2.39/2.39 MAYBE 2.39/2.39 2.39/2.39 Preprocessing Cost Relations 2.39/2.39 ===================================== 2.39/2.39 2.39/2.39 #### Computed strongly connected components 2.39/2.39 0. recursive : [f15/22,f25/22] 2.39/2.39 1. non_recursive : [exit_location/1] 2.39/2.39 2. recursive : [f31/1] 2.39/2.39 3. non_recursive : [f31_loop_cont/2] 2.39/2.39 4. non_recursive : [f15_loop_cont/26] 2.39/2.39 5. recursive : [f45/23,f46/23] 2.39/2.39 6. recursive : [f36/28,f45_loop_cont/29] 2.39/2.39 7. recursive : [f61/1] 2.39/2.39 8. non_recursive : [f61_loop_cont/2] 2.39/2.39 9. non_recursive : [f36_loop_cont/26] 2.39/2.39 10. non_recursive : [f0/25] 2.39/2.39 2.39/2.39 #### Obtained direct recursion through partial evaluation 2.39/2.39 0. SCC is partially evaluated into f15/22 2.39/2.39 1. SCC is completely evaluated into other SCCs 2.39/2.39 2. SCC is partially evaluated into f31/1 2.39/2.39 3. SCC is completely evaluated into other SCCs 2.39/2.39 4. SCC is partially evaluated into f15_loop_cont/26 2.39/2.39 5. SCC is partially evaluated into f45/23 2.39/2.39 6. SCC is partially evaluated into f36/28 2.39/2.39 7. SCC is partially evaluated into f61/1 2.39/2.39 8. SCC is completely evaluated into other SCCs 2.39/2.39 9. SCC is partially evaluated into f36_loop_cont/26 2.39/2.39 10. SCC is partially evaluated into f0/25 2.39/2.39 2.39/2.39 Control-Flow Refinement of Cost Relations 2.39/2.39 ===================================== 2.39/2.39 2.39/2.39 ### Specialization of cost equations f15/22 2.39/2.39 * CE 9 is refined into CE [31] 2.39/2.39 * CE 10 is refined into CE [32] 2.39/2.39 * CE 6 is refined into CE [33] 2.39/2.39 * CE 7 is refined into CE [34] 2.39/2.39 * CE 8 is refined into CE [35] 2.39/2.39 * CE 4 is refined into CE [36] 2.39/2.39 * CE 5 is refined into CE [37] 2.39/2.39 2.39/2.39 2.39/2.39 ### Cost equations --> "Loop" of f15/22 2.39/2.39 * CEs [33] --> Loop 29 2.39/2.39 * CEs [34] --> Loop 30 2.39/2.39 * CEs [35] --> Loop 31 2.39/2.39 * CEs [36] --> Loop 32 2.39/2.39 * CEs [37] --> Loop 33 2.39/2.39 * CEs [31] --> Loop 34 2.39/2.39 * CEs [32] --> Loop 35 2.39/2.39 2.39/2.39 ### Ranking functions of CR f15(A,B,C,D,E,F,R,S,T,U,V,W,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1) 2.39/2.39 * RF of phase [29,30,31,32,33]: [-C+R] 2.39/2.39 2.39/2.39 #### Partial ranking functions of CR f15(A,B,C,D,E,F,R,S,T,U,V,W,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1) 2.39/2.39 * Partial RF of phase [29,30,31,32,33]: 2.39/2.39 - RF of loop [29:1,30:1,31:1,32:1,33:1]: 2.39/2.39 -C+R 2.39/2.39 2.39/2.39 2.39/2.39 ### Specialization of cost equations f31/1 2.39/2.39 * CE 20 is refined into CE [38] 2.39/2.39 * CE 19 is refined into CE [39] 2.39/2.39 2.39/2.39 2.39/2.39 ### Cost equations --> "Loop" of f31/1 2.39/2.39 * CEs [39] --> Loop 36 2.39/2.39 * CEs [38] --> Loop 37 2.39/2.39 2.39/2.39 ### Ranking functions of CR f31(C1) 2.39/2.39 2.39/2.39 #### Partial ranking functions of CR f31(C1) 2.39/2.39 2.39/2.39 2.39/2.39 ### Specialization of cost equations f15_loop_cont/26 2.39/2.39 * CE 12 is refined into CE [40,41] 2.39/2.39 * CE 11 is refined into CE [42] 2.39/2.39 2.39/2.39 2.39/2.39 ### Cost equations --> "Loop" of f15_loop_cont/26 2.39/2.39 * CEs [40] --> Loop 38 2.39/2.39 * CEs [42] --> Loop 39 2.39/2.39 * CEs [41] --> Loop 40 2.39/2.39 2.39/2.39 ### Ranking functions of CR f15_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z) 2.39/2.39 2.39/2.39 #### Partial ranking functions of CR f15_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z) 2.39/2.39 2.39/2.39 2.39/2.39 ### Specialization of cost equations f45/23 2.39/2.39 * CE 28 is refined into CE [43] 2.39/2.39 * CE 25 is refined into CE [44] 2.39/2.39 * CE 26 is refined into CE [45] 2.39/2.39 * CE 23 is refined into CE [46] 2.39/2.39 * CE 24 is refined into CE [47] 2.39/2.39 * CE 27 is refined into CE [48] 2.39/2.39 * CE 21 is refined into CE [49] 2.39/2.39 * CE 22 is refined into CE [50] 2.39/2.39 2.39/2.39 2.39/2.39 ### Cost equations --> "Loop" of f45/23 2.39/2.39 * CEs [49] --> Loop 41 2.39/2.39 * CEs [50] --> Loop 42 2.39/2.39 * CEs [43] --> Loop 43 2.39/2.39 * CEs [44] --> Loop 44 2.39/2.39 * CEs [45] --> Loop 45 2.39/2.39 * CEs [46] --> Loop 46 2.39/2.39 * CEs [47] --> Loop 47 2.39/2.39 * CEs [48] --> Loop 48 2.39/2.39 2.39/2.39 ### Ranking functions of CR f45(A,B,C,D,E,J,K,L,M,N,O,P,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1) 2.39/2.39 2.39/2.39 #### Partial ranking functions of CR f45(A,B,C,D,E,J,K,L,M,N,O,P,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1) 2.39/2.39 2.39/2.39 2.39/2.39 ### Specialization of cost equations f36/28 2.39/2.39 * CE 15 is refined into CE [51] 2.39/2.39 * CE 13 is refined into CE [52,53,54] 2.39/2.39 * CE 16 is refined into CE [55] 2.39/2.39 * CE 14 is refined into CE [56,57,58,59,60,61,62,63,64] 2.39/2.39 2.39/2.39 2.39/2.39 ### Cost equations --> "Loop" of f36/28 2.39/2.39 * CEs [64] --> Loop 49 2.39/2.39 * CEs [63] --> Loop 50 2.39/2.39 * CEs [62] --> Loop 51 2.39/2.39 * CEs [61] --> Loop 52 2.39/2.39 * CEs [56] --> Loop 53 2.39/2.39 * CEs [60] --> Loop 54 2.39/2.39 * CEs [59] --> Loop 55 2.39/2.39 * CEs [58] --> Loop 56 2.39/2.39 * CEs [57] --> Loop 57 2.39/2.39 * CEs [51] --> Loop 58 2.39/2.39 * CEs [52] --> Loop 59 2.39/2.39 * CEs [53] --> Loop 60 2.39/2.39 * CEs [55] --> Loop 61 2.39/2.39 * CEs [54] --> Loop 62 2.39/2.39 2.39/2.39 ### Ranking functions of CR f36(A,B,C,D,E,H,I,J,K,L,M,N,O,P,Q,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1) 2.39/2.39 2.39/2.39 #### Partial ranking functions of CR f36(A,B,C,D,E,H,I,J,K,L,M,N,O,P,Q,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1) 2.39/2.39 * Partial RF of phase [49,50,51,52,53,54,55,56,57]: 2.39/2.39 - RF of loop [50:1,51:1,52:1,53:1,54:1,55:1,56:1,57:1]: 2.39/2.39 -C+H+1 depends on loops [49:1] 2.39/2.39 2.39/2.39 2.39/2.39 ### Specialization of cost equations f61/1 2.39/2.39 * CE 30 is refined into CE [65] 2.39/2.39 * CE 29 is refined into CE [66] 2.39/2.39 2.39/2.39 2.39/2.39 ### Cost equations --> "Loop" of f61/1 2.39/2.39 * CEs [66] --> Loop 63 2.39/2.39 * CEs [65] --> Loop 64 2.39/2.39 2.39/2.39 ### Ranking functions of CR f61(C1) 2.39/2.39 2.39/2.39 #### Partial ranking functions of CR f61(C1) 2.39/2.39 2.39/2.39 2.39/2.39 ### Specialization of cost equations f36_loop_cont/26 2.39/2.39 * CE 18 is refined into CE [67,68] 2.39/2.39 * CE 17 is refined into CE [69] 2.39/2.39 2.39/2.39 2.39/2.39 ### Cost equations --> "Loop" of f36_loop_cont/26 2.39/2.39 * CEs [67] --> Loop 65 2.39/2.39 * CEs [69] --> Loop 66 2.39/2.39 * CEs [68] --> Loop 67 2.39/2.39 2.39/2.39 ### Ranking functions of CR f36_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z) 2.39/2.39 2.39/2.39 #### Partial ranking functions of CR f36_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z) 2.39/2.39 2.39/2.39 2.39/2.39 ### Specialization of cost equations f0/25 2.39/2.39 * CE 1 is refined into CE [70,71,72,73,74,75] 2.39/2.39 * CE 2 is refined into CE [76,77,78,79,80,81,82,83,84,85,86] 2.39/2.39 * CE 3 is refined into CE [87,88,89,90,91,92,93,94,95,96,97] 2.39/2.39 2.39/2.39 2.39/2.39 ### Cost equations --> "Loop" of f0/25 2.39/2.39 * CEs [83,94] --> Loop 68 2.39/2.39 * CEs [73,75,80,82,84,85,86,91,93,95,96,97] --> Loop 69 2.39/2.39 * CEs [77,88] --> Loop 70 2.39/2.39 * CEs [70,71,72,74,76,78,79,81,87,89,90,92] --> Loop 71 2.39/2.39 2.39/2.39 ### Ranking functions of CR f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,C1) 2.39/2.39 2.39/2.39 #### Partial ranking functions of CR f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,C1) 2.39/2.39 2.39/2.39 2.39/2.39 Computing Bounds 2.39/2.39 ===================================== 2.39/2.39 2.39/2.39 #### Cost of chains of f15(A,B,C,D,E,F,R,S,T,U,V,W,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1): 2.39/2.39 * Chain [[29,30,31,32,33],35]: 5*it(29)+0 2.39/2.39 Such that:aux(3) =< -C+R 2.39/2.39 it(29) =< aux(3) 2.39/2.39 2.39/2.39 with precondition: [C1=3,C>=0,R>=C+1] 2.39/2.39 2.39/2.39 * Chain [[29,30,31,32,33],34]: 5*it(29)+0 2.39/2.39 Such that:aux(4) =< -C+D1 2.39/2.39 it(29) =< aux(4) 2.39/2.39 2.39/2.39 with precondition: [C1=4,R=D1,J1=K1,J1=L1,C>=0,R>=C+1] 2.39/2.39 2.39/2.39 * Chain [35]: 0 2.39/2.39 with precondition: [C1=3,C>=0] 2.39/2.39 2.39/2.39 * Chain [34]: 0 2.39/2.39 with precondition: [C1=4,E1=D,F1=E,G1=F,H1=S,I1=T,J1=U,K1=V,L1=W,C=D1,C>=0,C>=R] 2.39/2.39 2.39/2.39 2.39/2.39 #### Cost of chains of f31(C1): 2.39/2.39 * Chain [[36]]...: 1*it(36)+0 2.39/2.39 with precondition: [C1=3] 2.39/2.39 2.39/2.39 * Chain [[36],37]: 1*it(36)+0 2.39/2.39 with precondition: [C1=3] 2.39/2.39 2.39/2.39 * Chain [37]: 0 2.39/2.39 with precondition: [C1=3] 2.39/2.39 2.39/2.39 2.39/2.39 #### Cost of chains of f15_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z): 2.39/2.39 * Chain [40]...: 1*s(2)+0 2.39/2.39 with precondition: [A=4,H=0,R=0,Y=1] 2.39/2.39 2.39/2.39 * Chain [39]: 0 2.39/2.39 with precondition: [A=3,H=0,R=0,Y=1] 2.39/2.39 2.39/2.39 * Chain [38]: 1*s(3)+0 2.39/2.39 with precondition: [A=4,H=0,R=0,Y=1] 2.39/2.39 2.39/2.39 2.39/2.39 #### Cost of chains of f45(A,B,C,D,E,J,K,L,M,N,O,P,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1): 2.39/2.39 * Chain [[41,42]]...: 2*it(41)+0 2.39/2.39 with precondition: [L=M,B>=A,C1>=2,3>=C1] 2.39/2.39 2.39/2.39 * Chain [[41,42],48]: 2*it(41)+0 2.39/2.39 with precondition: [C1=2,I1=0,J1=0,K1=0,L=M,C+1=D1,D=E1,E=F1,O=L1,B>=A] 2.39/2.39 2.39/2.39 * Chain [[41,42],47]: 2*it(41)+0 2.39/2.39 with precondition: [C1=2,F1=0,L=M,C+1=D1,J1=I1,J1=K1,0>=J1+1,B>=A] 2.39/2.39 2.39/2.39 * Chain [[41,42],46]: 2*it(41)+0 2.39/2.39 with precondition: [C1=2,F1=0,L=M,C+1=D1,J1=I1,J1=K1,J1>=1,B>=A] 2.39/2.39 2.39/2.39 * Chain [[41,42],43]: 2*it(41)+0 2.39/2.39 with precondition: [C1=3,L=M,B>=A] 2.39/2.39 2.39/2.39 * Chain [48]: 0 2.39/2.39 with precondition: [L=0,M=0,C1=2,I1=0,J1=0,K1=0,D1=C+1,E1=D,F1=E,G1=J,H1=K,L1=O,M1=P] 2.39/2.39 2.39/2.39 * Chain [47]: 0 2.39/2.39 with precondition: [C1=2,F1=0,D1=C+1,G1=J,H1=K,M=L,M1=P,M=I1,M=J1,M=K1,0>=M+1,B>=A] 2.39/2.39 2.39/2.39 * Chain [46]: 0 2.39/2.39 with precondition: [C1=2,F1=0,D1=C+1,G1=J,H1=K,M=L,M1=P,M=I1,M=J1,M=K1,M>=1,B>=A] 2.39/2.39 2.39/2.39 * Chain [45]: 0 2.39/2.39 with precondition: [C1=2,D1=C+1,E1=D,F1=E,G1=J,H1=K,M=L,L1=O,M1=P,M=I1,M=J1,M=K1,0>=M+1,A>=B+1] 2.39/2.39 2.39/2.39 * Chain [44]: 0 2.39/2.39 with precondition: [C1=2,D1=C+1,E1=D,F1=E,G1=J,H1=K,M=L,L1=O,M1=P,M=I1,M=J1,M=K1,M>=1,A>=B+1] 2.39/2.39 2.39/2.39 * Chain [43]: 0 2.39/2.39 with precondition: [C1=3,M=L] 2.39/2.39 2.39/2.39 2.39/2.39 #### Cost of chains of f36(A,B,C,D,E,H,I,J,K,L,M,N,O,P,Q,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1): 2.39/2.39 * Chain [[49,50,51,52,53,54,55,56,57]]...: 17*it(49)+0 2.39/2.39 with precondition: [H>=C,Q=0] 2.39/2.39 2.39/2.39 * Chain [[49,50,51,52,53,54,55,56,57],62]...: 19*it(49)+0 2.39/2.39 with precondition: [Q=0,C1=3,B>=A,H>=C] 2.39/2.39 2.39/2.39 * Chain [[49,50,51,52,53,54,55,56,57],61]: 17*it(49)+0 2.39/2.39 with precondition: [Q=0,C1=3,H>=C] 2.39/2.39 2.39/2.39 * Chain [[49,50,51,52,53,54,55,56,57],60]: 19*it(49)+0 2.39/2.39 with precondition: [Q=0,C1=3,B>=A,H>=C] 2.39/2.39 2.39/2.39 * Chain [[49,50,51,52,53,54,55,56,57],59]: 17*it(49)+0 2.39/2.39 with precondition: [Q=0,C1=3,H>=C] 2.39/2.39 2.39/2.39 * Chain [[49,50,51,52,53,54,55,56,57],58]: 17*it(49)+0 2.39/2.39 with precondition: [Q=0,C1=5,O1=0,H>=C,D1>=H+1] 2.39/2.39 2.39/2.39 * Chain [62]...: 2*s(16)+0 2.39/2.39 with precondition: [Q=0,C1=3,B>=A,H>=C] 2.39/2.39 2.39/2.39 * Chain [61]: 0 2.39/2.39 with precondition: [Q=0,C1=3] 2.39/2.39 2.39/2.39 * Chain [60]: 2*s(17)+0 2.39/2.39 with precondition: [Q=0,C1=3,B>=A,H>=C] 2.39/2.39 2.39/2.39 * Chain [59]: 0 2.39/2.39 with precondition: [Q=0,C1=3,H>=C] 2.39/2.39 2.39/2.39 * Chain [58]: 0 2.39/2.39 with precondition: [Q=0,C1=5,O1=0,E1=D,F1=E,G1=I,H1=J,I1=K,J1=L,K1=M,L1=N,M1=O,N1=P,C=D1,C>=H+1] 2.39/2.39 2.39/2.39 2.39/2.39 #### Cost of chains of f61(C1): 2.39/2.39 * Chain [[63]]...: 1*it(63)+0 2.39/2.39 with precondition: [C1=3] 2.39/2.39 2.39/2.39 * Chain [[63],64]: 1*it(63)+0 2.39/2.39 with precondition: [C1=3] 2.39/2.39 2.39/2.39 * Chain [64]: 0 2.39/2.39 with precondition: [C1=3] 2.39/2.39 2.39/2.39 2.39/2.39 #### Cost of chains of f36_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z): 2.39/2.39 * Chain [67]...: 1*s(25)+0 2.39/2.39 with precondition: [A=5,H=0] 2.39/2.39 2.39/2.39 * Chain [66]: 0 2.39/2.39 with precondition: [A=3,H=0] 2.39/2.39 2.39/2.39 * Chain [65]: 1*s(26)+0 2.39/2.39 with precondition: [A=5,H=0] 2.39/2.39 2.39/2.39 2.39/2.39 #### Cost of chains of f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,C1): 2.39/2.39 * Chain [71]: 1*aux(10)+0 2.39/2.39 with precondition: [] 2.39/2.39 2.39/2.39 * Chain [70]: 1*aux(11)+0 2.39/2.39 with precondition: [B>=A] 2.39/2.39 2.39/2.39 * Chain [69]...: 1*aux(12)+0 2.39/2.39 with precondition: [] 2.39/2.39 2.39/2.39 * Chain [68]...: 1*aux(13)+0 2.39/2.39 with precondition: [B>=A] 2.39/2.39 2.39/2.39 2.39/2.39 Closed-form bounds of f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,C1): 2.39/2.39 ------------------------------------- 2.39/2.39 * Chain [71] with precondition: [] 2.39/2.39 - Upper bound: inf 2.39/2.39 - Complexity: infinity 2.39/2.39 * Chain [70] with precondition: [B>=A] 2.39/2.39 - Upper bound: inf 2.39/2.39 - Complexity: infinity 2.39/2.39 * Chain [69]... with precondition: [] 2.39/2.39 - Upper bound: inf 2.39/2.39 - Complexity: infinity 2.39/2.39 * Chain [68]... with precondition: [B>=A] 2.39/2.39 - Upper bound: inf 2.39/2.39 - Complexity: infinity 2.39/2.39 2.39/2.39 ### Maximum cost of f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,C1): inf 2.39/2.39 Asymptotic class: infinity 2.39/2.39 * Total analysis performed in 2189 ms. 2.39/2.39 2.40/2.49 EOF