0.03/0.40 * CEs [30] --> Loop 31 0.03/0.40 * CEs [32] --> Loop 32 0.03/0.40 0.03/0.40 ### Ranking functions of CR f3_loop_cont(A,B,C,D,E,F,G) 0.03/0.40 0.03/0.40 #### Partial ranking functions of CR f3_loop_cont(A,B,C,D,E,F,G) 0.03/0.40 0.03/0.40 0.03/0.40 ### Specialization of cost equations f2_loop_cont/7 0.03/0.40 * CE 11 is refined into CE [33,34,35,36,37,38] 0.03/0.40 * CE 10 is refined into CE [39] 0.03/0.40 0.03/0.40 0.03/0.40 ### Cost equations --> "Loop" of f2_loop_cont/7 0.03/0.40 * CEs [34,35] --> Loop 33 0.03/0.40 * CEs [37] --> Loop 34 0.03/0.40 * CEs [38] --> Loop 35 0.03/0.40 * CEs [36] --> Loop 36 0.03/0.40 * CEs [33] --> Loop 37 0.03/0.40 * CEs [39] --> Loop 38 0.03/0.40 0.03/0.40 ### Ranking functions of CR f2_loop_cont(A,B,C,D,E,F,G) 0.03/0.40 0.03/0.40 #### Partial ranking functions of CR f2_loop_cont(A,B,C,D,E,F,G) 0.03/0.40 0.03/0.40 0.03/0.40 ### Specialization of cost equations f1_loop_cont/7 0.03/0.40 * CE 6 is refined into CE [40,41,42,43,44,45,46,47,48,49] 0.03/0.40 * CE 5 is refined into CE [50] 0.03/0.40 0.03/0.40 0.03/0.40 ### Cost equations --> "Loop" of f1_loop_cont/7 0.03/0.40 * CEs [41,42] --> Loop 39 0.03/0.40 * CEs [43,45] --> Loop 40 0.03/0.40 * CEs [49] --> Loop 41 0.03/0.40 * CEs [48] --> Loop 42 0.03/0.40 * CEs [47] --> Loop 43 0.03/0.40 * CEs [46] --> Loop 44 0.03/0.40 * CEs [44] --> Loop 45 0.03/0.40 * CEs [40] --> Loop 46 0.03/0.40 * CEs [50] --> Loop 47 0.03/0.40 0.03/0.40 ### Ranking functions of CR f1_loop_cont(A,B,C,D,E,F,G) 0.03/0.40 0.03/0.40 #### Partial ranking functions of CR f1_loop_cont(A,B,C,D,E,F,G) 0.03/0.40 0.03/0.40 0.03/0.40 ### Specialization of cost equations f0/6 0.03/0.40 * CE 1 is refined into CE [51,52,53,54,55,56,57,58,59,60,61,62,63] 0.03/0.40 0.03/0.40 0.03/0.40 ### Cost equations --> "Loop" of f0/6 0.03/0.40 * CEs [52,53] --> Loop 48 0.03/0.40 * CEs [58] --> Loop 49 0.03/0.40 * CEs [63] --> Loop 50 0.03/0.40 * CEs [56,57] --> Loop 51 0.03/0.40 * CEs [62] --> Loop 52 0.03/0.40 * CEs [60,61] --> Loop 53 0.03/0.40 * CEs [54,55] --> Loop 54 0.03/0.40 * CEs [59] --> Loop 55 0.03/0.40 * CEs [51] --> Loop 56 0.03/0.40 0.03/0.40 ### Ranking functions of CR f0(A,B,C,D,E,F) 0.03/0.40 0.03/0.40 #### Partial ranking functions of CR f0(A,B,C,D,E,F) 0.03/0.40 0.03/0.40 0.03/0.40 Computing Bounds 0.03/0.40 ===================================== 0.03/0.40 0.03/0.40 #### Cost of chains of f1(A,B,C,F,G,H): 0.03/0.40 * Chain [[19],21]: 1*it(19)+0 0.03/0.40 Such that:it(19) =< A-B 0.03/0.40 0.03/0.40 with precondition: [F=2,A>=B+1] 0.03/0.40 0.03/0.40 * Chain [[19],20]: 1*it(19)+0 0.03/0.40 Such that:it(19) =< A-B 0.03/0.40 0.03/0.40 with precondition: [F=5,A=G,A=H,A>=B+1] 0.03/0.40 0.03/0.40 * Chain [21]: 0 0.03/0.40 with precondition: [F=2] 0.03/0.40 0.03/0.40 * Chain [20]: 0 0.03/0.40 with precondition: [F=5,B=G,B=H,B>=A] 0.03/0.40 0.03/0.40 0.03/0.40 #### Cost of chains of f2(C,D,F,G,H): 0.03/0.40 * Chain [[22],24]: 1*it(22)+0 0.03/0.40 Such that:it(22) =< C 0.03/0.40 0.03/0.40 with precondition: [F=2,C>=1] 0.03/0.40 0.03/0.40 * Chain [[22],23]: 1*it(22)+0 0.03/0.40 Such that:it(22) =< C 0.03/0.40 0.03/0.40 with precondition: [F=4,G=0,H=0,C>=1] 0.03/0.40 0.03/0.40 * Chain [24]: 0 0.03/0.40 with precondition: [F=2] 0.03/0.40 0.03/0.40 * Chain [23]: 0 0.03/0.40 with precondition: [F=4,C=G,C=H,0>=C] 0.03/0.40 0.03/0.40 0.03/0.40 #### Cost of chains of f3(A,D,E,F,G,H): 0.03/0.40 * Chain [[25],27]: 1*it(25)+0 0.03/0.40 Such that:it(25) =< A-D 0.03/0.40 0.03/0.40 with precondition: [F=2,A>=D+1] 0.03/0.40 0.03/0.40 * Chain [[25],26]: 1*it(25)+0 0.03/0.40 Such that:it(25) =< A-D 0.03/0.40 0.03/0.40 with precondition: [F=3,A=G,A=H,A>=D+1] 0.03/0.40 0.03/0.40 * Chain [27]: 0 0.03/0.40 with precondition: [F=2] 0.03/0.40 0.03/0.40 * Chain [26]: 0 0.03/0.40 with precondition: [F=3,D=G,D=H,D>=A] 0.03/0.40 0.03/0.40 0.03/0.40 #### Cost of chains of f4(E,F): 0.03/0.40 * Chain [[28],29]: 1*it(28)+0 0.03/0.40 Such that:it(28) =< E 0.03/0.40 0.03/0.40 with precondition: [F=2,E>=1] 0.03/0.40 0.03/0.40 * Chain [29]: 0 0.03/0.40 with precondition: [F=2] 0.03/0.40 0.03/0.40 0.03/0.40 #### Cost of chains of f3_loop_cont(A,B,C,D,E,F,G): 0.03/0.40 * Chain [32]: 0 0.03/0.40 with precondition: [A=2] 0.03/0.40 0.03/0.40 * Chain [31]: 0 0.03/0.40 with precondition: [A=3] 0.03/0.40 0.03/0.40 * Chain [30]: 1*s(1)+0 0.03/0.40 Such that:s(1) =< F 0.03/0.40 0.03/0.40 with precondition: [A=3,F>=1] 0.03/0.40 0.03/0.40 0.03/0.40 #### Cost of chains of f2_loop_cont(A,B,C,D,E,F,G): 0.03/0.40 * Chain [38]: 0 0.03/0.40 with precondition: [A=2] 0.03/0.40 0.03/0.40 * Chain [37]: 0 0.03/0.40 with precondition: [A=4] 0.03/0.40 0.03/0.40 * Chain [36]: 1*s(2)+1*s(3)+0 0.03/0.40 Such that:s(3) =< B 0.03/0.40 s(2) =< B-E 0.03/0.40 0.03/0.40 with precondition: [A=4,B>=1,B>=E+1] 0.03/0.40 0.03/0.40 * Chain [35]: 1*s(4)+0 0.03/0.40 Such that:s(4) =< E 0.03/0.40 0.03/0.40 with precondition: [A=4,E>=1,E>=B] 0.03/0.40 0.03/0.40 * Chain [34]: 0 0.03/0.40 with precondition: [A=4,E>=B] 0.03/0.40 0.03/0.40 * Chain [33]: 2*s(5)+0 0.03/0.40 Such that:aux(1) =< B-E 0.03/0.40 s(5) =< aux(1) 0.03/0.40 0.03/0.40 with precondition: [A=4,B>=E+1] 0.03/0.40 0.03/0.40 0.03/0.40 #### Cost of chains of f1_loop_cont(A,B,C,D,E,F,G): 0.03/0.40 * Chain [47]: 0 0.03/0.40 with precondition: [A=2] 0.03/0.40 0.03/0.40 * Chain [46]: 0 0.03/0.40 with precondition: [A=5] 0.03/0.40 0.03/0.40 * Chain [45]: 1*s(7)+0 0.03/0.40 Such that:s(7) =< D 0.03/0.40 0.03/0.40 with precondition: [A=5,0>=B,D>=1] 0.03/0.40 0.03/0.40 * Chain [44]: 0 0.03/0.40 with precondition: [A=5,0>=D] 0.03/0.40 0.03/0.40 * Chain [43]: 1*s(8)+1*s(9)+0 0.03/0.40 Such that:s(8) =< B 0.03/0.40 s(9) =< B-D 0.03/0.40 0.03/0.40 with precondition: [A=5,0>=D,B>=1] 0.03/0.40 0.03/0.40 * Chain [42]: 0 0.03/0.40 with precondition: [A=5,0>=D,D>=B] 0.03/0.40 0.03/0.40 * Chain [41]: 2*s(11)+0 0.03/0.40 Such that:s(10) =< B-D 0.03/0.40 s(11) =< s(10) 0.03/0.40 0.03/0.40 with precondition: [A=5,0>=D,B>=D+1] 0.03/0.40 0.03/0.40 * Chain [40]: 2*s(12)+4*s(13)+0 0.03/0.40 Such that:aux(3) =< B 0.03/0.40 aux(4) =< D 0.03/0.40 s(12) =< aux(4) 0.03/0.40 s(13) =< aux(3) 0.03/0.40 0.03/0.40 with precondition: [A=5,B>=1,D>=1] 0.03/0.40 0.03/0.40 * Chain [39]: 2*s(18)+0 0.03/0.40 Such that:aux(5) =< D 0.03/0.40 s(18) =< aux(5) 0.03/0.40 0.03/0.40 with precondition: [A=5,D>=1] 0.03/0.40 0.03/0.40 0.03/0.40 #### Cost of chains of f0(A,B,C,D,E,F): 0.03/0.40 * Chain [56]: 0 0.03/0.40 with precondition: [] 0.03/0.40 0.03/0.40 * Chain [55]: 1*s(20)+0 0.03/0.40 Such that:s(20) =< B 0.03/0.40 0.03/0.40 with precondition: [0>=A,B>=1] 0.03/0.40 0.03/0.40 * Chain [54]: 2*s(21)+0 0.03/0.40 Such that:aux(6) =< A-B 0.03/0.40 s(21) =< aux(6) 0.03/0.40 0.03/0.40 with precondition: [0>=A,A>=B+1] 0.03/0.40 0.03/0.40 * Chain [53]: 0 0.03/0.40 with precondition: [0>=B,B>=A] 0.03/0.40 0.03/0.40 * Chain [52]: 2*s(25)+4*s(26)+0 0.03/0.40 Such that:s(23) =< A 0.03/0.40 s(24) =< B 0.03/0.40 s(25) =< s(24) 0.03/0.40 s(26) =< s(23) 0.03/0.40 0.03/0.40 with precondition: [A>=1,B>=A] 0.03/0.40 0.03/0.40 * Chain [51]: 2*s(27)+8*s(30)+0 0.03/0.40 Such that:aux(8) =< A 0.03/0.40 aux(9) =< A-B 0.03/0.40 s(27) =< aux(9) 0.03/0.40 s(30) =< aux(8) 0.03/0.40 0.03/0.40 with precondition: [A>=1,A>=B+1] 0.03/0.40 0.03/0.40 * Chain [50]: 2*s(36)+0 0.03/0.40 Such that:s(35) =< B 0.03/0.40 s(36) =< s(35) 0.03/0.40 0.03/0.40 with precondition: [B>=1,B>=A] 0.03/0.40 0.03/0.40 * Chain [49]: 0 0.03/0.40 with precondition: [B>=A] 0.03/0.40 0.03/0.40 * Chain [48]: 2*s(37)+0 0.03/0.40 Such that:aux(10) =< A-B 0.03/0.40 s(37) =< aux(10) 0.03/0.40 0.03/0.40 with precondition: [A>=B+1] 0.03/0.40 0.03/0.40 0.03/0.40 Closed-form bounds of f0(A,B,C,D,E,F): 0.03/0.40 ------------------------------------- 0.03/0.40 * Chain [56] with precondition: [] 0.03/0.40 - Upper bound: 0 0.03/0.40 - Complexity: constant 0.03/0.40 * Chain [55] with precondition: [0>=A,B>=1] 0.03/0.40 - Upper bound: B 0.03/0.40 - Complexity: n 0.03/0.40 * Chain [54] with precondition: [0>=A,A>=B+1] 0.03/0.40 - Upper bound: 2*A-2*B 0.03/0.40 - Complexity: n 0.03/0.40 * Chain [53] with precondition: [0>=B,B>=A] 0.03/0.40 - Upper bound: 0 0.03/0.40 - Complexity: constant 0.03/0.40 * Chain [52] with precondition: [A>=1,B>=A] 0.03/0.40 - Upper bound: 4*A+2*B 0.03/0.40 - Complexity: n 0.03/0.40 * Chain [51] with precondition: [A>=1,A>=B+1] 0.03/0.40 - Upper bound: 10*A-2*B 0.03/0.40 - Complexity: n 0.03/0.40 * Chain [50] with precondition: [B>=1,B>=A] 0.03/0.40 - Upper bound: 2*B 0.03/0.40 - Complexity: n 0.03/0.40 * Chain [49] with precondition: [B>=A] 0.03/0.40 - Upper bound: 0 0.03/0.40 - Complexity: constant 0.03/0.40 * Chain [48] with precondition: [A>=B+1] 0.03/0.40 - Upper bound: 2*A-2*B 0.03/0.40 - Complexity: n 0.03/0.40 0.03/0.40 ### Maximum cost of f0(A,B,C,D,E,F): max([nat(A-B)*2+nat(A)*8,nat(A)*4+nat(B)+nat(B)]) 0.03/0.40 Asymptotic class: n 0.03/0.40 * Total analysis performed in 329 ms. 0.03/0.40 0.03/0.50 EOF