1.62/1.69 MAYBE 1.62/1.69 1.62/1.69 Preprocessing Cost Relations 1.62/1.69 ===================================== 1.62/1.69 1.62/1.69 #### Computed strongly connected components 1.62/1.69 0. recursive : [f1/29] 1.62/1.69 1. non_recursive : [f10/51] 1.62/1.69 2. non_recursive : [exit_location/1] 1.62/1.69 3. recursive : [f116/36] 1.62/1.69 4. non_recursive : [f300/51] 1.62/1.69 5. recursive : [f8/25] 1.62/1.69 6. non_recursive : [f8_loop_cont/52] 1.62/1.69 7. non_recursive : [f116_loop_cont/52] 1.62/1.69 8. non_recursive : [f1_loop_cont/52] 1.62/1.69 9. non_recursive : [f9/51] 1.62/1.69 1.62/1.69 #### Obtained direct recursion through partial evaluation 1.62/1.69 0. SCC is partially evaluated into f1/29 1.62/1.69 1. SCC is completely evaluated into other SCCs 1.62/1.69 2. SCC is completely evaluated into other SCCs 1.62/1.69 3. SCC is partially evaluated into f116/36 1.62/1.69 4. SCC is completely evaluated into other SCCs 1.62/1.69 5. SCC is partially evaluated into f8/25 1.62/1.69 6. SCC is partially evaluated into f8_loop_cont/52 1.62/1.69 7. SCC is partially evaluated into f116_loop_cont/52 1.62/1.69 8. SCC is partially evaluated into f1_loop_cont/52 1.62/1.69 9. SCC is partially evaluated into f9/51 1.62/1.69 1.62/1.69 Control-Flow Refinement of Cost Relations 1.62/1.69 ===================================== 1.62/1.69 1.62/1.69 ### Specialization of cost equations f1/29 1.62/1.69 * CE 5 is refined into CE [20] 1.62/1.69 * CE 4 is refined into CE [21] 1.62/1.69 * CE 3 is refined into CE [22] 1.62/1.69 1.62/1.69 1.62/1.69 ### Cost equations --> "Loop" of f1/29 1.62/1.69 * CEs [22] --> Loop 20 1.62/1.69 * CEs [20] --> Loop 21 1.62/1.69 * CEs [21] --> Loop 22 1.62/1.69 1.62/1.69 ### Ranking functions of CR f1(A,B,C,F,Q,R,S,T,U,V,W,X,Y,Z,A1,R2,S2,T2,U2,V2,W2,X2,Y2,Z2,A3,B3,C3,D3,E3) 1.62/1.69 * RF of phase [20]: [A-B,-B+Q] 1.62/1.69 1.62/1.69 #### Partial ranking functions of CR f1(A,B,C,F,Q,R,S,T,U,V,W,X,Y,Z,A1,R2,S2,T2,U2,V2,W2,X2,Y2,Z2,A3,B3,C3,D3,E3) 1.62/1.69 * Partial RF of phase [20]: 1.62/1.69 - RF of loop [20:1]: 1.62/1.69 A-B 1.62/1.69 -B+Q 1.62/1.69 1.62/1.69 1.62/1.69 ### Specialization of cost equations f116/36 1.62/1.69 * CE 11 is refined into CE [23] 1.62/1.69 * CE 8 is discarded (unfeasible) 1.62/1.69 * CE 10 is refined into CE [24] 1.62/1.69 * CE 9 is refined into CE [25] 1.62/1.69 1.62/1.69 1.62/1.69 ### Cost equations --> "Loop" of f116/36 1.62/1.69 * CEs [25] --> Loop 23 1.62/1.69 * CEs [23] --> Loop 24 1.62/1.69 * CEs [24] --> Loop 25 1.62/1.69 1.62/1.69 ### Ranking functions of CR f116(A,C,F,O,P,U,B1,C1,D1,G1,H1,I1,J1,L1,M1,N1,O1,P1,R2,S2,T2,U2,V2,W2,X2,Y2,Z2,A3,B3,C3,D3,E3,F3,G3,H3,I3) 1.62/1.69 1.62/1.69 #### Partial ranking functions of CR f116(A,C,F,O,P,U,B1,C1,D1,G1,H1,I1,J1,L1,M1,N1,O1,P1,R2,S2,T2,U2,V2,W2,X2,Y2,Z2,A3,B3,C3,D3,E3,F3,G3,H3,I3) 1.62/1.69 1.62/1.69 1.62/1.69 ### Specialization of cost equations f8/25 1.62/1.69 * CE 17 is refined into CE [26] 1.62/1.69 * CE 16 is refined into CE [27] 1.62/1.69 * CE 15 is refined into CE [28] 1.62/1.69 1.62/1.69 1.62/1.69 ### Cost equations --> "Loop" of f8/25 1.62/1.69 * CEs [28] --> Loop 26 1.62/1.69 * CEs [26] --> Loop 27 1.62/1.69 * CEs [27] --> Loop 28 1.62/1.69 1.62/1.69 ### Ranking functions of CR f8(A,U,V,Y,C1,D1,E1,G1,H1,I1,J1,K1,R2,S2,T2,U2,V2,W2,X2,Y2,Z2,A3,B3,C3,D3) 1.62/1.69 * RF of phase [26]: [E1+1] 1.62/1.69 1.62/1.69 #### Partial ranking functions of CR f8(A,U,V,Y,C1,D1,E1,G1,H1,I1,J1,K1,R2,S2,T2,U2,V2,W2,X2,Y2,Z2,A3,B3,C3,D3) 1.62/1.69 * Partial RF of phase [26]: 1.62/1.69 - RF of loop [26:1]: 1.62/1.69 E1+1 1.62/1.69 1.62/1.69 1.62/1.69 ### Specialization of cost equations f8_loop_cont/52 1.62/1.69 * CE 19 is refined into CE [29] 1.62/1.69 * CE 18 is refined into CE [30] 1.62/1.69 1.62/1.69 1.62/1.69 ### Cost equations --> "Loop" of f8_loop_cont/52 1.62/1.69 * CEs [29] --> Loop 29 1.62/1.69 * CEs [30] --> Loop 30 1.62/1.69 1.62/1.69 ### Ranking functions of CR f8_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,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1,V1,W1,X1,Y1,Z1) 1.62/1.69 1.62/1.69 #### Partial ranking functions of CR f8_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,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1,V1,W1,X1,Y1,Z1) 1.62/1.69 1.62/1.69 1.62/1.69 ### Specialization of cost equations f116_loop_cont/52 1.62/1.69 * CE 14 is refined into CE [31,32,33,34] 1.62/1.69 * CE 12 is refined into CE [35] 1.62/1.69 * CE 13 is refined into CE [36] 1.62/1.69 1.62/1.69 1.62/1.69 ### Cost equations --> "Loop" of f116_loop_cont/52 1.62/1.69 * CEs [34] --> Loop 31 1.62/1.69 * CEs [33] --> Loop 32 1.62/1.69 * CEs [32] --> Loop 33 1.62/1.69 * CEs [31] --> Loop 34 1.62/1.69 * CEs [35] --> Loop 35 1.62/1.69 * CEs [36] --> Loop 36 1.62/1.69 1.62/1.69 ### Ranking functions of CR f116_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,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1,V1,W1,X1,Y1,Z1) 1.62/1.69 1.62/1.69 #### Partial ranking functions of CR f116_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,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1,V1,W1,X1,Y1,Z1) 1.62/1.69 1.62/1.69 1.62/1.69 ### Specialization of cost equations f1_loop_cont/52 1.62/1.69 * CE 7 is refined into CE [37,38,39,40,41,42] 1.62/1.69 * CE 6 is refined into CE [43] 1.62/1.69 1.62/1.69 1.62/1.69 ### Cost equations --> "Loop" of f1_loop_cont/52 1.62/1.69 * CEs [42] --> Loop 37 1.62/1.69 * CEs [41] --> Loop 38 1.62/1.69 * CEs [38,39] --> Loop 39 1.62/1.69 * CEs [40] --> Loop 40 1.62/1.69 * CEs [37] --> Loop 41 1.62/1.69 * CEs [43] --> Loop 42 1.62/1.69 1.62/1.69 ### Ranking functions of CR f1_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,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1,V1,W1,X1,Y1,Z1) 1.62/1.69 1.62/1.69 #### Partial ranking functions of CR f1_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,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1,V1,W1,X1,Y1,Z1) 1.62/1.69 1.62/1.69 1.62/1.69 ### Specialization of cost equations f9/51 1.62/1.69 * CE 2 is refined into CE [44,45,46,47,48,49,50,51,52,53,54,55] 1.62/1.69 * CE 1 is refined into CE [56] 1.62/1.69 1.62/1.69 1.62/1.69 ### Cost equations --> "Loop" of f9/51 1.62/1.69 * CEs [54,55] --> Loop 43 1.62/1.69 * CEs [49] --> Loop 44 1.62/1.69 * CEs [51] --> Loop 45 1.62/1.69 * CEs [50,52,53] --> Loop 46 1.62/1.69 * CEs [48] --> Loop 47 1.62/1.69 * CEs [47] --> Loop 48 1.62/1.69 * CEs [44] --> Loop 49 1.62/1.69 * CEs [46] --> Loop 50 1.62/1.69 * CEs [45] --> Loop 51 1.62/1.69 * CEs [56] --> Loop 52 1.62/1.69 1.62/1.69 ### Ranking functions of CR f9(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,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1,V1,W1,X1,R2) 1.62/1.69 1.62/1.69 #### Partial ranking functions of CR f9(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,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1,V1,W1,X1,R2) 1.62/1.69 1.62/1.69 1.62/1.69 Computing Bounds 1.62/1.69 ===================================== 1.62/1.69 1.62/1.69 #### Cost of chains of f1(A,B,C,F,Q,R,S,T,U,V,W,X,Y,Z,A1,R2,S2,T2,U2,V2,W2,X2,Y2,Z2,A3,B3,C3,D3,E3): 1.62/1.69 * Chain [[20],22]: 1*it(20)+0 1.62/1.69 Such that:it(20) =< A-B 1.62/1.69 1.62/1.69 with precondition: [C=0,R2=6,T2=0,A=Q,R=T,Y2=Z2,S2=D3,B>=2,F>=A,E3>=A,A>=B+1] 1.62/1.69 1.62/1.69 * Chain [[20],21]: 1*it(20)+0 1.62/1.69 Such that:it(20) =< -B+Q 1.62/1.69 1.62/1.69 with precondition: [R2=3,A=Q,R=T,B>=2,A>=B+1] 1.62/1.69 1.62/1.69 * Chain [22]: 0 1.62/1.69 with precondition: [C=0,R2=6,T2=0,A=B,A=Q,T=R,D3=S2,T=Y2,T=Z2,A>=2,F>=A,E3>=A] 1.62/1.69 1.62/1.69 * Chain [21]: 0 1.62/1.69 with precondition: [R2=3,Q=A,T=R,B>=2,Q>=B] 1.62/1.69 1.62/1.69 1.62/1.69 #### Cost of chains of f116(A,C,F,O,P,U,B1,C1,D1,G1,H1,I1,J1,L1,M1,N1,O1,P1,R2,S2,T2,U2,V2,W2,X2,Y2,Z2,A3,B3,C3,D3,E3,F3,G3,H3,I3): 1.62/1.69 * Chain [25]: 0 1.62/1.69 with precondition: [P=0,U=0,R2=5,V2=1,W2=0,A3=0,C3=0,E3+1=0,F3=M1,G3=N1,H3=O1,X2+1=S2,F=T2,F=U2,Y2=Z2,Y2=B3,Y2=D3,A>=2,C>=0,F>=0,I3>=0] 1.62/1.69 1.62/1.69 * Chain [24]: 0 1.62/1.69 with precondition: [R2=3,1>=P,A>=2,P>=0] 1.62/1.69 1.62/1.69 * Chain [23,24]: 1 1.62/1.69 with precondition: [P=0,R2=3,U=M1,A>=2,C>=0,F>=0] 1.62/1.69 1.62/1.69 1.62/1.69 #### Cost of chains of f8(A,U,V,Y,C1,D1,E1,G1,H1,I1,J1,K1,R2,S2,T2,U2,V2,W2,X2,Y2,Z2,A3,B3,C3,D3): 1.62/1.69 * Chain [[26],28]: 1*it(26)+0 1.62/1.69 Such that:it(26) =< E1-Y2 1.62/1.69 1.62/1.69 with precondition: [U=0,D1=0,G1=0,I1=0,R2=2,T2=0,V=H1,V=J1,V=U2,Y2=D3,A>=2,Y2>=0,E1>=Y2+1] 1.62/1.69 1.62/1.69 * Chain [[26],27]: 1*it(26)+0 1.62/1.69 Such that:it(26) =< E1+1 1.62/1.69 1.62/1.69 with precondition: [U=0,G1=0,I1=0,R2=3,V=H1,V=J1,A>=2,E1>=0] 1.62/1.69 1.62/1.69 * Chain [28]: 0 1.62/1.69 with precondition: [R2=2,T2=U,U2=V,G1=D1,D3=K1,E1=Y2,A>=2,E1>=0] 1.62/1.69 1.62/1.69 * Chain [27]: 0 1.62/1.69 with precondition: [R2=3,A>=2] 1.62/1.69 1.62/1.69 1.62/1.69 #### Cost of chains of f8_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,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1,V1,W1,X1,Y1,Z1): 1.62/1.69 * Chain [30]: 0 1.62/1.69 with precondition: [A=2,U1=2] 1.62/1.69 1.62/1.69 * Chain [29]: 0 1.62/1.69 with precondition: [A=3,U1=2] 1.62/1.69 1.62/1.69 1.62/1.69 #### Cost of chains of f116_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,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1,V1,W1,X1,Y1,Z1): 1.62/1.69 * Chain [36]: 0 1.62/1.69 with precondition: [A=3,U1=2,B>=2] 1.62/1.69 1.62/1.69 * Chain [35]: 0 1.62/1.69 with precondition: [A=4,U1=2,B>=2] 1.62/1.69 1.62/1.69 * Chain [34]: 1*s(1)+0 1.62/1.69 Such that:s(1) =< F1 1.62/1.69 1.62/1.69 with precondition: [A=5,V=0,E1=0,H1=0,J1=0,U1=2,W=I1,W=K1,B>=2,F1>=1] 1.62/1.69 1.62/1.69 * Chain [33]: 1*s(2)+0 1.62/1.69 Such that:s(2) =< F1+1 1.62/1.69 1.62/1.69 with precondition: [A=5,V=0,H1=0,J1=0,U1=2,W=I1,W=K1,B>=2,F1>=0] 1.62/1.69 1.62/1.69 * Chain [32]: 0 1.62/1.69 with precondition: [A=5,U1=2,H1=E1,B>=2,F1>=0] 1.62/1.69 1.62/1.69 * Chain [31]: 0 1.62/1.69 with precondition: [A=5,U1=2,B>=2] 1.62/1.69 1.62/1.69 1.62/1.69 #### Cost of chains of f1_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,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1,V1,W1,X1,Y1,Z1): 1.62/1.69 * Chain [42]: 0 1.62/1.69 with precondition: [A=3,Q=0,U1=2,B>=2] 1.62/1.69 1.62/1.69 * Chain [41]: 1*s(3)+0 1.62/1.69 Such that:s(3) =< F1 1.62/1.69 1.62/1.69 with precondition: [A=6,Q=0,V=0,W=0,U1=2,B>=2,D>=0,G>=0,F1>=1] 1.62/1.69 1.62/1.69 * Chain [40]: 0 1.62/1.69 with precondition: [A=6,Q=0,V=0,U1=2,B>=2,D>=0,G>=0] 1.62/1.69 1.62/1.69 * Chain [39]: 1*s(4)+0 1.62/1.69 Such that:s(4) =< F1+1 1.62/1.69 1.62/1.69 with precondition: [A=6,Q=0,V=0,U1=2,B>=2,D>=0,G>=0,F1>=0] 1.62/1.69 1.62/1.69 * Chain [38]: 1 1.62/1.69 with precondition: [A=6,Q=0,U1=2,N1=V,B>=2,D>=0,G>=0] 1.62/1.69 1.62/1.69 * Chain [37]: 0 1.62/1.69 with precondition: [A=6,Q=0,U1=2,B>=2] 1.62/1.69 1.62/1.69 1.62/1.69 #### Cost of chains of f9(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,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1,V1,W1,X1,R2): 1.62/1.69 * Chain [52]: 0 1.62/1.69 with precondition: [] 1.62/1.69 1.62/1.69 * Chain [51]: 0 1.62/1.69 with precondition: [C=0,S=0,W=0,F>=2] 1.62/1.69 1.62/1.69 * Chain [50]: 1*s(5)+0 1.62/1.69 Such that:s(5) =< E1+1 1.62/1.69 1.62/1.69 with precondition: [C=0,S=0,W=0,F>=2,E1>=0] 1.62/1.69 1.62/1.69 * Chain [49]: 1*s(6)+0 1.62/1.69 Such that:s(6) =< E1 1.62/1.69 1.62/1.69 with precondition: [C=0,S=0,W=0,F>=2,E1>=1] 1.62/1.69 1.62/1.69 * Chain [48]: 1 1.62/1.69 with precondition: [C=0,S=W,S=M1,F>=2] 1.62/1.69 1.62/1.69 * Chain [47]: 0 1.62/1.69 with precondition: [C=0,W=S,F>=2] 1.62/1.69 1.62/1.69 * Chain [46]: 3*s(7)+1 1.62/1.69 Such that:aux(1) =< F 1.62/1.69 s(7) =< aux(1) 1.62/1.69 1.62/1.69 with precondition: [C=0,W=S,F>=3] 1.62/1.69 1.62/1.69 * Chain [45]: 1*s(10)+1*s(11)+0 1.62/1.69 Such that:s(10) =< F 1.62/1.69 s(11) =< E1+1 1.62/1.69 1.62/1.69 with precondition: [C=0,W=S,F>=3,E1>=0] 1.62/1.69 1.62/1.69 * Chain [44]: 1*s(12)+1*s(13)+0 1.62/1.69 Such that:s(12) =< F 1.62/1.69 s(13) =< E1 1.62/1.69 1.62/1.69 with precondition: [C=0,W=S,F>=3,E1>=1] 1.62/1.69 1.62/1.69 * Chain [43]: 1*aux(2)+0 1.62/1.69 with precondition: [W=S] 1.62/1.69 1.62/1.69 1.62/1.69 Closed-form bounds of f9(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,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1,V1,W1,X1,R2): 1.62/1.69 ------------------------------------- 1.62/1.69 * Chain [52] with precondition: [] 1.62/1.69 - Upper bound: 0 1.62/1.69 - Complexity: constant 1.62/1.69 * Chain [51] with precondition: [C=0,S=0,W=0,F>=2] 1.62/1.69 - Upper bound: 0 1.62/1.69 - Complexity: constant 1.62/1.69 * Chain [50] with precondition: [C=0,S=0,W=0,F>=2,E1>=0] 1.62/1.69 - Upper bound: E1+1 1.62/1.69 - Complexity: n 1.62/1.69 * Chain [49] with precondition: [C=0,S=0,W=0,F>=2,E1>=1] 1.62/1.69 - Upper bound: E1 1.62/1.69 - Complexity: n 1.62/1.69 * Chain [48] with precondition: [C=0,S=W,S=M1,F>=2] 1.62/1.69 - Upper bound: 1 1.62/1.69 - Complexity: constant 1.62/1.69 * Chain [47] with precondition: [C=0,W=S,F>=2] 1.62/1.69 - Upper bound: 0 1.62/1.69 - Complexity: constant 1.62/1.69 * Chain [46] with precondition: [C=0,W=S,F>=3] 1.62/1.69 - Upper bound: 3*F+1 1.62/1.69 - Complexity: n 1.62/1.69 * Chain [45] with precondition: [C=0,W=S,F>=3,E1>=0] 1.62/1.69 - Upper bound: F+E1+1 1.62/1.69 - Complexity: n 1.62/1.69 * Chain [44] with precondition: [C=0,W=S,F>=3,E1>=1] 1.62/1.69 - Upper bound: F+E1 1.62/1.69 - Complexity: n 1.62/1.69 * Chain [43] with precondition: [W=S] 1.62/1.69 - Upper bound: inf 1.62/1.69 - Complexity: infinity 1.62/1.69 1.62/1.69 ### Maximum cost of f9(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,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1,V1,W1,X1,R2): inf 1.62/1.69 Asymptotic class: infinity 1.62/1.69 * Total analysis performed in 1491 ms. 1.62/1.69 1.69/1.79 EOF