1.09/1.14 MAYBE 1.09/1.14 1.09/1.14 Preprocessing Cost Relations 1.09/1.14 ===================================== 1.09/1.14 1.09/1.14 #### Computed strongly connected components 1.09/1.14 0. recursive : [f1/29] 1.09/1.14 1. non_recursive : [exit_location/1] 1.09/1.14 2. recursive : [f12/9] 1.09/1.14 3. non_recursive : [f12_loop_cont/2] 1.09/1.14 4. non_recursive : [f1_loop_cont/30] 1.09/1.14 5. non_recursive : [f9/29] 1.09/1.14 6. non_recursive : [f8/29] 1.09/1.14 1.09/1.14 #### Obtained direct recursion through partial evaluation 1.09/1.14 0. SCC is partially evaluated into f1/29 1.09/1.14 1. SCC is completely evaluated into other SCCs 1.09/1.14 2. SCC is partially evaluated into f12/9 1.09/1.14 3. SCC is completely evaluated into other SCCs 1.09/1.14 4. SCC is partially evaluated into f1_loop_cont/30 1.09/1.14 5. SCC is completely evaluated into other SCCs 1.09/1.14 6. SCC is partially evaluated into f8/29 1.09/1.14 1.09/1.14 Control-Flow Refinement of Cost Relations 1.09/1.14 ===================================== 1.09/1.14 1.09/1.14 ### Specialization of cost equations f1/29 1.09/1.14 * CE 7 is refined into CE [16] 1.09/1.14 * CE 6 is refined into CE [17] 1.09/1.14 * CE 5 is refined into CE [18] 1.09/1.14 * CE 4 is refined into CE [19] 1.09/1.14 * CE 8 is refined into CE [20] 1.09/1.14 * CE 3 is refined into CE [21] 1.09/1.14 1.09/1.14 1.09/1.14 ### Cost equations --> "Loop" of f1/29 1.09/1.14 * CEs [21] --> Loop 15 1.09/1.14 * CEs [16] --> Loop 16 1.09/1.14 * CEs [17] --> Loop 17 1.09/1.14 * CEs [18] --> Loop 18 1.09/1.14 * CEs [19] --> Loop 19 1.09/1.14 * CEs [20] --> Loop 20 1.09/1.14 1.09/1.14 ### Ranking functions of CR f1(B,C,D,I,J,K,L,M,N,O,Q,Y,Z,B1,V1,W1,X1,Y1,Z1,A2,B2,C2,D2,E2,F2,G2,H2,I2,J2) 1.09/1.14 * RF of phase [15]: [C-J,I-J] 1.09/1.14 1.09/1.14 #### Partial ranking functions of CR f1(B,C,D,I,J,K,L,M,N,O,Q,Y,Z,B1,V1,W1,X1,Y1,Z1,A2,B2,C2,D2,E2,F2,G2,H2,I2,J2) 1.09/1.14 * Partial RF of phase [15]: 1.09/1.14 - RF of loop [15:1]: 1.09/1.14 C-J 1.09/1.14 I-J 1.09/1.14 1.09/1.14 1.09/1.14 ### Specialization of cost equations f12/9 1.09/1.14 * CE 15 is refined into CE [22] 1.09/1.14 * CE 14 is refined into CE [23] 1.09/1.14 * CE 12 is refined into CE [24] 1.09/1.14 * CE 13 is refined into CE [25] 1.09/1.14 * CE 11 is refined into CE [26] 1.09/1.14 1.09/1.14 1.09/1.14 ### Cost equations --> "Loop" of f12/9 1.09/1.14 * CEs [23] --> Loop 21 1.09/1.14 * CEs [24] --> Loop 22 1.09/1.14 * CEs [25] --> Loop 23 1.09/1.14 * CEs [26] --> Loop 24 1.09/1.14 * CEs [22] --> Loop 25 1.09/1.14 1.09/1.14 ### Ranking functions of CR f12(A,B,C,D,E,F,G,H,V1) 1.09/1.14 1.09/1.14 #### Partial ranking functions of CR f12(A,B,C,D,E,F,G,H,V1) 1.09/1.14 1.09/1.14 1.09/1.14 ### Specialization of cost equations f1_loop_cont/30 1.09/1.14 * CE 10 is refined into CE [27,28,29,30,31] 1.09/1.14 * CE 9 is refined into CE [32] 1.09/1.14 1.09/1.14 1.09/1.14 ### Cost equations --> "Loop" of f1_loop_cont/30 1.09/1.14 * CEs [29] --> Loop 26 1.09/1.14 * CEs [28] --> Loop 27 1.09/1.14 * CEs [27] --> Loop 28 1.09/1.14 * CEs [32] --> Loop 29 1.09/1.14 * CEs [31] --> Loop 30 1.09/1.14 * CEs [30] --> Loop 31 1.09/1.14 1.09/1.14 ### 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) 1.09/1.14 1.09/1.14 #### 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) 1.09/1.14 1.09/1.14 1.09/1.14 ### Specialization of cost equations f8/29 1.09/1.14 * CE 1 is refined into CE [33] 1.09/1.14 * CE 2 is refined into CE [34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59] 1.09/1.14 1.09/1.14 1.09/1.14 ### Cost equations --> "Loop" of f8/29 1.09/1.14 * CEs [38,41,44,47,50,53,56,59] --> Loop 32 1.09/1.14 * CEs [37,40,43,46,49,52,55,58] --> Loop 33 1.09/1.14 * CEs [33,34,35,36,39,42,45,48,51,54,57] --> Loop 34 1.09/1.14 1.09/1.14 ### Ranking functions of CR f8(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,V1) 1.09/1.14 1.09/1.14 #### Partial ranking functions of CR f8(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,V1) 1.09/1.14 1.09/1.14 1.09/1.14 Computing Bounds 1.09/1.14 ===================================== 1.09/1.14 1.09/1.14 #### Cost of chains of f1(B,C,D,I,J,K,L,M,N,O,Q,Y,Z,B1,V1,W1,X1,Y1,Z1,A2,B2,C2,D2,E2,F2,G2,H2,I2,J2): 1.09/1.14 * Chain [[15],20]: 1*it(15)+0 1.09/1.14 Such that:it(15) =< C-J 1.09/1.14 1.09/1.14 with precondition: [V1=2,C=I,K=M,J>=2,C>=J+1] 1.09/1.14 1.09/1.14 * Chain [[15],19]: 1*it(15)+0 1.09/1.14 Such that:it(15) =< -J+F2+1 1.09/1.14 1.09/1.14 with precondition: [V1=3,C=I,K=M,C=F2+1,0>=W1+1,0>=Y1+1,J>=2,X1>=2,A2>=2,C>=J+1,J2>=X1] 1.09/1.14 1.09/1.14 * Chain [[15],18]: 1*it(15)+0 1.09/1.14 Such that:it(15) =< -J+F2+1 1.09/1.14 1.09/1.14 with precondition: [V1=3,C=I,K=M,C=F2+1,0>=W1+1,J>=2,X1>=2,Y1>=1,A2>=2,C>=J+1,J2>=X1] 1.09/1.14 1.09/1.14 * Chain [[15],17]: 1*it(15)+0 1.09/1.14 Such that:it(15) =< -J+F2+1 1.09/1.14 1.09/1.14 with precondition: [V1=3,C=I,K=M,C=F2+1,0>=Y1+1,J>=2,W1>=1,X1>=2,A2>=2,C>=J+1,J2>=X1] 1.09/1.14 1.09/1.14 * Chain [[15],16]: 1*it(15)+0 1.09/1.14 Such that:it(15) =< C-J 1.09/1.14 1.09/1.14 with precondition: [V1=3,C=I,K=M,C=F2+1,J>=2,W1>=1,X1>=2,Y1>=1,A2>=2,C>=J+1,J2>=X1] 1.09/1.14 1.09/1.14 * Chain [20]: 0 1.09/1.14 with precondition: [V1=2,I=C,M=K,J>=2,I>=J] 1.09/1.14 1.09/1.14 * Chain [19]: 0 1.09/1.14 with precondition: [V1=3,I=C,I=J,M=K,E2=N,F2=O,M=W1,0>=M+1,0>=Y1+1,I>=2,X1>=2,A2>=2,J2>=X1] 1.09/1.14 1.09/1.14 * Chain [18]: 0 1.09/1.14 with precondition: [V1=3,I=C,I=J,M=K,E2=N,F2=O,M=W1,0>=M+1,I>=2,X1>=2,Y1>=1,A2>=2,J2>=X1] 1.09/1.14 1.09/1.14 * Chain [17]: 0 1.09/1.14 with precondition: [V1=3,I=C,I=J,M=K,E2=N,F2=O,M=W1,0>=Y1+1,I>=2,M>=1,X1>=2,A2>=2,J2>=X1] 1.09/1.14 1.09/1.14 * Chain [16]: 0 1.09/1.14 with precondition: [V1=3,I=C,I=J,M=K,E2=N,F2=O,M=W1,I>=2,M>=1,X1>=2,Y1>=1,A2>=2,J2>=X1] 1.09/1.14 1.09/1.14 1.09/1.14 #### Cost of chains of f12(A,B,C,D,E,F,G,H,V1): 1.09/1.14 * Chain [[23,24]]...: 2*it(23)+0 1.09/1.14 with precondition: [A>=0,0>=B+1,V1=2] 1.09/1.14 1.09/1.14 * Chain [[23,24],25]: 2*it(23)+0 1.09/1.14 with precondition: [V1=2,0>=B+1,A>=0] 1.09/1.14 1.09/1.14 * Chain [[21,22]]...: 2*it(21)+0 1.09/1.14 with precondition: [A>=0,B>=1,V1=2] 1.09/1.14 1.09/1.14 * Chain [[21,22],25]: 2*it(21)+0 1.09/1.14 with precondition: [V1=2,A>=0,B>=1] 1.09/1.14 1.09/1.14 * Chain [25]: 0 1.09/1.14 with precondition: [V1=2] 1.09/1.14 1.09/1.14 1.09/1.14 #### 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): 1.09/1.14 * Chain [31]...: 2*s(1)+0 1.09/1.14 with precondition: [A=3,T=2,0>=C+1,B>=0] 1.09/1.14 1.09/1.14 * Chain [30]...: 2*s(2)+0 1.09/1.14 with precondition: [A=3,T=2,B>=0,C>=1] 1.09/1.14 1.09/1.14 * Chain [29]: 0 1.09/1.14 with precondition: [A=2,T=2] 1.09/1.14 1.09/1.14 * Chain [28]: 0 1.09/1.14 with precondition: [A=3,T=2] 1.09/1.14 1.09/1.14 * Chain [27]: 2*s(3)+0 1.09/1.14 with precondition: [A=3,T=2,0>=C+1,B>=0] 1.09/1.14 1.09/1.14 * Chain [26]: 2*s(4)+0 1.09/1.14 with precondition: [A=3,T=2,B>=0,C>=1] 1.09/1.14 1.09/1.14 1.09/1.14 #### Cost of chains of f8(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,V1): 1.09/1.14 * Chain [34]: 1*aux(1)+0 1.09/1.14 with precondition: [] 1.09/1.14 1.09/1.14 * Chain [33]: 1*aux(2)+0 1.09/1.14 with precondition: [A>=0] 1.09/1.14 1.09/1.14 * Chain [32]...: 1*aux(3)+0 1.09/1.14 with precondition: [A>=0] 1.09/1.14 1.09/1.14 1.09/1.14 Closed-form bounds of f8(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,V1): 1.09/1.14 ------------------------------------- 1.09/1.14 * Chain [34] with precondition: [] 1.09/1.14 - Upper bound: inf 1.09/1.14 - Complexity: infinity 1.09/1.14 * Chain [33] with precondition: [A>=0] 1.09/1.14 - Upper bound: inf 1.09/1.14 - Complexity: infinity 1.09/1.14 * Chain [32]... with precondition: [A>=0] 1.09/1.14 - Upper bound: inf 1.09/1.14 - Complexity: infinity 1.09/1.14 1.09/1.14 ### Maximum cost of f8(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,V1): inf 1.09/1.14 Asymptotic class: infinity 1.09/1.14 * Total analysis performed in 1011 ms. 1.09/1.14 1.15/1.24 EOF