1.13/1.14 MAYBE 1.13/1.14 1.13/1.14 Preprocessing Cost Relations 1.13/1.14 ===================================== 1.13/1.14 1.13/1.14 #### Computed strongly connected components 1.13/1.14 0. recursive : [f6/32] 1.13/1.14 1. non_recursive : [exit_location/1] 1.13/1.14 2. recursive : [f11/5] 1.13/1.14 3. non_recursive : [f11_loop_cont/2] 1.13/1.14 4. non_recursive : [f12/32] 1.13/1.14 5. non_recursive : [f6_loop_cont/33] 1.13/1.14 6. non_recursive : [f26/32] 1.13/1.14 1.13/1.14 #### Obtained direct recursion through partial evaluation 1.13/1.14 0. SCC is partially evaluated into f6/32 1.13/1.14 1. SCC is completely evaluated into other SCCs 1.13/1.14 2. SCC is partially evaluated into f11/5 1.13/1.14 3. SCC is completely evaluated into other SCCs 1.13/1.14 4. SCC is partially evaluated into f12/32 1.13/1.14 5. SCC is partially evaluated into f6_loop_cont/33 1.13/1.14 6. SCC is partially evaluated into f26/32 1.13/1.14 1.13/1.14 Control-Flow Refinement of Cost Relations 1.13/1.14 ===================================== 1.13/1.14 1.13/1.14 ### Specialization of cost equations f6/32 1.13/1.14 * CE 5 is refined into CE [14] 1.13/1.14 * CE 4 is refined into CE [15] 1.13/1.14 * CE 6 is refined into CE [16] 1.13/1.14 * CE 2 is refined into CE [17] 1.13/1.14 * CE 3 is refined into CE [18] 1.13/1.14 1.13/1.14 1.13/1.14 ### Cost equations --> "Loop" of f6/32 1.13/1.14 * CEs [17] --> Loop 14 1.13/1.14 * CEs [18] --> Loop 15 1.13/1.14 * CEs [14] --> Loop 16 1.13/1.14 * CEs [15] --> Loop 17 1.13/1.14 * CEs [16] --> Loop 18 1.13/1.14 1.13/1.14 ### Ranking functions of CR f6(A,B,C,D,E,F,G,H,I,J,K,L,M,N,Z,E1,Q1,R1,S1,T1,U1,V1,W1,X1,Y1,Z1,A2,B2,C2,D2,E2,F2) 1.13/1.14 * RF of phase [14,15]: [-G+5,H,-I+5,J] 1.13/1.14 1.13/1.14 #### Partial ranking functions of CR f6(A,B,C,D,E,F,G,H,I,J,K,L,M,N,Z,E1,Q1,R1,S1,T1,U1,V1,W1,X1,Y1,Z1,A2,B2,C2,D2,E2,F2) 1.13/1.14 * Partial RF of phase [14,15]: 1.13/1.14 - RF of loop [14:1,15:1]: 1.13/1.14 -G+5 1.13/1.14 H 1.13/1.14 -I+5 1.13/1.14 J 1.13/1.14 1.13/1.14 1.13/1.14 ### Specialization of cost equations f11/5 1.13/1.14 * CE 13 is refined into CE [19] 1.13/1.14 * CE 11 is refined into CE [20] 1.13/1.14 * CE 12 is refined into CE [21] 1.13/1.14 1.13/1.14 1.13/1.14 ### Cost equations --> "Loop" of f11/5 1.13/1.14 * CEs [20] --> Loop 19 1.13/1.14 * CEs [21] --> Loop 20 1.13/1.14 * CEs [19] --> Loop 21 1.13/1.14 1.13/1.14 ### Ranking functions of CR f11(A,B,C,D,Q1) 1.13/1.14 1.13/1.14 #### Partial ranking functions of CR f11(A,B,C,D,Q1) 1.13/1.14 1.13/1.14 1.13/1.14 ### Specialization of cost equations f12/32 1.13/1.14 * CE 9 is refined into CE [22,23,24] 1.13/1.14 * CE 10 is refined into CE [25,26,27] 1.13/1.14 1.13/1.14 1.13/1.14 ### Cost equations --> "Loop" of f12/32 1.13/1.14 * CEs [24] --> Loop 22 1.13/1.14 * CEs [27] --> Loop 23 1.13/1.14 * CEs [22,23] --> Loop 24 1.13/1.14 * CEs [25,26] --> Loop 25 1.13/1.14 1.13/1.14 ### Ranking functions of CR f12(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,Q1) 1.13/1.14 1.13/1.14 #### Partial ranking functions of CR f12(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,Q1) 1.13/1.14 1.13/1.14 1.13/1.14 ### Specialization of cost equations f6_loop_cont/33 1.13/1.14 * CE 7 is refined into CE [28,29,30,31] 1.13/1.14 * CE 8 is refined into CE [32] 1.13/1.14 1.13/1.14 1.13/1.14 ### Cost equations --> "Loop" of f6_loop_cont/33 1.13/1.14 * CEs [29] --> Loop 26 1.13/1.14 * CEs [28] --> Loop 27 1.13/1.14 * CEs [32] --> Loop 28 1.13/1.14 * CEs [31] --> Loop 29 1.13/1.14 * CEs [30] --> Loop 30 1.13/1.14 1.13/1.14 ### Ranking functions of CR f6_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) 1.13/1.14 1.13/1.14 #### Partial ranking functions of CR f6_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) 1.13/1.14 1.13/1.14 1.13/1.14 ### Specialization of cost equations f26/32 1.13/1.14 * CE 1 is refined into CE [33,34,35,36,37,38,39,40,41,42] 1.13/1.14 1.13/1.14 1.13/1.14 ### Cost equations --> "Loop" of f26/32 1.13/1.14 * CEs [36,38,40,42] --> Loop 31 1.13/1.14 * CEs [33,34,35,37,39,41] --> Loop 32 1.13/1.14 1.13/1.14 ### Ranking functions of CR f26(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,Q1) 1.13/1.14 1.13/1.14 #### Partial ranking functions of CR f26(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,Q1) 1.13/1.14 1.13/1.14 1.13/1.14 Computing Bounds 1.13/1.14 ===================================== 1.13/1.14 1.13/1.14 #### Cost of chains of f6(A,B,C,D,E,F,G,H,I,J,K,L,M,N,Z,E1,Q1,R1,S1,T1,U1,V1,W1,X1,Y1,Z1,A2,B2,C2,D2,E2,F2): 1.13/1.14 * Chain [[14,15],18]: 2*it(14)+0 1.13/1.14 Such that:aux(9) =< J 1.13/1.14 it(14) =< aux(9) 1.13/1.14 1.13/1.14 with precondition: [Q1=2,G=I,G+H=5,G+J=5,4>=G,G>=1] 1.13/1.14 1.13/1.14 * Chain [[14,15],17]: 2*it(14)+0 1.13/1.14 Such that:aux(10) =< J 1.13/1.14 aux(11) =< J-Z1 1.13/1.14 it(14) =< aux(10) 1.13/1.14 it(14) =< aux(11) 1.13/1.14 1.13/1.14 with precondition: [Q1=3,G=I,R1=S1,R1=T1,F=U1,F=V1,W1=Y1,G+H=5,G+J=5,W1+X1=5,W1+Z1=5,W1+C2=5,4>=W1,G>=1,R1>=B+1,W1>=G+1] 1.13/1.14 1.13/1.14 * Chain [[14,15],16]: 2*it(14)+0 1.13/1.14 Such that:aux(12) =< J 1.13/1.14 aux(13) =< J-Z1 1.13/1.14 it(14) =< aux(12) 1.13/1.14 it(14) =< aux(13) 1.13/1.14 1.13/1.14 with precondition: [Q1=3,G=I,R1=S1,R1=T1,F=U1,F=V1,W1=Y1,G+H=5,G+J=5,W1+X1=5,W1+Z1=5,W1+C2=5,4>=W1,G>=1,W1>=G+1,B>=R1+1] 1.13/1.14 1.13/1.14 * Chain [18]: 0 1.13/1.14 with precondition: [Q1=2,J=H,G+J=5,I+J=5,4>=J] 1.13/1.14 1.13/1.14 * Chain [17]: 0 1.13/1.14 with precondition: [Q1=3,E=F,J=H,A2=K,B2=L,C2=M,R1=S1,R1=T1,E=U1,E=V1,J=X1,J=Z1,G+J=5,I+J=5,J+W1=5,J+Y1=5,4>=J,J>=1,R1>=B+1] 1.13/1.14 1.13/1.14 * Chain [16]: 0 1.13/1.14 with precondition: [Q1=3,E=F,J=H,A2=K,B2=L,C2=M,R1=S1,R1=T1,E=U1,E=V1,J=X1,J=Z1,G+J=5,I+J=5,J+W1=5,J+Y1=5,4>=J,J>=1,B>=R1+1] 1.13/1.14 1.13/1.14 1.13/1.14 #### Cost of chains of f11(A,B,C,D,Q1): 1.13/1.14 * Chain [[20]]...: 1*it(20)+0 1.13/1.14 with precondition: [A=D,A=C,B>=A+1,Q1=2] 1.13/1.14 1.13/1.14 * Chain [[20],21]: 1*it(20)+0 1.13/1.14 with precondition: [Q1=2,A=C,A=D,B>=A+1] 1.13/1.14 1.13/1.14 * Chain [[19]]...: 1*it(19)+0 1.13/1.14 with precondition: [A=D,A=C,A>=B+1,Q1=2] 1.13/1.14 1.13/1.14 * Chain [[19],21]: 1*it(19)+0 1.13/1.14 with precondition: [Q1=2,A=C,A=D,A>=B+1] 1.13/1.14 1.13/1.14 * Chain [21]: 0 1.13/1.14 with precondition: [Q1=2,A=C,A=D] 1.13/1.14 1.13/1.14 1.13/1.14 #### Cost of chains of f12(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,Q1): 1.13/1.14 * Chain [25]: 1*aux(14)+0 1.13/1.14 with precondition: [O=2,P=3,S=4,U=0,D1=4,X=W,X=Y,B>=A+1] 1.13/1.14 1.13/1.14 * Chain [24]: 1*aux(15)+0 1.13/1.14 with precondition: [O=2,P=3,S=4,U=0,D1=4,X=W,X=Y,A>=B+1] 1.13/1.14 1.13/1.14 * Chain [23]...: 1*s(3)+0 1.13/1.14 with precondition: [O=2,P=3,S=4,U=0,D1=4,X=W,X=Y,B>=A+1] 1.13/1.14 1.13/1.14 * Chain [22]...: 1*s(4)+0 1.13/1.14 with precondition: [O=2,P=3,S=4,U=0,D1=4,X=W,X=Y,A>=B+1] 1.13/1.14 1.13/1.14 1.13/1.14 #### Cost of chains of f6_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): 1.13/1.14 * Chain [30]...: 1*s(5)+0 1.13/1.14 with precondition: [A=3,P=2,Q=3,T=4,V=0,E1=4,Y=X,Y=Z,C>=B+1] 1.13/1.14 1.13/1.14 * Chain [29]...: 1*s(6)+0 1.13/1.14 with precondition: [A=3,P=2,Q=3,T=4,V=0,E1=4,Y=X,Y=Z,B>=C+1] 1.13/1.14 1.13/1.14 * Chain [28]: 0 1.13/1.14 with precondition: [A=2,P=2,Q=3,T=4,V=0,E1=4,Y=X,Y=Z] 1.13/1.14 1.13/1.14 * Chain [27]: 1*s(7)+0 1.13/1.14 with precondition: [A=3,P=2,Q=3,T=4,V=0,E1=4,Y=X,Y=Z,C>=B+1] 1.13/1.14 1.13/1.14 * Chain [26]: 1*s(8)+0 1.13/1.14 with precondition: [A=3,P=2,Q=3,T=4,V=0,E1=4,Y=X,Y=Z,B>=C+1] 1.13/1.14 1.13/1.14 1.13/1.14 #### Cost of chains of f26(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,Q1): 1.13/1.14 * Chain [32]: 1*aux(18)+0 1.13/1.14 with precondition: [] 1.13/1.14 1.13/1.14 * Chain [31]...: 1*aux(21)+0 1.13/1.14 with precondition: [] 1.13/1.14 1.13/1.14 1.13/1.14 Closed-form bounds of f26(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,Q1): 1.13/1.14 ------------------------------------- 1.13/1.14 * Chain [32] with precondition: [] 1.13/1.14 - Upper bound: inf 1.13/1.14 - Complexity: infinity 1.13/1.14 * Chain [31]... with precondition: [] 1.13/1.14 - Upper bound: inf 1.13/1.14 - Complexity: infinity 1.13/1.14 1.13/1.14 ### Maximum cost of f26(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,Q1): inf 1.13/1.14 Asymptotic class: infinity 1.13/1.14 * Total analysis performed in 1020 ms. 1.13/1.14 1.15/1.25 EOF