3.21/3.22 MAYBE 3.21/3.22 3.21/3.22 Preprocessing Cost Relations 3.21/3.22 ===================================== 3.21/3.22 3.21/3.22 #### Computed strongly connected components 3.21/3.22 0. recursive : [f2/49] 3.21/3.22 1. recursive : [f1/30,f2_loop_cont/31] 3.21/3.22 2. non_recursive : [exit_location/1] 3.21/3.22 3. non_recursive : [f1_loop_cont/2] 3.21/3.22 4. non_recursive : [f999/30] 3.21/3.22 3.21/3.22 #### Obtained direct recursion through partial evaluation 3.21/3.22 0. SCC is partially evaluated into f2/49 3.21/3.22 1. SCC is partially evaluated into f1/30 3.21/3.22 2. SCC is completely evaluated into other SCCs 3.21/3.22 3. SCC is completely evaluated into other SCCs 3.21/3.22 4. SCC is partially evaluated into f999/30 3.21/3.22 3.21/3.22 Control-Flow Refinement of Cost Relations 3.21/3.22 ===================================== 3.21/3.22 3.21/3.22 ### Specialization of cost equations f2/49 3.21/3.22 * CE 12 is refined into CE [13] 3.21/3.22 * CE 7 is refined into CE [14] 3.21/3.22 * CE 9 is refined into CE [15] 3.21/3.22 * CE 10 is refined into CE [16] 3.21/3.22 * CE 11 is refined into CE [17] 3.21/3.22 * CE 8 is refined into CE [18] 3.21/3.22 3.21/3.22 3.21/3.22 ### Cost equations --> "Loop" of f2/49 3.21/3.22 * CEs [17] --> Loop 13 3.21/3.22 * CEs [18] --> Loop 14 3.21/3.22 * CEs [13] --> Loop 15 3.21/3.22 * CEs [15] --> Loop 16 3.21/3.22 * CEs [14] --> Loop 17 3.21/3.22 * CEs [16] --> Loop 18 3.21/3.22 3.21/3.22 ### Ranking functions of CR f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,T,U,V,W,X,Y,Z,A1,B1,C1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1,V1,W1,X1,Y1,Z1,A2,B2,C2) 3.21/3.22 3.21/3.22 #### Partial ranking functions of CR f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,T,U,V,W,X,Y,Z,A1,B1,C1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1,V1,W1,X1,Y1,Z1,A2,B2,C2) 3.21/3.22 3.21/3.22 3.21/3.22 ### Specialization of cost equations f1/30 3.21/3.22 * CE 2 is refined into CE [19,20] 3.21/3.22 * CE 6 is refined into CE [21] 3.21/3.22 * CE 3 is refined into CE [22,23,24,25,26,27,28] 3.21/3.22 * CE 5 is refined into CE [29] 3.21/3.22 * CE 4 is refined into CE [30] 3.21/3.22 3.21/3.22 3.21/3.22 ### Cost equations --> "Loop" of f1/30 3.21/3.22 * CEs [29] --> Loop 19 3.21/3.22 * CEs [30] --> Loop 20 3.21/3.22 * CEs [27] --> Loop 21 3.21/3.22 * CEs [26] --> Loop 22 3.21/3.22 * CEs [25] --> Loop 23 3.21/3.22 * CEs [24] --> Loop 24 3.21/3.22 * CEs [23] --> Loop 25 3.21/3.22 * CEs [22] --> Loop 26 3.21/3.22 * CEs [28] --> Loop 27 3.21/3.22 * CEs [19] --> Loop 28 3.21/3.22 * CEs [21] --> Loop 29 3.21/3.22 * CEs [20] --> Loop 30 3.21/3.22 3.21/3.22 ### Ranking functions of CR f1(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,E1) 3.21/3.22 3.21/3.22 #### Partial ranking functions of CR f1(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,E1) 3.21/3.22 * Partial RF of phase [19,20,21,22,23,24,25,26,27]: 3.21/3.22 - RF of loop [19:1]: 3.21/3.22 C depends on loops [20:1,21:1,22:1,23:1,24:1,25:1,26:1,27:1] 3.21/3.22 - RF of loop [20:1]: 3.21/3.22 C+H depends on loops [21:1,22:1,23:1,24:1,25:1,26:1,27:1] 3.21/3.22 - RF of loop [24:1]: 3.21/3.22 C+D+H depends on loops [21:1,22:1,23:1,25:1,26:1,27:1] 3.21/3.22 - RF of loop [26:1]: 3.21/3.22 C/2+D/2+H/2+I/2-1/2 depends on loops [21:1,23:1,25:1,27:1] 3.21/3.22 3.21/3.22 3.21/3.22 ### Specialization of cost equations f999/30 3.21/3.22 * CE 1 is refined into CE [31,32,33,34] 3.21/3.22 3.21/3.22 3.21/3.22 ### Cost equations --> "Loop" of f999/30 3.21/3.22 * CEs [33,34] --> Loop 31 3.21/3.22 * CEs [31,32] --> Loop 32 3.21/3.22 3.21/3.22 ### Ranking functions of CR f999(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,E1) 3.21/3.22 3.21/3.22 #### Partial ranking functions of CR f999(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,E1) 3.21/3.22 3.21/3.22 3.21/3.22 Computing Bounds 3.21/3.22 ===================================== 3.21/3.22 3.21/3.22 #### Cost of chains of f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,T,U,V,W,X,Y,Z,A1,B1,C1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1,V1,W1,X1,Y1,Z1,A2,B2,C2): 3.21/3.22 * Chain [[13,14]]...: 2*it(13)+0 3.21/3.22 with precondition: [A=0,B=0,C=0,E1>=2,3>=E1] 3.21/3.22 3.21/3.22 * Chain [[13,14],18]: 2*it(13)+0 3.21/3.22 with precondition: [A=0,B=0,C=0,E1=2,F1=1,G1=1,I1=0,J1=0,K1=0,L1=0,M1=0,N1=0,J+Q1=L+O1,G+N+Y+A1=S1+Y1+A2,F+M+X+Z+B1=R1+X1+Z1+B2,H1+O1+P1+T1+U1+V1+W1+1=D+E+H+I+J+K+T+U+V+W,H1>=0,O1>=J+1,H1+T1+U1+2*O1>=2*J+D+H+I+T+U+1,H1+O1+T1+U1+1>=D+H+I+J+T+U] 3.21/3.22 3.21/3.22 * Chain [[13,14],17]: 2*it(13)+0 3.21/3.22 with precondition: [A=0,B=0,C=0,E1=2,F1=1,G1=1,I1=0,M1=0,J+Q1=L+O1,G+N+Y+A1=L1+S1+Y1+A2,F+M+X+Z+B1=K1+R1+X1+Z1+B2,D+E+H+I+J+K+T+U+V+W=H1+J1+N1+O1+P1+T1+U1+V1+W1+1,H1>=0,O1>=J,H1+N1+T1+U1+2*O1>=2*J+D+H+I+T+U,H1+N1+O1+T1+U1+1>=D+H+I+J+T+U] 3.21/3.22 3.21/3.22 * Chain [[13,14],16]: 2*it(13)+0 3.21/3.22 with precondition: [A=0,B=0,C=0,E1=2,I1=0,J1=0,K1=0,L1=0,N1=0,O1=0,Q1=0,H=M1,L+G1=J+F1,G+N+Y+A1=S1+Y1+A2,F+M+X+Z+B1=R1+X1+Z1+B2,D+E+I+K+L+T+U+V+W=F1+H1+P1+T1+U1+V1+W1,F1>=L+1,H1+T1+U1+2*F1>=2*L+D+I+T+U+2,F1+H1+T1+U1>=D+I+L+T+U] 3.21/3.22 3.21/3.22 * Chain [[13,14],15]: 2*it(13)+0 3.21/3.22 with precondition: [A=0,B=0,C=0,E1=3] 3.21/3.22 3.21/3.22 * Chain [18]: 0 3.21/3.22 with precondition: [A=0,B=0,C=0,E1=2,F1=1,G1=1,I1=0,J1=0,K1=0,L1=0,M1=0,N1=0,O1=J+1,Q1=L+1,T1=T,U1=U,V1=V,W1=W,X1=X,Y1=Y,Z1=Z,A2=A1,B2=B1,C2=C1,P1=E+K,R1=F+M,S1=G+N,D+H+I=H1+2,D>=1,D+H+I>=2] 3.21/3.22 3.21/3.22 * Chain [17]: 0 3.21/3.22 with precondition: [A=0,B=0,C=0,E1=2,F1=1,G1=1,I1=0,M1=0,J1=E,K1=F,L1=G,N1=I,O1=J,P1=K,Q1=L,R1=M,S1=N,T1=T,U1=U,V1=V,W1=W,X1=X,Y1=Y,Z1=Z,A2=A1,B2=B1,C2=C1,D+H=H1+1,D+H>=1] 3.21/3.22 3.21/3.22 * Chain [16]: 0 3.21/3.22 with precondition: [A=0,B=0,C=0,E1=2,I1=0,J1=0,K1=0,L1=0,N1=0,O1=0,Q1=0,M1=H,G1=J+1,F1=L+1,T1=T,U1=U,V1=V,W1=W,X1=X,Y1=Y,Z1=Z,A2=A1,B2=B1,C2=C1,P1=E+K,R1=F+M,S1=G+N,D+I=H1+1,D>=1] 3.21/3.22 3.21/3.22 * Chain [15]: 0 3.21/3.22 with precondition: [A=0,B=0,C=0,E1=3] 3.21/3.22 3.21/3.22 3.21/3.22 #### Cost of chains of f1(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,E1): 3.21/3.22 * Chain [[19,20,21,22,23,24,25,26,27]]...: 17*it(19)+0 3.21/3.22 with precondition: [O=0,P=0,Q=0,R=0,S=0,E1=3] 3.21/3.22 3.21/3.22 * Chain [[19,20,21,22,23,24,25,26,27],30]...: 19*it(19)+0 3.21/3.22 with precondition: [O=0,P=0,Q=0,R=0,S=0,E1=3] 3.21/3.22 3.21/3.22 * Chain [[19,20,21,22,23,24,25,26,27],29]: 17*it(19)+0 3.21/3.23 with precondition: [O=0,P=0,Q=0,R=0,S=0,E1=3] 3.21/3.23 3.21/3.23 * Chain [[19,20,21,22,23,24,25,26,27],28]: 18*it(19)+0 3.21/3.23 with precondition: [O=0,P=0,Q=0,R=0,S=0,E1=3] 3.21/3.23 3.21/3.23 * Chain [30]...: 2*s(14)+0 3.21/3.23 with precondition: [O=0,P=0,Q=0,R=0,S=0,E1=3,A>=1,B>=1] 3.21/3.23 3.21/3.23 * Chain [29]: 0 3.21/3.23 with precondition: [O=0,P=0,Q=0,R=0,S=0,E1=3] 3.21/3.23 3.21/3.23 * Chain [28]: 1*s(15)+0 3.21/3.23 with precondition: [O=0,P=0,Q=0,R=0,S=0,E1=3,A>=1,B>=1] 3.21/3.23 3.21/3.23 3.21/3.23 #### Cost of chains of f999(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,E1): 3.21/3.23 * Chain [32]: 1*aux(46)+0 3.21/3.23 with precondition: [A=0,B=0,C=0,D=0,E=0,F=0,G=0,I=0,J=0,K=0,L=0,M=0,N=0,O=0,P=0,Q=0,R=0,S=0,T=0,U=0,V=0,W=0,X=0,Y=0,Z=0,A1=0,B1=0,H>=1] 3.21/3.23 3.21/3.23 * Chain [31]...: 1*aux(47)+0 3.21/3.23 with precondition: [A=0,B=0,C=0,D=0,E=0,F=0,G=0,I=0,J=0,K=0,L=0,M=0,N=0,O=0,P=0,Q=0,R=0,S=0,T=0,U=0,V=0,W=0,X=0,Y=0,Z=0,A1=0,B1=0,H>=1] 3.21/3.23 3.21/3.23 3.21/3.23 Closed-form bounds of f999(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,E1): 3.21/3.23 ------------------------------------- 3.21/3.23 * Chain [32] with precondition: [A=0,B=0,C=0,D=0,E=0,F=0,G=0,I=0,J=0,K=0,L=0,M=0,N=0,O=0,P=0,Q=0,R=0,S=0,T=0,U=0,V=0,W=0,X=0,Y=0,Z=0,A1=0,B1=0,H>=1] 3.21/3.23 - Upper bound: inf 3.21/3.23 - Complexity: infinity 3.21/3.23 * Chain [31]... with precondition: [A=0,B=0,C=0,D=0,E=0,F=0,G=0,I=0,J=0,K=0,L=0,M=0,N=0,O=0,P=0,Q=0,R=0,S=0,T=0,U=0,V=0,W=0,X=0,Y=0,Z=0,A1=0,B1=0,H>=1] 3.21/3.23 - Upper bound: inf 3.21/3.23 - Complexity: infinity 3.21/3.23 3.21/3.23 ### Maximum cost of f999(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,E1): inf 3.21/3.23 Asymptotic class: infinity 3.21/3.23 * Total analysis performed in 2970 ms. 3.21/3.23 3.23/3.33 EOF