2.05/2.07 MAYBE 2.05/2.07 2.05/2.07 Preprocessing Cost Relations 2.05/2.07 ===================================== 2.05/2.07 2.05/2.07 #### Computed strongly connected components 2.05/2.07 0. recursive : [f13/37] 2.05/2.07 1. non_recursive : [exit_location/1] 2.05/2.07 2. recursive : [f54/1] 2.05/2.07 3. non_recursive : [f54_loop_cont/2] 2.05/2.07 4. non_recursive : [f47/24] 2.05/2.07 5. non_recursive : [f39/24] 2.05/2.07 6. non_recursive : [f13_loop_cont/25] 2.05/2.07 7. non_recursive : [f0/24] 2.05/2.07 2.05/2.07 #### Obtained direct recursion through partial evaluation 2.05/2.07 0. SCC is partially evaluated into f13/37 2.05/2.07 1. SCC is completely evaluated into other SCCs 2.05/2.07 2. SCC is partially evaluated into f54/1 2.05/2.07 3. SCC is completely evaluated into other SCCs 2.05/2.07 4. SCC is partially evaluated into f47/24 2.05/2.07 5. SCC is partially evaluated into f39/24 2.05/2.07 6. SCC is partially evaluated into f13_loop_cont/25 2.05/2.07 7. SCC is partially evaluated into f0/24 2.05/2.07 2.05/2.07 Control-Flow Refinement of Cost Relations 2.05/2.07 ===================================== 2.05/2.07 2.05/2.07 ### Specialization of cost equations f13/37 2.05/2.07 * CE 8 is refined into CE [19] 2.05/2.07 * CE 5 is refined into CE [20] 2.05/2.07 * CE 6 is refined into CE [21] 2.05/2.07 * CE 4 is refined into CE [22] 2.05/2.07 * CE 3 is refined into CE [23] 2.05/2.07 * CE 7 is refined into CE [24] 2.05/2.07 2.05/2.07 2.05/2.07 ### Cost equations --> "Loop" of f13/37 2.05/2.07 * CEs [24] --> Loop 18 2.05/2.07 * CEs [19] --> Loop 19 2.05/2.07 * CEs [20] --> Loop 20 2.05/2.07 * CEs [21] --> Loop 21 2.05/2.07 * CEs [22] --> Loop 22 2.05/2.07 * CEs [23] --> Loop 23 2.05/2.07 2.05/2.07 ### Ranking functions of CR f13(A,B,C,E,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1) 2.05/2.07 * RF of phase [18]: [-A+B] 2.05/2.07 2.05/2.07 #### Partial ranking functions of CR f13(A,B,C,E,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1) 2.05/2.07 * Partial RF of phase [18]: 2.05/2.07 - RF of loop [18:1]: 2.05/2.07 -A+B 2.05/2.07 2.05/2.07 2.05/2.07 ### Specialization of cost equations f54/1 2.05/2.07 * CE 18 is refined into CE [25] 2.05/2.07 * CE 17 is refined into CE [26] 2.05/2.07 2.05/2.07 2.05/2.07 ### Cost equations --> "Loop" of f54/1 2.05/2.07 * CEs [26] --> Loop 24 2.05/2.07 * CEs [25] --> Loop 25 2.05/2.07 2.05/2.07 ### Ranking functions of CR f54(C1) 2.05/2.07 2.05/2.07 #### Partial ranking functions of CR f54(C1) 2.05/2.07 2.05/2.07 2.05/2.07 ### Specialization of cost equations f47/24 2.05/2.07 * CE 12 is refined into CE [27,28] 2.05/2.07 * CE 13 is refined into CE [29,30] 2.05/2.07 2.05/2.07 2.05/2.07 ### Cost equations --> "Loop" of f47/24 2.05/2.07 * CEs [28] --> Loop 26 2.05/2.07 * CEs [30] --> Loop 27 2.05/2.07 * CEs [27] --> Loop 28 2.05/2.07 * CEs [29] --> Loop 29 2.05/2.07 2.05/2.07 ### Ranking functions of CR f47(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,C1) 2.05/2.07 2.05/2.07 #### Partial ranking functions of CR f47(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,C1) 2.05/2.07 2.05/2.07 2.05/2.07 ### Specialization of cost equations f39/24 2.05/2.07 * CE 14 is refined into CE [31,32,33,34] 2.05/2.07 * CE 15 is refined into CE [35,36,37,38] 2.05/2.07 * CE 16 is refined into CE [39,40,41,42] 2.05/2.07 2.05/2.07 2.05/2.07 ### Cost equations --> "Loop" of f39/24 2.05/2.07 * CEs [34] --> Loop 30 2.05/2.07 * CEs [33] --> Loop 31 2.05/2.07 * CEs [38] --> Loop 32 2.05/2.07 * CEs [37] --> Loop 33 2.05/2.07 * CEs [42] --> Loop 34 2.05/2.07 * CEs [41] --> Loop 35 2.05/2.07 * CEs [32] --> Loop 36 2.05/2.07 * CEs [31] --> Loop 37 2.05/2.07 * CEs [36] --> Loop 38 2.05/2.07 * CEs [35] --> Loop 39 2.05/2.07 * CEs [40] --> Loop 40 2.05/2.07 * CEs [39] --> Loop 41 2.05/2.07 2.05/2.07 ### Ranking functions of CR f39(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,C1) 2.05/2.07 2.05/2.07 #### Partial ranking functions of CR f39(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,C1) 2.05/2.07 2.05/2.07 2.05/2.07 ### Specialization of cost equations f13_loop_cont/25 2.05/2.07 * CE 11 is refined into CE [43] 2.05/2.07 * CE 10 is refined into CE [44,45,46,47,48,49,50,51,52,53,54,55] 2.05/2.07 * CE 9 is refined into CE [56,57,58,59] 2.05/2.07 2.05/2.07 2.05/2.07 ### Cost equations --> "Loop" of f13_loop_cont/25 2.05/2.07 * CEs [55] --> Loop 42 2.05/2.07 * CEs [54] --> Loop 43 2.05/2.07 * CEs [53] --> Loop 44 2.05/2.07 * CEs [52] --> Loop 45 2.05/2.07 * CEs [51] --> Loop 46 2.05/2.07 * CEs [50] --> Loop 47 2.05/2.07 * CEs [59] --> Loop 48 2.05/2.07 * CEs [58] --> Loop 49 2.05/2.07 * CEs [43] --> Loop 50 2.05/2.07 * CEs [49] --> Loop 51 2.05/2.07 * CEs [48] --> Loop 52 2.05/2.07 * CEs [47] --> Loop 53 2.05/2.07 * CEs [46] --> Loop 54 2.05/2.07 * CEs [45] --> Loop 55 2.05/2.07 * CEs [44] --> Loop 56 2.05/2.07 * CEs [57] --> Loop 57 2.05/2.07 * CEs [56] --> Loop 58 2.05/2.07 2.05/2.07 ### 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,X,Y) 2.05/2.07 2.05/2.07 #### 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,X,Y) 2.05/2.07 2.05/2.07 2.05/2.07 ### Specialization of cost equations f0/24 2.05/2.07 * 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] 2.05/2.07 * 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] 2.05/2.07 2.05/2.07 2.05/2.07 ### Cost equations --> "Loop" of f0/24 2.05/2.07 * CEs [66,88] --> Loop 59 2.05/2.07 * CEs [62,74,76,77,84,96,98,99] --> Loop 60 2.05/2.07 * CEs [60,64,68,70,71,81,82,86,90,92,93,103] --> Loop 61 2.05/2.07 * CEs [80,102] --> Loop 62 2.05/2.07 * CEs [67,89] --> Loop 63 2.05/2.07 * CEs [63,75,78,79,85,97,100,101] --> Loop 64 2.05/2.07 * CEs [61,65,69,72,73,83,87,91,94,95] --> Loop 65 2.05/2.07 2.05/2.07 ### 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,C1) 2.05/2.07 2.05/2.07 #### 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,C1) 2.05/2.07 2.05/2.07 2.05/2.07 Computing Bounds 2.05/2.07 ===================================== 2.05/2.07 2.05/2.07 #### Cost of chains of f13(A,B,C,E,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1): 2.05/2.07 * Chain [[18],23]: 1*it(18)+0 2.05/2.07 Such that:it(18) =< -A+B 2.05/2.07 2.05/2.07 with precondition: [C1=2,E1=1,Q1=1,R1=1,S1=1,T1=0,B=D1,E=J1,F1=K1,F1=L1,F1=M1,F1=N1,R=O1,R=P1,0>=F1,B>=A+1] 2.05/2.07 2.05/2.07 * Chain [[18],22]: 1*it(18)+0 2.05/2.07 Such that:it(18) =< -A+D1 2.05/2.07 2.05/2.07 with precondition: [C1=2,E1=1,Q1=1,R1=1,S1=1,T1=0,E=J1,F1=K1,F1=L1,F1=M1,R=O1,R=P1,0>=N1,F1>=1,D1>=A+1,B>=D1+1] 2.05/2.07 2.05/2.07 * Chain [[18],21]: 1*it(18)+0 2.05/2.07 Such that:it(18) =< -A+D1 2.05/2.07 2.05/2.07 with precondition: [C1=3,P1=0,T1=0,E=J1,F1=K1,F1=L1,F1=M1,F1=N1,R=O1,E1=Q1,E1=R1,E1=S1,0>=E1,0>=F1,D1>=A+1,B>=D1+1] 2.05/2.07 2.05/2.07 * Chain [[18],20]: 1*it(18)+0 2.05/2.07 Such that:it(18) =< -A+D1 2.05/2.07 2.05/2.07 with precondition: [C1=3,P1=0,T1=0,E=J1,F1=K1,F1=L1,F1=M1,F1=N1,R=O1,E1=Q1,E1=R1,E1=S1,0>=F1,E1>=2,D1>=A+1,B>=D1+1] 2.05/2.07 2.05/2.07 * Chain [[18],19]: 1*it(18)+0 2.05/2.07 Such that:it(18) =< -A+B 2.05/2.07 2.05/2.07 with precondition: [C1=4,B>=A+1] 2.05/2.07 2.05/2.07 * Chain [23]: 0 2.05/2.07 with precondition: [C1=2,E1=C,F1=H,G1=I,H1=J,I1=K,J1=L,K1=M,L1=N,M1=O,N1=P,O1=Q,P1=R,Q1=S,R1=T,S1=U,T1=V,A=D1,A>=B] 2.05/2.07 2.05/2.07 * Chain [22]: 0 2.05/2.07 with precondition: [C1=2,E1=C,J1=E,N1=P,O1=Q,P1=R,Q1=S,R1=T,S1=U,T1=V,A=D1,F1=K1,F1=L1,F1=M1,F1>=1,B>=A+1] 2.05/2.07 2.05/2.07 * Chain [21]: 0 2.05/2.07 with precondition: [C1=3,P1=0,T1=0,J1=E,O1=R,A=D1,F1=K1,F1=L1,F1=M1,F1=N1,E1=Q1,E1=R1,E1=S1,0>=E1,0>=F1,B>=A+1] 2.05/2.07 2.05/2.07 * Chain [20]: 0 2.05/2.07 with precondition: [C1=3,P1=0,T1=0,J1=E,O1=R,A=D1,F1=K1,F1=L1,F1=M1,F1=N1,E1=Q1,E1=R1,E1=S1,0>=F1,E1>=2,B>=A+1] 2.05/2.07 2.05/2.07 * Chain [19]: 0 2.05/2.07 with precondition: [C1=4] 2.05/2.07 2.05/2.07 2.05/2.07 #### Cost of chains of f54(C1): 2.05/2.07 * Chain [[24]]...: 1*it(24)+0 2.05/2.07 with precondition: [C1=4] 2.05/2.07 2.05/2.07 * Chain [[24],25]: 1*it(24)+0 2.05/2.07 with precondition: [C1=4] 2.05/2.07 2.05/2.07 * Chain [25]: 0 2.05/2.07 with precondition: [C1=4] 2.05/2.07 2.05/2.07 2.05/2.07 #### Cost of chains of f47(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,C1): 2.05/2.07 * Chain [29]: 1*s(2)+0 2.05/2.07 with precondition: [F=0,W=0,0>=D] 2.05/2.07 2.05/2.07 * Chain [28]: 1*s(3)+0 2.05/2.07 with precondition: [F=0,W=0,D>=1] 2.05/2.07 2.05/2.07 * Chain [27]...: 1*s(4)+0 2.05/2.07 with precondition: [F=0,W=0,0>=D] 2.05/2.07 2.05/2.07 * Chain [26]...: 1*s(5)+0 2.05/2.07 with precondition: [F=0,W=0,D>=1] 2.05/2.07 2.05/2.07 2.05/2.07 #### Cost of chains of f39(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,C1): 2.05/2.07 * Chain [41]: 1*s(6)+0 2.05/2.07 with precondition: [C=2,F=0,W=0,0>=D] 2.05/2.07 2.05/2.07 * Chain [40]: 1*s(7)+0 2.05/2.07 with precondition: [C=2,F=0,W=0,D>=1] 2.05/2.07 2.05/2.07 * Chain [39]: 1*s(8)+0 2.05/2.07 with precondition: [F=0,W=0,1>=C,0>=D] 2.05/2.07 2.05/2.07 * Chain [38]: 1*s(9)+0 2.05/2.07 with precondition: [F=0,W=0,1>=C,D>=1] 2.05/2.07 2.05/2.07 * Chain [37]: 1*s(10)+0 2.05/2.07 with precondition: [F=0,W=0,0>=D,C>=3] 2.05/2.07 2.05/2.07 * Chain [36]: 1*s(11)+0 2.05/2.07 with precondition: [F=0,W=0,C>=3,D>=1] 2.05/2.07 2.05/2.07 * Chain [35]...: 1*s(12)+0 2.05/2.07 with precondition: [C=2,F=0,W=0,0>=D] 2.05/2.07 2.05/2.07 * Chain [34]...: 1*s(13)+0 2.05/2.07 with precondition: [C=2,F=0,W=0,D>=1] 2.05/2.07 2.05/2.07 * Chain [33]...: 1*s(14)+0 2.05/2.07 with precondition: [F=0,W=0,1>=C,0>=D] 2.05/2.07 2.05/2.07 * Chain [32]...: 1*s(15)+0 2.05/2.07 with precondition: [F=0,W=0,1>=C,D>=1] 2.05/2.07 2.05/2.07 * Chain [31]...: 1*s(16)+0 2.05/2.07 with precondition: [F=0,W=0,0>=D,C>=3] 2.05/2.07 2.05/2.07 * Chain [30]...: 1*s(17)+0 2.05/2.07 with precondition: [F=0,W=0,C>=3,D>=1] 2.05/2.07 2.05/2.07 2.05/2.07 #### 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,X,Y): 2.05/2.07 * Chain [58]: 1*s(18)+0 2.05/2.07 with precondition: [A=2,G=0,X=0,0>=E] 2.05/2.07 2.05/2.07 * Chain [57]: 1*s(19)+0 2.05/2.07 with precondition: [A=2,G=0,X=0,E>=1] 2.05/2.07 2.05/2.07 * Chain [56]: 1*s(20)+0 2.05/2.07 with precondition: [A=3,D=2,G=0,X=0,0>=E] 2.05/2.07 2.05/2.07 * Chain [55]: 1*s(21)+0 2.05/2.07 with precondition: [A=3,D=2,G=0,X=0,E>=1] 2.05/2.07 2.05/2.07 * Chain [54]: 1*s(22)+0 2.05/2.07 with precondition: [A=3,G=0,X=0,1>=D,0>=E] 2.05/2.07 2.05/2.07 * Chain [53]: 1*s(23)+0 2.05/2.07 with precondition: [A=3,G=0,X=0,1>=D,E>=1] 2.05/2.07 2.05/2.07 * Chain [52]: 1*s(24)+0 2.05/2.07 with precondition: [A=3,G=0,X=0,0>=E,D>=3] 2.05/2.07 2.05/2.07 * Chain [51]: 1*s(25)+0 2.05/2.07 with precondition: [A=3,G=0,X=0,D>=3,E>=1] 2.05/2.07 2.05/2.07 * Chain [50]: 0 2.05/2.07 with precondition: [A=4,G=0,X=0] 2.05/2.07 2.05/2.07 * Chain [49]...: 1*s(26)+0 2.05/2.07 with precondition: [A=2,G=0,X=0,0>=E] 2.05/2.07 2.05/2.07 * Chain [48]...: 1*s(27)+0 2.05/2.07 with precondition: [A=2,G=0,X=0,E>=1] 2.05/2.07 2.05/2.07 * Chain [47]...: 1*s(28)+0 2.05/2.07 with precondition: [A=3,D=2,G=0,X=0,0>=E] 2.05/2.07 2.05/2.07 * Chain [46]...: 1*s(29)+0 2.05/2.07 with precondition: [A=3,D=2,G=0,X=0,E>=1] 2.05/2.07 2.05/2.07 * Chain [45]...: 1*s(30)+0 2.05/2.07 with precondition: [A=3,G=0,X=0,1>=D,0>=E] 2.05/2.07 2.05/2.07 * Chain [44]...: 1*s(31)+0 2.05/2.07 with precondition: [A=3,G=0,X=0,1>=D,E>=1] 2.05/2.07 2.05/2.07 * Chain [43]...: 1*s(32)+0 2.05/2.07 with precondition: [A=3,G=0,X=0,0>=E,D>=3] 2.05/2.07 2.05/2.07 * Chain [42]...: 1*s(33)+0 2.05/2.07 with precondition: [A=3,G=0,X=0,D>=3,E>=1] 2.05/2.07 2.05/2.07 2.05/2.07 #### 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,C1): 2.05/2.07 * Chain [65]...: 2*s(34)+10*s(35)+0 2.05/2.07 Such that:aux(2) =< -A+B 2.05/2.07 s(34) =< aux(2) 2.05/2.07 2.05/2.07 with precondition: [B>=A+1] 2.05/2.07 2.05/2.07 * Chain [64]...: 8*s(46)+8*s(47)+0 2.05/2.07 Such that:aux(3) =< -A+B 2.05/2.07 s(46) =< aux(3) 2.05/2.07 2.05/2.07 with precondition: [B>=A+2] 2.05/2.07 2.05/2.07 * Chain [63]...: 1*aux(4)+0 2.05/2.07 with precondition: [A>=B] 2.05/2.07 2.05/2.07 * Chain [62]: 0 2.05/2.07 with precondition: [] 2.05/2.07 2.05/2.07 * Chain [61]: 4*s(64)+10*s(65)+0 2.05/2.07 Such that:aux(5) =< -A+B 2.05/2.07 s(64) =< aux(5) 2.05/2.07 2.05/2.07 with precondition: [B>=A+1] 2.05/2.07 2.05/2.07 * Chain [60]: 8*s(78)+8*s(79)+0 2.05/2.07 Such that:aux(6) =< -A+B 2.05/2.07 s(78) =< aux(6) 2.05/2.07 2.05/2.07 with precondition: [B>=A+2] 2.05/2.07 2.05/2.07 * Chain [59]: 1*aux(7)+0 2.05/2.07 with precondition: [A>=B] 2.05/2.07 2.05/2.07 2.05/2.07 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,C1): 2.05/2.07 ------------------------------------- 2.05/2.07 * Chain [65]... with precondition: [B>=A+1] 2.05/2.07 - Upper bound: inf 2.05/2.07 - Complexity: infinity 2.05/2.07 * Chain [64]... with precondition: [B>=A+2] 2.05/2.07 - Upper bound: inf 2.05/2.07 - Complexity: infinity 2.05/2.07 * Chain [63]... with precondition: [A>=B] 2.05/2.07 - Upper bound: inf 2.05/2.07 - Complexity: infinity 2.05/2.07 * Chain [62] with precondition: [] 2.05/2.07 - Upper bound: 0 2.05/2.07 - Complexity: constant 2.05/2.07 * Chain [61] with precondition: [B>=A+1] 2.05/2.07 - Upper bound: inf 2.05/2.07 - Complexity: infinity 2.05/2.07 * Chain [60] with precondition: [B>=A+2] 2.05/2.07 - Upper bound: inf 2.05/2.07 - Complexity: infinity 2.05/2.07 * Chain [59] with precondition: [A>=B] 2.05/2.07 - Upper bound: inf 2.05/2.07 - Complexity: infinity 2.05/2.07 2.05/2.07 ### 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,C1): inf 2.05/2.07 Asymptotic class: infinity 2.05/2.07 * Total analysis performed in 1912 ms. 2.05/2.07 2.07/2.17 EOF