0.04/0.54 WORST_CASE(?,O(n^2)) 0.04/0.54 0.04/0.54 Preprocessing Cost Relations 0.04/0.54 ===================================== 0.04/0.54 0.04/0.54 #### Computed strongly connected components 0.04/0.54 0. recursive : [f10/7] 0.04/0.54 1. non_recursive : [exit_location/1] 0.04/0.54 2. recursive : [f21/8] 0.04/0.54 3. recursive : [f18/8,f21_loop_cont/9] 0.04/0.54 4. recursive : [f32/4] 0.04/0.54 5. non_recursive : [f41/8] 0.04/0.54 6. non_recursive : [f32_loop_cont/9] 0.04/0.54 7. non_recursive : [f18_loop_cont/9] 0.04/0.54 8. non_recursive : [f10_loop_cont/9] 0.04/0.54 9. non_recursive : [f0/8] 0.04/0.54 0.04/0.54 #### Obtained direct recursion through partial evaluation 0.04/0.54 0. SCC is partially evaluated into f10/7 0.04/0.54 1. SCC is completely evaluated into other SCCs 0.04/0.54 2. SCC is partially evaluated into f21/8 0.04/0.54 3. SCC is partially evaluated into f18/8 0.04/0.54 4. SCC is partially evaluated into f32/4 0.04/0.54 5. SCC is completely evaluated into other SCCs 0.04/0.54 6. SCC is partially evaluated into f32_loop_cont/9 0.04/0.54 7. SCC is partially evaluated into f18_loop_cont/9 0.04/0.54 8. SCC is partially evaluated into f10_loop_cont/9 0.04/0.54 9. SCC is partially evaluated into f0/8 0.04/0.54 0.04/0.54 Control-Flow Refinement of Cost Relations 0.04/0.54 ===================================== 0.04/0.54 0.04/0.54 ### Specialization of cost equations f10/7 0.04/0.54 * CE 4 is refined into CE [21] 0.04/0.54 * CE 3 is refined into CE [22] 0.04/0.54 * CE 2 is refined into CE [23] 0.04/0.54 0.04/0.54 0.04/0.54 ### Cost equations --> "Loop" of f10/7 0.04/0.54 * CEs [23] --> Loop 21 0.04/0.54 * CEs [21] --> Loop 22 0.04/0.54 * CEs [22] --> Loop 23 0.04/0.54 0.04/0.54 ### Ranking functions of CR f10(B,C,D,E,I,J,K) 0.04/0.54 * RF of phase [21]: [-B+C] 0.04/0.54 0.04/0.54 #### Partial ranking functions of CR f10(B,C,D,E,I,J,K) 0.04/0.54 * Partial RF of phase [21]: 0.04/0.54 - RF of loop [21:1]: 0.04/0.54 -B+C 0.04/0.54 0.04/0.54 0.04/0.54 ### Specialization of cost equations f21/8 0.04/0.54 * CE 15 is refined into CE [24] 0.04/0.54 * CE 14 is refined into CE [25] 0.04/0.54 * CE 13 is refined into CE [26] 0.04/0.54 0.04/0.54 0.04/0.54 ### Cost equations --> "Loop" of f21/8 0.04/0.54 * CEs [26] --> Loop 24 0.04/0.54 * CEs [24] --> Loop 25 0.04/0.54 * CEs [25] --> Loop 26 0.04/0.54 0.04/0.54 ### Ranking functions of CR f21(D,E,F,G,I,J,K,L) 0.04/0.54 * RF of phase [24]: [D-E-F-1] 0.04/0.54 0.04/0.54 #### Partial ranking functions of CR f21(D,E,F,G,I,J,K,L) 0.04/0.54 * Partial RF of phase [24]: 0.04/0.54 - RF of loop [24:1]: 0.04/0.54 D-E-F-1 0.04/0.54 0.04/0.54 0.04/0.54 ### Specialization of cost equations f18/8 0.04/0.54 * CE 9 is refined into CE [27] 0.04/0.54 * CE 7 is refined into CE [28,29] 0.04/0.54 * CE 10 is refined into CE [30] 0.04/0.54 * CE 8 is refined into CE [31] 0.04/0.54 0.04/0.54 0.04/0.54 ### Cost equations --> "Loop" of f18/8 0.04/0.54 * CEs [31] --> Loop 27 0.04/0.54 * CEs [27] --> Loop 28 0.04/0.54 * CEs [28,29] --> Loop 29 0.04/0.54 * CEs [30] --> Loop 30 0.04/0.54 0.04/0.54 ### Ranking functions of CR f18(D,E,F,G,I,J,K,L) 0.04/0.54 * RF of phase [27]: [D-E-1] 0.04/0.54 0.04/0.54 #### Partial ranking functions of CR f18(D,E,F,G,I,J,K,L) 0.04/0.54 * Partial RF of phase [27]: 0.04/0.54 - RF of loop [27:1]: 0.04/0.54 D-E-1 0.04/0.54 0.04/0.54 0.04/0.54 ### Specialization of cost equations f32/4 0.04/0.54 * CE 17 is refined into CE [32] 0.04/0.54 * CE 18 is refined into CE [33] 0.04/0.54 * CE 16 is refined into CE [34] 0.04/0.54 0.04/0.54 0.04/0.54 ### Cost equations --> "Loop" of f32/4 0.04/0.54 * CEs [34] --> Loop 31 0.04/0.54 * CEs [32] --> Loop 32 0.04/0.54 * CEs [33] --> Loop 33 0.04/0.54 0.04/0.54 ### Ranking functions of CR f32(D,E,I,J) 0.04/0.54 * RF of phase [31]: [D-E-1] 0.04/0.54 0.04/0.54 #### Partial ranking functions of CR f32(D,E,I,J) 0.04/0.54 * Partial RF of phase [31]: 0.04/0.54 - RF of loop [31:1]: 0.04/0.54 D-E-1 0.04/0.54 0.04/0.54 0.04/0.54 ### Specialization of cost equations f32_loop_cont/9 0.04/0.54 * CE 19 is refined into CE [35] 0.04/0.54 * CE 20 is refined into CE [36] 0.04/0.54 0.04/0.54 0.04/0.54 ### Cost equations --> "Loop" of f32_loop_cont/9 0.04/0.54 * CEs [35] --> Loop 34 0.04/0.54 * CEs [36] --> Loop 35 0.04/0.54 0.04/0.54 ### Ranking functions of CR f32_loop_cont(A,B,C,D,E,F,G,H,I) 0.04/0.54 0.04/0.54 #### Partial ranking functions of CR f32_loop_cont(A,B,C,D,E,F,G,H,I) 0.04/0.54 0.04/0.54 0.04/0.54 ### Specialization of cost equations f18_loop_cont/9 0.04/0.54 * CE 12 is refined into CE [37,38,39,40] 0.04/0.54 * CE 11 is refined into CE [41] 0.04/0.54 0.04/0.54 0.04/0.54 ### Cost equations --> "Loop" of f18_loop_cont/9 0.04/0.54 * CEs [38,39] --> Loop 36 0.04/0.54 * CEs [40] --> Loop 37 0.04/0.54 * CEs [37] --> Loop 38 0.04/0.54 * CEs [41] --> Loop 39 0.04/0.54 0.04/0.54 ### Ranking functions of CR f18_loop_cont(A,B,C,D,E,F,G,H,I) 0.04/0.54 0.04/0.54 #### Partial ranking functions of CR f18_loop_cont(A,B,C,D,E,F,G,H,I) 0.04/0.54 0.04/0.54 0.04/0.54 ### Specialization of cost equations f10_loop_cont/9 0.04/0.54 * CE 5 is refined into CE [42] 0.04/0.54 * CE 6 is refined into CE [43,44,45,46,47,48,49,50,51] 0.04/0.54 0.04/0.54 0.04/0.54 ### Cost equations --> "Loop" of f10_loop_cont/9 0.04/0.54 * CEs [42] --> Loop 40 0.04/0.54 * CEs [45] --> Loop 41 0.04/0.54 * CEs [44,46] --> Loop 42 0.04/0.54 * CEs [49] --> Loop 43 0.04/0.54 * CEs [48] --> Loop 44 0.04/0.54 * CEs [51] --> Loop 45 0.04/0.54 * CEs [47] --> Loop 46 0.04/0.54 * CEs [50] --> Loop 47 0.04/0.54 * CEs [43] --> Loop 48 0.04/0.54 0.04/0.54 ### Ranking functions of CR f10_loop_cont(A,B,C,D,E,F,G,H,I) 0.04/0.54 0.04/0.54 #### Partial ranking functions of CR f10_loop_cont(A,B,C,D,E,F,G,H,I) 0.04/0.54 0.04/0.54 0.04/0.54 ### Specialization of cost equations f0/8 0.04/0.54 * CE 1 is refined into CE [52,53,54,55,56,57,58,59,60,61,62] 0.04/0.54 0.04/0.54 0.04/0.54 ### Cost equations --> "Loop" of f0/8 0.04/0.54 * CEs [60] --> Loop 49 0.04/0.54 * CEs [57,59] --> Loop 50 0.04/0.54 * CEs [55,62] --> Loop 51 0.04/0.54 * CEs [52,53,54] --> Loop 52 0.04/0.54 * CEs [56,58] --> Loop 53 0.04/0.54 * CEs [61] --> Loop 54 0.04/0.54 0.04/0.54 ### Ranking functions of CR f0(A,B,C,D,E,F,G,I) 0.04/0.54 0.04/0.54 #### Partial ranking functions of CR f0(A,B,C,D,E,F,G,I) 0.04/0.54 0.04/0.54 0.04/0.54 Computing Bounds 0.04/0.54 ===================================== 0.04/0.54 0.04/0.54 #### Cost of chains of f10(B,C,D,E,I,J,K): 0.04/0.54 * Chain [[21],23]: 1*it(21)+0 0.04/0.54 Such that:it(21) =< -B+C 0.04/0.54 0.04/0.54 with precondition: [I=2,K=0,C=J,B>=0,C>=B+1] 0.04/0.54 0.04/0.54 * Chain [[21],22]: 1*it(21)+0 0.04/0.54 Such that:it(21) =< -B+C 0.04/0.54 0.04/0.54 with precondition: [I=3,B>=0,C>=B+1] 0.04/0.54 0.04/0.54 * Chain [23]: 0 0.04/0.54 with precondition: [I=2,K=0,B=J,B>=0,B>=C] 0.04/0.54 0.04/0.54 * Chain [22]: 0 0.04/0.54 with precondition: [I=3,B>=0] 0.04/0.54 0.04/0.54 0.04/0.54 #### Cost of chains of f21(D,E,F,G,I,J,K,L): 0.04/0.54 * Chain [[24],26]: 1*it(24)+0 0.04/0.54 Such that:it(24) =< D-F-J 0.04/0.54 0.04/0.54 with precondition: [I=2,E+1=J,D=E+K+1,F>=0,D>=E+F+2] 0.04/0.54 0.04/0.54 * Chain [[24],25]: 1*it(24)+0 0.04/0.54 Such that:it(24) =< D-E-F 0.04/0.54 0.04/0.54 with precondition: [I=3,F>=0,D>=E+F+2] 0.04/0.54 0.04/0.54 * Chain [25]: 0 0.04/0.54 with precondition: [I=3,F>=0,D>=E+2] 0.04/0.54 0.04/0.54 0.04/0.54 #### Cost of chains of f18(D,E,F,G,I,J,K,L): 0.04/0.54 * Chain [[27],30]: 1*it(27)+1*s(3)+0 0.04/0.54 Such that:aux(3) =< D-E 0.04/0.54 it(27) =< aux(3) 0.04/0.54 s(3) =< it(27)*aux(3) 0.04/0.54 0.04/0.54 with precondition: [I=3,D>=E+2] 0.04/0.54 0.04/0.54 * Chain [[27],29]: 2*it(27)+1*s(3)+0 0.04/0.54 Such that:aux(4) =< D-E 0.04/0.54 it(27) =< aux(4) 0.04/0.54 s(3) =< it(27)*aux(4) 0.04/0.54 0.04/0.54 with precondition: [I=3,D>=E+3] 0.04/0.54 0.04/0.54 * Chain [[27],28]: 1*it(27)+1*s(3)+0 0.04/0.54 Such that:aux(5) =< D-E 0.04/0.54 it(27) =< aux(5) 0.04/0.54 s(3) =< it(27)*aux(5) 0.04/0.54 0.04/0.54 with precondition: [I=5,J=0,K=1,D>=E+2] 0.04/0.54 0.04/0.54 * Chain [30]: 0 0.04/0.54 with precondition: [I=3] 0.04/0.54 0.04/0.54 * Chain [29]: 1*s(4)+0 0.04/0.54 Such that:s(4) =< D-E 0.04/0.54 0.04/0.54 with precondition: [I=3,D>=E+2] 0.04/0.54 0.04/0.54 * Chain [28]: 0 0.04/0.54 with precondition: [I=5,J=0,K=F,L=G,E+1>=D] 0.04/0.54 0.04/0.54 0.04/0.54 #### Cost of chains of f32(D,E,I,J): 0.04/0.54 * Chain [[31],33]: 1*it(31)+0 0.04/0.54 Such that:it(31) =< D-E 0.04/0.54 0.04/0.54 with precondition: [I=3,D>=E+2] 0.04/0.54 0.04/0.54 * Chain [[31],32]: 1*it(31)+0 0.04/0.54 Such that:it(31) =< D-E 0.04/0.54 0.04/0.54 with precondition: [I=4,D=J+1,D>=E+2] 0.04/0.54 0.04/0.54 * Chain [33]: 0 0.04/0.54 with precondition: [I=3] 0.04/0.54 0.04/0.54 * Chain [32]: 0 0.04/0.54 with precondition: [I=4,E=J,E+1>=D] 0.04/0.54 0.04/0.54 0.04/0.54 #### Cost of chains of f32_loop_cont(A,B,C,D,E,F,G,H,I): 0.04/0.54 * Chain [35]: 0 0.04/0.54 with precondition: [A=3,E=D] 0.04/0.54 0.04/0.54 * Chain [34]: 0 0.04/0.54 with precondition: [A=4,E=D] 0.04/0.54 0.04/0.54 0.04/0.54 #### Cost of chains of f18_loop_cont(A,B,C,D,E,F,G,H,I): 0.04/0.54 * Chain [39]: 0 0.04/0.54 with precondition: [A=3,E=D] 0.04/0.54 0.04/0.54 * Chain [38]: 0 0.04/0.54 with precondition: [A=5,E=D] 0.04/0.54 0.04/0.54 * Chain [37]: 0 0.04/0.54 with precondition: [A=5,E=D,F+1>=E] 0.04/0.54 0.04/0.54 * Chain [36]: 2*s(9)+0 0.04/0.54 Such that:aux(7) =< D-F 0.04/0.54 s(9) =< aux(7) 0.04/0.54 0.04/0.54 with precondition: [A=5,E=D,E>=F+2] 0.04/0.54 0.04/0.54 0.04/0.54 #### Cost of chains of f10_loop_cont(A,B,C,D,E,F,G,H,I): 0.04/0.54 * Chain [48]: 0 0.04/0.54 with precondition: [A=2,E=D] 0.04/0.54 0.04/0.54 * Chain [47]: 0 0.04/0.54 with precondition: [A=2,E=D,1>=E,F+1>=E] 0.04/0.54 0.04/0.54 * Chain [46]: 1*s(12)+1*s(13)+0 0.04/0.54 Such that:s(11) =< D-F 0.04/0.54 s(12) =< s(11) 0.04/0.54 s(13) =< s(12)*s(11) 0.04/0.54 0.04/0.54 with precondition: [A=2,E=D,1>=E,E>=F+2] 0.04/0.54 0.04/0.54 * Chain [45]: 2*s(15)+0 0.04/0.54 Such that:s(14) =< D 0.04/0.54 s(15) =< s(14) 0.04/0.54 0.04/0.54 with precondition: [A=2,E=D,E>=2,F+1>=E] 0.04/0.54 0.04/0.54 * Chain [44]: 1*s(17)+1*s(18)+2*s(20)+0 0.04/0.54 Such that:s(19) =< D 0.04/0.54 s(16) =< D-F 0.04/0.54 s(20) =< s(19) 0.04/0.54 s(17) =< s(16) 0.04/0.54 s(18) =< s(17)*s(16) 0.04/0.54 0.04/0.54 with precondition: [A=2,E=D,E>=2,E>=F+2] 0.04/0.54 0.04/0.54 * Chain [43]: 0 0.04/0.54 with precondition: [A=2,E=D,F+1>=E] 0.04/0.54 0.04/0.54 * Chain [42]: 3*s(22)+2*s(23)+0 0.04/0.54 Such that:aux(8) =< D-F 0.04/0.54 s(22) =< aux(8) 0.04/0.54 s(23) =< s(22)*aux(8) 0.04/0.54 0.04/0.54 with precondition: [A=2,E=D,E>=F+2] 0.04/0.54 0.04/0.54 * Chain [41]: 2*s(28)+1*s(29)+0 0.04/0.54 Such that:s(27) =< D-F 0.04/0.54 s(28) =< s(27) 0.04/0.54 s(29) =< s(28)*s(27) 0.04/0.54 0.04/0.54 with precondition: [A=2,E=D,E>=F+3] 0.04/0.54 0.04/0.54 * Chain [40]: 0 0.04/0.54 with precondition: [A=3,E=D] 0.04/0.54 0.04/0.54 0.04/0.54 #### Cost of chains of f0(A,B,C,D,E,F,G,I): 0.04/0.54 * Chain [54]: 0 0.04/0.54 with precondition: [] 0.04/0.54 0.04/0.54 * Chain [53]: 2 0.04/0.54 with precondition: [C=1] 0.04/0.54 0.04/0.54 * Chain [52]: 0 0.04/0.54 with precondition: [0>=C] 0.04/0.54 0.04/0.54 * Chain [51]: 2*s(32)+0 0.04/0.54 Such that:aux(10) =< C 0.04/0.54 s(32) =< aux(10) 0.04/0.54 0.04/0.54 with precondition: [C>=1] 0.04/0.54 0.04/0.54 * Chain [50]: 8*s(34)+3*s(39)+0 0.04/0.54 Such that:aux(13) =< C 0.04/0.54 s(34) =< aux(13) 0.04/0.54 s(39) =< s(34)*aux(13) 0.04/0.54 0.04/0.54 with precondition: [C>=2] 0.04/0.54 0.04/0.54 * Chain [49]: 3*s(44)+1*s(47)+0 0.04/0.54 Such that:aux(14) =< C 0.04/0.54 s(44) =< aux(14) 0.04/0.54 s(47) =< s(44)*aux(14) 0.04/0.54 0.04/0.54 with precondition: [C>=3] 0.04/0.54 0.04/0.54 0.04/0.54 Closed-form bounds of f0(A,B,C,D,E,F,G,I): 0.04/0.54 ------------------------------------- 0.04/0.54 * Chain [54] with precondition: [] 0.04/0.54 - Upper bound: 0 0.04/0.54 - Complexity: constant 0.04/0.54 * Chain [53] with precondition: [C=1] 0.04/0.54 - Upper bound: 2 0.04/0.54 - Complexity: constant 0.04/0.54 * Chain [52] with precondition: [0>=C] 0.04/0.54 - Upper bound: 0 0.04/0.54 - Complexity: constant 0.04/0.54 * Chain [51] with precondition: [C>=1] 0.04/0.54 - Upper bound: 2*C 0.04/0.54 - Complexity: n 0.04/0.54 * Chain [50] with precondition: [C>=2] 0.04/0.54 - Upper bound: 3*C*C+8*C 0.04/0.54 - Complexity: n^2 0.04/0.54 * Chain [49] with precondition: [C>=3] 0.04/0.54 - Upper bound: 3*C+C*C 0.04/0.54 - Complexity: n^2 0.04/0.54 0.04/0.54 ### Maximum cost of f0(A,B,C,D,E,F,G,I): max([2,nat(C)*2*nat(C)+nat(C)*5+(nat(C)*nat(C)+nat(C))+nat(C)*2]) 0.04/0.54 Asymptotic class: n^2 0.04/0.54 * Total analysis performed in 456 ms. 0.04/0.54 0.54/0.64 EOF