1.78/1.83 MAYBE 1.78/1.83 1.78/1.83 Preprocessing Cost Relations 1.78/1.83 ===================================== 1.78/1.83 1.78/1.83 #### Computed strongly connected components 1.78/1.83 0. recursive : [f13/33] 1.78/1.83 1. non_recursive : [exit_location/1] 1.78/1.83 2. recursive : [f52/1] 1.78/1.83 3. non_recursive : [f52_loop_cont/2] 1.78/1.83 4. non_recursive : [f45/22] 1.78/1.83 5. non_recursive : [f37/22] 1.78/1.83 6. non_recursive : [f13_loop_cont/23] 1.78/1.83 7. non_recursive : [f0/22] 1.78/1.83 1.78/1.83 #### Obtained direct recursion through partial evaluation 1.78/1.83 0. SCC is partially evaluated into f13/33 1.78/1.83 1. SCC is completely evaluated into other SCCs 1.78/1.83 2. SCC is partially evaluated into f52/1 1.78/1.83 3. SCC is completely evaluated into other SCCs 1.78/1.83 4. SCC is partially evaluated into f45/22 1.78/1.83 5. SCC is partially evaluated into f37/22 1.78/1.83 6. SCC is partially evaluated into f13_loop_cont/23 1.78/1.83 7. SCC is partially evaluated into f0/22 1.78/1.83 1.78/1.83 Control-Flow Refinement of Cost Relations 1.78/1.83 ===================================== 1.78/1.83 1.78/1.83 ### Specialization of cost equations f13/33 1.78/1.83 * CE 8 is refined into CE [19] 1.78/1.83 * CE 5 is refined into CE [20] 1.78/1.83 * CE 6 is refined into CE [21] 1.78/1.83 * CE 4 is refined into CE [22] 1.78/1.83 * CE 3 is refined into CE [23] 1.78/1.83 * CE 7 is refined into CE [24] 1.78/1.83 1.78/1.83 1.78/1.83 ### Cost equations --> "Loop" of f13/33 1.78/1.83 * CEs [24] --> Loop 18 1.78/1.83 * CEs [19] --> Loop 19 1.78/1.83 * CEs [20] --> Loop 20 1.78/1.83 * CEs [21] --> Loop 21 1.78/1.83 * CEs [22] --> Loop 22 1.78/1.83 * CEs [23] --> Loop 23 1.78/1.83 1.78/1.83 ### Ranking functions of CR f13(A,B,C,E,H,I,J,K,L,M,N,O,P,Q,R,S,T,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1,P1) 1.78/1.83 * RF of phase [18]: [-A+B] 1.78/1.83 1.78/1.83 #### Partial ranking functions of CR f13(A,B,C,E,H,I,J,K,L,M,N,O,P,Q,R,S,T,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1,P1) 1.78/1.83 * Partial RF of phase [18]: 1.78/1.83 - RF of loop [18:1]: 1.78/1.83 -A+B 1.78/1.83 1.78/1.83 1.78/1.83 ### Specialization of cost equations f52/1 1.78/1.83 * CE 18 is refined into CE [25] 1.78/1.83 * CE 17 is refined into CE [26] 1.78/1.83 1.78/1.83 1.78/1.83 ### Cost equations --> "Loop" of f52/1 1.78/1.83 * CEs [26] --> Loop 24 1.78/1.83 * CEs [25] --> Loop 25 1.78/1.83 1.78/1.83 ### Ranking functions of CR f52(A1) 1.78/1.83 1.78/1.83 #### Partial ranking functions of CR f52(A1) 1.78/1.83 1.78/1.83 1.78/1.83 ### Specialization of cost equations f45/22 1.78/1.83 * CE 12 is refined into CE [27,28] 1.78/1.83 * CE 13 is refined into CE [29,30] 1.78/1.83 1.78/1.83 1.78/1.83 ### Cost equations --> "Loop" of f45/22 1.78/1.83 * CEs [28] --> Loop 26 1.78/1.83 * CEs [30] --> Loop 27 1.78/1.83 * CEs [27] --> Loop 28 1.78/1.83 * CEs [29] --> Loop 29 1.78/1.83 1.78/1.83 ### Ranking functions of CR f45(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,A1) 1.78/1.83 1.78/1.83 #### Partial ranking functions of CR f45(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,A1) 1.78/1.83 1.78/1.83 1.78/1.83 ### Specialization of cost equations f37/22 1.78/1.83 * CE 14 is refined into CE [31,32,33,34] 1.78/1.83 * CE 15 is refined into CE [35,36,37,38] 1.78/1.83 * CE 16 is refined into CE [39,40,41,42] 1.78/1.83 1.78/1.83 1.78/1.83 ### Cost equations --> "Loop" of f37/22 1.78/1.83 * CEs [34] --> Loop 30 1.78/1.83 * CEs [33] --> Loop 31 1.78/1.83 * CEs [38] --> Loop 32 1.78/1.83 * CEs [37] --> Loop 33 1.78/1.83 * CEs [42] --> Loop 34 1.78/1.83 * CEs [41] --> Loop 35 1.78/1.83 * CEs [32] --> Loop 36 1.78/1.83 * CEs [31] --> Loop 37 1.78/1.83 * CEs [36] --> Loop 38 1.78/1.83 * CEs [35] --> Loop 39 1.78/1.83 * CEs [40] --> Loop 40 1.78/1.83 * CEs [39] --> Loop 41 1.78/1.83 1.78/1.83 ### Ranking functions of CR f37(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,A1) 1.78/1.83 1.78/1.83 #### Partial ranking functions of CR f37(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,A1) 1.78/1.83 1.78/1.83 1.78/1.83 ### Specialization of cost equations f13_loop_cont/23 1.78/1.83 * CE 11 is refined into CE [43] 1.78/1.83 * CE 10 is refined into CE [44,45,46,47,48,49,50,51,52,53,54,55] 1.78/1.83 * CE 9 is refined into CE [56,57,58,59] 1.78/1.83 1.78/1.83 1.78/1.83 ### Cost equations --> "Loop" of f13_loop_cont/23 1.78/1.83 * CEs [55] --> Loop 42 1.78/1.83 * CEs [54] --> Loop 43 1.78/1.83 * CEs [53] --> Loop 44 1.78/1.83 * CEs [52] --> Loop 45 1.78/1.83 * CEs [51] --> Loop 46 1.78/1.83 * CEs [50] --> Loop 47 1.78/1.83 * CEs [59] --> Loop 48 1.78/1.83 * CEs [58] --> Loop 49 1.78/1.83 * CEs [43] --> Loop 50 1.78/1.83 * CEs [49] --> Loop 51 1.78/1.83 * CEs [48] --> Loop 52 1.78/1.83 * CEs [47] --> Loop 53 1.78/1.83 * CEs [46] --> Loop 54 1.78/1.83 * CEs [45] --> Loop 55 1.78/1.83 * CEs [44] --> Loop 56 1.78/1.83 * CEs [57] --> Loop 57 1.78/1.83 * CEs [56] --> Loop 58 1.78/1.83 1.78/1.83 ### Ranking functions of CR f13_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) 1.78/1.83 1.78/1.83 #### Partial ranking functions of CR f13_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) 1.78/1.83 1.78/1.83 1.78/1.83 ### Specialization of cost equations f0/22 1.78/1.83 * CE 1 is refined into CE [60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81] 1.78/1.83 * CE 2 is refined into CE [82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103] 1.78/1.83 1.78/1.83 1.78/1.83 ### Cost equations --> "Loop" of f0/22 1.78/1.83 * CEs [66,88] --> Loop 59 1.78/1.83 * CEs [62,74,76,77,84,96,98,99] --> Loop 60 1.78/1.83 * CEs [60,64,68,70,71,81,82,86,90,92,93,103] --> Loop 61 1.78/1.83 * CEs [80,102] --> Loop 62 1.78/1.83 * CEs [67,89] --> Loop 63 1.78/1.83 * CEs [63,75,78,79,85,97,100,101] --> Loop 64 1.78/1.83 * CEs [61,65,69,72,73,83,87,91,94,95] --> Loop 65 1.78/1.83 1.78/1.83 ### 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,A1) 1.78/1.83 1.78/1.83 #### 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,A1) 1.78/1.83 1.78/1.83 1.78/1.83 Computing Bounds 1.78/1.83 ===================================== 1.78/1.83 1.78/1.83 #### Cost of chains of f13(A,B,C,E,H,I,J,K,L,M,N,O,P,Q,R,S,T,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1,P1): 1.78/1.83 * Chain [[18],23]: 1*it(18)+0 1.78/1.83 Such that:it(18) =< -A+B 1.78/1.83 1.78/1.83 with precondition: [A1=2,C1=1,N1=1,O1=1,P1=0,B=B1,E=H1,D1=I1,D1=J1,D1=K1,Q=L1,Q=M1,0>=D1,B>=A+1] 1.78/1.83 1.78/1.83 * Chain [[18],22]: 1*it(18)+0 1.78/1.83 Such that:it(18) =< -A+B1 1.78/1.83 1.78/1.83 with precondition: [A1=2,C1=1,N1=1,O1=1,P1=0,E=H1,D1=I1,D1=J1,Q=L1,Q=M1,0>=K1,D1>=1,B1>=A+1,B>=B1+1] 1.78/1.83 1.78/1.83 * Chain [[18],21]: 1*it(18)+0 1.78/1.83 Such that:it(18) =< -A+B1 1.78/1.83 1.78/1.83 with precondition: [A1=3,M1=0,P1=0,E=H1,D1=I1,D1=J1,D1=K1,Q=L1,C1=N1,C1=O1,0>=C1,0>=D1,B1>=A+1,B>=B1+1] 1.78/1.83 1.78/1.83 * Chain [[18],20]: 1*it(18)+0 1.78/1.83 Such that:it(18) =< -A+B1 1.78/1.83 1.78/1.83 with precondition: [A1=3,M1=0,P1=0,E=H1,D1=I1,D1=J1,D1=K1,Q=L1,C1=N1,C1=O1,0>=D1,C1>=2,B1>=A+1,B>=B1+1] 1.78/1.83 1.78/1.83 * Chain [[18],19]: 1*it(18)+0 1.78/1.83 Such that:it(18) =< -A+B 1.78/1.83 1.78/1.83 with precondition: [A1=4,B>=A+1] 1.78/1.83 1.78/1.83 * Chain [23]: 0 1.78/1.83 with precondition: [A1=2,C1=C,D1=H,E1=I,F1=J,G1=K,H1=L,I1=M,J1=N,K1=O,L1=P,M1=Q,N1=R,O1=S,P1=T,A=B1,A>=B] 1.78/1.83 1.78/1.83 * Chain [22]: 0 1.78/1.83 with precondition: [A1=2,C1=C,H1=E,K1=O,L1=P,M1=Q,N1=R,O1=S,P1=T,A=B1,D1=I1,D1=J1,D1>=1,B>=A+1] 1.78/1.83 1.78/1.83 * Chain [21]: 0 1.78/1.83 with precondition: [A1=3,M1=0,P1=0,H1=E,L1=Q,A=B1,D1=I1,D1=J1,D1=K1,C1=N1,C1=O1,0>=C1,0>=D1,B>=A+1] 1.78/1.83 1.78/1.83 * Chain [20]: 0 1.78/1.83 with precondition: [A1=3,M1=0,P1=0,H1=E,L1=Q,A=B1,D1=I1,D1=J1,D1=K1,C1=N1,C1=O1,0>=D1,C1>=2,B>=A+1] 1.78/1.83 1.78/1.83 * Chain [19]: 0 1.78/1.83 with precondition: [A1=4] 1.78/1.83 1.78/1.83 1.78/1.83 #### Cost of chains of f52(A1): 1.78/1.83 * Chain [[24]]...: 1*it(24)+0 1.78/1.83 with precondition: [A1=4] 1.78/1.83 1.78/1.83 * Chain [[24],25]: 1*it(24)+0 1.78/1.83 with precondition: [A1=4] 1.78/1.83 1.78/1.83 * Chain [25]: 0 1.78/1.83 with precondition: [A1=4] 1.78/1.83 1.78/1.83 1.78/1.83 #### Cost of chains of f45(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,A1): 1.78/1.83 * Chain [29]: 1*s(2)+0 1.78/1.83 with precondition: [F=0,U=0,0>=D] 1.78/1.83 1.78/1.83 * Chain [28]: 1*s(3)+0 1.78/1.83 with precondition: [F=0,U=0,D>=1] 1.78/1.83 1.78/1.83 * Chain [27]...: 1*s(4)+0 1.78/1.83 with precondition: [F=0,U=0,0>=D] 1.78/1.83 1.78/1.83 * Chain [26]...: 1*s(5)+0 1.78/1.83 with precondition: [F=0,U=0,D>=1] 1.78/1.83 1.78/1.83 1.78/1.83 #### Cost of chains of f37(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,A1): 1.78/1.83 * Chain [41]: 1*s(6)+0 1.78/1.83 with precondition: [C=2,F=0,U=0,0>=D] 1.78/1.83 1.78/1.83 * Chain [40]: 1*s(7)+0 1.78/1.83 with precondition: [C=2,F=0,U=0,D>=1] 1.78/1.83 1.78/1.83 * Chain [39]: 1*s(8)+0 1.78/1.83 with precondition: [F=0,U=0,1>=C,0>=D] 1.78/1.83 1.78/1.83 * Chain [38]: 1*s(9)+0 1.78/1.83 with precondition: [F=0,U=0,1>=C,D>=1] 1.78/1.83 1.78/1.83 * Chain [37]: 1*s(10)+0 1.78/1.83 with precondition: [F=0,U=0,0>=D,C>=3] 1.78/1.83 1.78/1.83 * Chain [36]: 1*s(11)+0 1.78/1.83 with precondition: [F=0,U=0,C>=3,D>=1] 1.78/1.83 1.78/1.83 * Chain [35]...: 1*s(12)+0 1.78/1.83 with precondition: [C=2,F=0,U=0,0>=D] 1.78/1.83 1.78/1.83 * Chain [34]...: 1*s(13)+0 1.78/1.83 with precondition: [C=2,F=0,U=0,D>=1] 1.78/1.83 1.78/1.83 * Chain [33]...: 1*s(14)+0 1.78/1.83 with precondition: [F=0,U=0,1>=C,0>=D] 1.78/1.83 1.78/1.83 * Chain [32]...: 1*s(15)+0 1.78/1.83 with precondition: [F=0,U=0,1>=C,D>=1] 1.78/1.83 1.78/1.83 * Chain [31]...: 1*s(16)+0 1.78/1.83 with precondition: [F=0,U=0,0>=D,C>=3] 1.78/1.83 1.78/1.83 * Chain [30]...: 1*s(17)+0 1.78/1.83 with precondition: [F=0,U=0,C>=3,D>=1] 1.78/1.83 1.78/1.83 1.78/1.83 #### Cost of chains of f13_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): 1.78/1.83 * Chain [58]: 1*s(18)+0 1.78/1.83 with precondition: [A=2,G=0,V=0,0>=E] 1.78/1.83 1.78/1.83 * Chain [57]: 1*s(19)+0 1.78/1.83 with precondition: [A=2,G=0,V=0,E>=1] 1.78/1.83 1.78/1.83 * Chain [56]: 1*s(20)+0 1.78/1.83 with precondition: [A=3,D=2,G=0,V=0,0>=E] 1.78/1.83 1.78/1.83 * Chain [55]: 1*s(21)+0 1.78/1.83 with precondition: [A=3,D=2,G=0,V=0,E>=1] 1.78/1.83 1.78/1.83 * Chain [54]: 1*s(22)+0 1.78/1.83 with precondition: [A=3,G=0,V=0,1>=D,0>=E] 1.78/1.83 1.78/1.83 * Chain [53]: 1*s(23)+0 1.78/1.83 with precondition: [A=3,G=0,V=0,1>=D,E>=1] 1.78/1.83 1.78/1.83 * Chain [52]: 1*s(24)+0 1.78/1.83 with precondition: [A=3,G=0,V=0,0>=E,D>=3] 1.78/1.83 1.78/1.83 * Chain [51]: 1*s(25)+0 1.78/1.83 with precondition: [A=3,G=0,V=0,D>=3,E>=1] 1.78/1.83 1.78/1.83 * Chain [50]: 0 1.78/1.83 with precondition: [A=4,G=0,V=0] 1.78/1.83 1.78/1.83 * Chain [49]...: 1*s(26)+0 1.78/1.83 with precondition: [A=2,G=0,V=0,0>=E] 1.78/1.83 1.78/1.83 * Chain [48]...: 1*s(27)+0 1.78/1.83 with precondition: [A=2,G=0,V=0,E>=1] 1.78/1.83 1.78/1.83 * Chain [47]...: 1*s(28)+0 1.78/1.83 with precondition: [A=3,D=2,G=0,V=0,0>=E] 1.78/1.83 1.78/1.83 * Chain [46]...: 1*s(29)+0 1.78/1.83 with precondition: [A=3,D=2,G=0,V=0,E>=1] 1.78/1.83 1.78/1.83 * Chain [45]...: 1*s(30)+0 1.78/1.83 with precondition: [A=3,G=0,V=0,1>=D,0>=E] 1.78/1.83 1.78/1.83 * Chain [44]...: 1*s(31)+0 1.78/1.83 with precondition: [A=3,G=0,V=0,1>=D,E>=1] 1.78/1.83 1.78/1.83 * Chain [43]...: 1*s(32)+0 1.78/1.83 with precondition: [A=3,G=0,V=0,0>=E,D>=3] 1.78/1.83 1.78/1.83 * Chain [42]...: 1*s(33)+0 1.78/1.83 with precondition: [A=3,G=0,V=0,D>=3,E>=1] 1.78/1.83 1.78/1.83 1.78/1.83 #### 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,A1): 1.78/1.83 * Chain [65]...: 2*s(34)+10*s(35)+0 1.78/1.83 Such that:aux(2) =< -A+B 1.78/1.83 s(34) =< aux(2) 1.78/1.83 1.78/1.83 with precondition: [B>=A+1] 1.78/1.83 1.78/1.83 * Chain [64]...: 8*s(46)+8*s(47)+0 1.78/1.83 Such that:aux(3) =< -A+B 1.78/1.83 s(46) =< aux(3) 1.78/1.83 1.78/1.83 with precondition: [B>=A+2] 1.78/1.83 1.78/1.83 * Chain [63]...: 1*aux(4)+0 1.78/1.83 with precondition: [A>=B] 1.78/1.83 1.78/1.83 * Chain [62]: 0 1.78/1.83 with precondition: [] 1.78/1.83 1.78/1.83 * Chain [61]: 4*s(64)+10*s(65)+0 1.78/1.83 Such that:aux(5) =< -A+B 1.78/1.83 s(64) =< aux(5) 1.78/1.83 1.78/1.83 with precondition: [B>=A+1] 1.78/1.83 1.78/1.83 * Chain [60]: 8*s(78)+8*s(79)+0 1.78/1.83 Such that:aux(6) =< -A+B 1.78/1.83 s(78) =< aux(6) 1.78/1.83 1.78/1.83 with precondition: [B>=A+2] 1.78/1.83 1.78/1.83 * Chain [59]: 1*aux(7)+0 1.78/1.83 with precondition: [A>=B] 1.78/1.83 1.78/1.83 1.78/1.83 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,A1): 1.78/1.83 ------------------------------------- 1.78/1.83 * Chain [65]... with precondition: [B>=A+1] 1.78/1.83 - Upper bound: inf 1.78/1.83 - Complexity: infinity 1.78/1.83 * Chain [64]... with precondition: [B>=A+2] 1.78/1.83 - Upper bound: inf 1.78/1.83 - Complexity: infinity 1.78/1.83 * Chain [63]... with precondition: [A>=B] 1.78/1.83 - Upper bound: inf 1.78/1.83 - Complexity: infinity 1.78/1.83 * Chain [62] with precondition: [] 1.78/1.83 - Upper bound: 0 1.78/1.83 - Complexity: constant 1.78/1.83 * Chain [61] with precondition: [B>=A+1] 1.78/1.83 - Upper bound: inf 1.78/1.83 - Complexity: infinity 1.78/1.83 * Chain [60] with precondition: [B>=A+2] 1.78/1.83 - Upper bound: inf 1.78/1.83 - Complexity: infinity 1.78/1.83 * Chain [59] with precondition: [A>=B] 1.78/1.83 - Upper bound: inf 1.78/1.83 - Complexity: infinity 1.78/1.83 1.78/1.83 ### 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,A1): inf 1.78/1.83 Asymptotic class: infinity 1.78/1.83 * Total analysis performed in 1685 ms. 1.78/1.83 1.83/1.93 EOF