1.05/1.08 MAYBE 1.05/1.08 1.05/1.08 Preprocessing Cost Relations 1.05/1.08 ===================================== 1.05/1.08 1.05/1.08 #### Computed strongly connected components 1.05/1.08 0. recursive : [f6/32] 1.05/1.08 1. non_recursive : [exit_location/1] 1.05/1.08 2. recursive : [f11/5] 1.05/1.08 3. non_recursive : [f11_loop_cont/2] 1.05/1.08 4. non_recursive : [f6_loop_cont/33] 1.05/1.08 5. non_recursive : [f26/32] 1.05/1.08 1.05/1.08 #### Obtained direct recursion through partial evaluation 1.05/1.08 0. SCC is partially evaluated into f6/32 1.05/1.08 1. SCC is completely evaluated into other SCCs 1.05/1.08 2. SCC is partially evaluated into f11/5 1.05/1.08 3. SCC is completely evaluated into other SCCs 1.05/1.08 4. SCC is partially evaluated into f6_loop_cont/33 1.05/1.08 5. SCC is partially evaluated into f26/32 1.05/1.08 1.05/1.08 Control-Flow Refinement of Cost Relations 1.05/1.08 ===================================== 1.05/1.08 1.05/1.08 ### Specialization of cost equations f6/32 1.05/1.08 * CE 4 is refined into CE [12] 1.05/1.08 * CE 5 is refined into CE [13] 1.05/1.08 * CE 6 is refined into CE [14] 1.05/1.08 * CE 2 is refined into CE [15] 1.05/1.08 * CE 3 is refined into CE [16] 1.05/1.08 1.05/1.08 1.05/1.08 ### Cost equations --> "Loop" of f6/32 1.05/1.08 * CEs [15] --> Loop 12 1.05/1.08 * CEs [16] --> Loop 13 1.05/1.08 * CEs [12] --> Loop 14 1.05/1.08 * CEs [13] --> Loop 15 1.05/1.08 * CEs [14] --> Loop 16 1.05/1.08 1.05/1.08 ### 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) 1.05/1.08 * RF of phase [12,13]: [-G+5,H,-I+5,J] 1.05/1.08 1.05/1.08 #### 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) 1.05/1.08 * Partial RF of phase [12,13]: 1.05/1.08 - RF of loop [12:1,13:1]: 1.05/1.08 -G+5 1.05/1.08 H 1.05/1.08 -I+5 1.05/1.08 J 1.05/1.08 1.05/1.08 1.05/1.08 ### Specialization of cost equations f11/5 1.05/1.08 * CE 11 is refined into CE [17] 1.05/1.08 * CE 9 is refined into CE [18] 1.05/1.08 * CE 10 is refined into CE [19] 1.05/1.08 1.05/1.08 1.05/1.08 ### Cost equations --> "Loop" of f11/5 1.05/1.08 * CEs [18] --> Loop 17 1.05/1.08 * CEs [19] --> Loop 18 1.05/1.08 * CEs [17] --> Loop 19 1.05/1.08 1.05/1.08 ### Ranking functions of CR f11(A,B,C,D,Q1) 1.05/1.08 1.05/1.08 #### Partial ranking functions of CR f11(A,B,C,D,Q1) 1.05/1.08 1.05/1.08 1.05/1.08 ### Specialization of cost equations f6_loop_cont/33 1.05/1.08 * CE 8 is refined into CE [20,21,22,23,24] 1.05/1.08 * CE 7 is refined into CE [25] 1.05/1.08 1.05/1.08 1.05/1.08 ### Cost equations --> "Loop" of f6_loop_cont/33 1.05/1.08 * CEs [22] --> Loop 20 1.05/1.08 * CEs [21] --> Loop 21 1.05/1.08 * CEs [20] --> Loop 22 1.05/1.08 * CEs [25] --> Loop 23 1.05/1.08 * CEs [24] --> Loop 24 1.05/1.08 * CEs [23] --> Loop 25 1.05/1.08 1.05/1.08 ### 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) 1.05/1.08 1.05/1.08 #### 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) 1.05/1.08 1.05/1.08 1.05/1.08 ### Specialization of cost equations f26/32 1.05/1.08 * CE 1 is refined into CE [26,27,28,29,30,31,32,33,34,35,36,37,38,39] 1.05/1.08 1.05/1.08 1.05/1.08 ### Cost equations --> "Loop" of f26/32 1.05/1.08 * CEs [30,33,36,39] --> Loop 26 1.05/1.08 * CEs [26,27,28,29,31,32,34,35,37,38] --> Loop 27 1.05/1.08 1.05/1.08 ### 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) 1.05/1.08 1.05/1.08 #### 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) 1.05/1.08 1.05/1.08 1.05/1.08 Computing Bounds 1.05/1.08 ===================================== 1.05/1.08 1.05/1.08 #### 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): 1.05/1.08 * Chain [[12,13],16]: 2*it(12)+0 1.05/1.08 Such that:aux(9) =< J 1.05/1.08 it(12) =< aux(9) 1.05/1.08 1.05/1.08 with precondition: [Q1=2,G=I,G+H=5,G+J=5,4>=G,G>=1] 1.05/1.08 1.05/1.08 * Chain [[12,13],15]: 2*it(12)+0 1.05/1.08 Such that:aux(10) =< J 1.05/1.08 aux(11) =< J-Z1 1.05/1.08 it(12) =< aux(10) 1.05/1.08 it(12) =< aux(11) 1.05/1.08 1.05/1.08 with precondition: [Q1=3,G=I,R1=S1,R1=T1,E=U1,E=V1,W1=Y1,G+H=5,G+J=5,W1+X1=5,W1+Z1=5,W1+C2=5,4>=W1,G>=1,R1>=A+1,W1>=G+1] 1.05/1.08 1.05/1.08 * Chain [[12,13],14]: 2*it(12)+0 1.05/1.08 Such that:aux(12) =< J 1.05/1.08 aux(13) =< J-Z1 1.05/1.08 it(12) =< aux(12) 1.05/1.08 it(12) =< aux(13) 1.05/1.08 1.05/1.08 with precondition: [Q1=3,G=I,R1=S1,R1=T1,E=U1,E=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,A>=R1+1] 1.05/1.08 1.05/1.08 * Chain [16]: 0 1.05/1.08 with precondition: [Q1=2,J=H,G+J=5,I+J=5,4>=J] 1.05/1.08 1.05/1.08 * Chain [15]: 0 1.05/1.08 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>=A+1] 1.05/1.08 1.05/1.08 * Chain [14]: 0 1.05/1.08 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,A>=R1+1] 1.05/1.08 1.05/1.08 1.05/1.08 #### Cost of chains of f11(A,B,C,D,Q1): 1.05/1.08 * Chain [[18]]...: 1*it(18)+0 1.05/1.08 with precondition: [B>=A+1,Q1=2] 1.05/1.08 1.05/1.08 * Chain [[18],19]: 1*it(18)+0 1.05/1.08 with precondition: [Q1=2,B>=A+1] 1.05/1.08 1.05/1.08 * Chain [[17]]...: 1*it(17)+0 1.05/1.08 with precondition: [A>=B+1,Q1=2] 1.05/1.08 1.05/1.08 * Chain [[17],19]: 1*it(17)+0 1.05/1.08 with precondition: [Q1=2,A>=B+1] 1.05/1.08 1.05/1.08 * Chain [19]: 0 1.05/1.08 with precondition: [Q1=2] 1.05/1.08 1.05/1.08 1.05/1.08 #### 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): 1.05/1.08 * Chain [25]...: 1*s(1)+0 1.05/1.08 with precondition: [A=3,P=2,Q=3,T=4,V=0,E1=4,Y=X,Y=Z,C>=B+1] 1.05/1.08 1.05/1.08 * Chain [24]...: 1*s(2)+0 1.05/1.08 with precondition: [A=3,P=2,Q=3,T=4,V=0,E1=4,Y=X,Y=Z,B>=C+1] 1.05/1.08 1.05/1.08 * Chain [23]: 0 1.05/1.08 with precondition: [A=2,P=2,Q=3,T=4,V=0,E1=4,Y=X,Y=Z] 1.05/1.08 1.05/1.08 * Chain [22]: 0 1.05/1.08 with precondition: [A=3,P=2,Q=3,T=4,V=0,E1=4,Y=X,Y=Z] 1.05/1.08 1.05/1.08 * Chain [21]: 1*s(3)+0 1.05/1.08 with precondition: [A=3,P=2,Q=3,T=4,V=0,E1=4,Y=X,Y=Z,C>=B+1] 1.05/1.08 1.05/1.09 * Chain [20]: 1*s(4)+0 1.05/1.09 with precondition: [A=3,P=2,Q=3,T=4,V=0,E1=4,Y=X,Y=Z,B>=C+1] 1.05/1.09 1.05/1.09 1.05/1.09 #### 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): 1.05/1.09 * Chain [27]: 1*aux(16)+0 1.05/1.09 with precondition: [] 1.05/1.09 1.05/1.09 * Chain [26]...: 1*aux(19)+0 1.05/1.09 with precondition: [] 1.05/1.09 1.05/1.09 1.05/1.09 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): 1.05/1.09 ------------------------------------- 1.05/1.09 * Chain [27] with precondition: [] 1.05/1.09 - Upper bound: inf 1.05/1.09 - Complexity: infinity 1.05/1.09 * Chain [26]... with precondition: [] 1.05/1.09 - Upper bound: inf 1.05/1.09 - Complexity: infinity 1.05/1.09 1.05/1.09 ### 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 1.05/1.09 Asymptotic class: infinity 1.05/1.09 * Total analysis performed in 964 ms. 1.05/1.09 1.10/1.19 EOF