1.03/1.03 MAYBE 1.03/1.03 1.03/1.03 Preprocessing Cost Relations 1.03/1.03 ===================================== 1.03/1.03 1.03/1.03 #### Computed strongly connected components 1.03/1.03 0. recursive : [f1/40] 1.03/1.03 1. non_recursive : [f10/26] 1.03/1.03 2. non_recursive : [exit_location/1] 1.03/1.03 3. recursive : [f8/25] 1.03/1.03 4. non_recursive : [f8_loop_cont/27] 1.03/1.03 5. non_recursive : [f1_loop_cont/27] 1.03/1.03 6. non_recursive : [f9/26] 1.03/1.03 1.03/1.03 #### Obtained direct recursion through partial evaluation 1.03/1.03 0. SCC is partially evaluated into f1/40 1.03/1.03 1. SCC is completely evaluated into other SCCs 1.03/1.03 2. SCC is completely evaluated into other SCCs 1.03/1.03 3. SCC is partially evaluated into f8/25 1.03/1.03 4. SCC is partially evaluated into f8_loop_cont/27 1.03/1.03 5. SCC is partially evaluated into f1_loop_cont/27 1.03/1.03 6. SCC is partially evaluated into f9/26 1.03/1.03 1.03/1.03 Control-Flow Refinement of Cost Relations 1.03/1.03 ===================================== 1.03/1.03 1.03/1.03 ### Specialization of cost equations f1/40 1.03/1.03 * CE 4 is refined into CE [14] 1.03/1.03 * CE 5 is refined into CE [15] 1.03/1.03 * CE 6 is refined into CE [16] 1.03/1.03 * CE 3 is refined into CE [17] 1.03/1.03 1.03/1.03 1.03/1.03 ### Cost equations --> "Loop" of f1/40 1.03/1.03 * CEs [17] --> Loop 13 1.03/1.03 * CEs [14] --> Loop 14 1.03/1.03 * CEs [15] --> Loop 15 1.03/1.03 * CEs [16] --> Loop 16 1.03/1.03 1.03/1.03 ### Ranking functions of CR f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,V,W,Y,R1,S1,T1,U1,V1,W1,X1,Y1,Z1,A2,B2,C2,D2,E2,F2,G2,H2,I2,J2,K2) 1.03/1.03 * RF of phase [13]: [A-B,-B+K] 1.03/1.03 1.03/1.03 #### Partial ranking functions of CR f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,V,W,Y,R1,S1,T1,U1,V1,W1,X1,Y1,Z1,A2,B2,C2,D2,E2,F2,G2,H2,I2,J2,K2) 1.03/1.03 * Partial RF of phase [13]: 1.03/1.03 - RF of loop [13:1]: 1.03/1.03 A-B 1.03/1.03 -B+K 1.03/1.03 1.03/1.03 1.03/1.03 ### Specialization of cost equations f8/25 1.03/1.03 * CE 11 is refined into CE [18] 1.03/1.03 * CE 10 is refined into CE [19] 1.03/1.03 * CE 9 is refined into CE [20] 1.03/1.03 1.03/1.03 1.03/1.03 ### Cost equations --> "Loop" of f8/25 1.03/1.03 * CEs [20] --> Loop 17 1.03/1.03 * CEs [18] --> Loop 18 1.03/1.03 * CEs [19] --> Loop 19 1.03/1.03 1.03/1.03 ### Ranking functions of CR f8(H,J,K,L,M,N,O,P,Q,R,S,T,R1,S1,T1,U1,V1,W1,X1,Y1,Z1,A2,B2,C2,D2) 1.03/1.03 * RF of phase [17]: [R+1] 1.03/1.03 1.03/1.03 #### Partial ranking functions of CR f8(H,J,K,L,M,N,O,P,Q,R,S,T,R1,S1,T1,U1,V1,W1,X1,Y1,Z1,A2,B2,C2,D2) 1.03/1.03 * Partial RF of phase [17]: 1.03/1.03 - RF of loop [17:1]: 1.03/1.03 R+1 1.03/1.03 1.03/1.03 1.03/1.03 ### Specialization of cost equations f8_loop_cont/27 1.03/1.03 * CE 13 is refined into CE [21] 1.03/1.03 * CE 12 is refined into CE [22] 1.03/1.03 1.03/1.03 1.03/1.03 ### Cost equations --> "Loop" of f8_loop_cont/27 1.03/1.03 * CEs [21] --> Loop 20 1.03/1.03 * CEs [22] --> Loop 21 1.03/1.03 1.03/1.03 ### 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) 1.03/1.03 1.03/1.03 #### 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) 1.03/1.03 1.03/1.03 1.03/1.03 ### Specialization of cost equations f1_loop_cont/27 1.03/1.03 * CE 8 is refined into CE [23,24,25,26] 1.03/1.04 * CE 7 is refined into CE [27] 1.03/1.04 1.03/1.04 1.03/1.04 ### Cost equations --> "Loop" of f1_loop_cont/27 1.03/1.04 * CEs [26] --> Loop 22 1.03/1.04 * CEs [25] --> Loop 23 1.03/1.04 * CEs [24] --> Loop 24 1.03/1.04 * CEs [23] --> Loop 25 1.03/1.04 * CEs [27] --> Loop 26 1.03/1.04 1.03/1.04 ### 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) 1.03/1.04 1.03/1.04 #### 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) 1.03/1.04 1.03/1.04 1.03/1.04 ### Specialization of cost equations f9/26 1.03/1.04 * CE 1 is refined into CE [28] 1.03/1.04 * CE 2 is refined into CE [29,30,31,32,33,34,35,36,37,38] 1.03/1.04 1.03/1.04 1.03/1.04 ### Cost equations --> "Loop" of f9/26 1.03/1.04 * CEs [31,33,35,37] --> Loop 27 1.03/1.04 * CEs [28,29,30,32,34,36,38] --> Loop 28 1.03/1.04 1.03/1.04 ### 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,R1) 1.03/1.04 1.03/1.04 #### 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,R1) 1.03/1.04 1.03/1.04 1.03/1.04 Computing Bounds 1.03/1.04 ===================================== 1.03/1.04 1.03/1.04 #### Cost of chains of f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,V,W,Y,R1,S1,T1,U1,V1,W1,X1,Y1,Z1,A2,B2,C2,D2,E2,F2,G2,H2,I2,J2,K2): 1.03/1.04 * Chain [[13],16]: 1*it(13)+0 1.03/1.04 Such that:it(13) =< A-B 1.03/1.04 1.03/1.04 with precondition: [R1=3,C=E,A=K,B>=2,A>=B+1] 1.03/1.04 1.03/1.04 * Chain [[13],15]: 1*it(13)+0 1.03/1.04 Such that:it(13) =< A-B 1.03/1.04 1.03/1.04 with precondition: [R1=4,A2=0,E2=0,C=E,A=K,A=Y1+1,Z1=C2,Z1=D2,Z1=F2,Z1=G2,0>=Z1+1,B>=2,T1>=2,B2>=2,A>=B+1] 1.03/1.04 1.03/1.04 * Chain [[13],14]: 1*it(13)+0 1.03/1.04 Such that:it(13) =< A-B 1.03/1.04 1.03/1.04 with precondition: [R1=4,A2=0,E2=0,C=E,A=K,A=Y1+1,Z1=C2,Z1=D2,Z1=F2,Z1=G2,B>=2,T1>=2,Z1>=1,B2>=2,A>=B+1] 1.03/1.04 1.03/1.04 * Chain [16]: 0 1.03/1.04 with precondition: [R1=3,K=A,E=C,B>=2,K>=B] 1.03/1.04 1.03/1.04 * Chain [15]: 0 1.03/1.04 with precondition: [R1=4,A2=0,E2=0,A=B,E=C,X1=F,Y1=G,A=K,E=Z1,E=C2,E=D2,E=F2,E=G2,0>=E+1,A>=2,T1>=2,B2>=2] 1.03/1.04 1.03/1.04 * Chain [14]: 0 1.03/1.04 with precondition: [R1=4,A2=0,E2=0,A=B,E=C,X1=F,Y1=G,A=K,E=Z1,E=C2,E=D2,E=F2,E=G2,A>=2,E>=1,T1>=2,B2>=2] 1.03/1.04 1.03/1.04 1.03/1.04 #### Cost of chains of f8(H,J,K,L,M,N,O,P,Q,R,S,T,R1,S1,T1,U1,V1,W1,X1,Y1,Z1,A2,B2,C2,D2): 1.03/1.04 * Chain [[17],19]: 1*it(17)+0 1.03/1.04 Such that:it(17) =< R-D2 1.03/1.04 1.03/1.04 with precondition: [H=0,J=0,R1=2,B2=D2,U1>=2,B2>=0,R>=B2+1] 1.03/1.04 1.03/1.04 * Chain [[17],18]: 1*it(17)+0 1.03/1.04 Such that:it(17) =< R+1 1.03/1.04 1.03/1.04 with precondition: [J=0,R1=3,R>=0] 1.03/1.04 1.03/1.04 * Chain [19]: 0 1.03/1.04 with precondition: [R1=2,J=H,V1=L,C2=S,D2=T,R=B2,R>=0,U1>=2] 1.03/1.04 1.03/1.04 * Chain [18]: 0 1.03/1.04 with precondition: [R1=3] 1.03/1.04 1.03/1.04 1.03/1.04 #### 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): 1.03/1.04 * Chain [21]: 0 1.03/1.04 with precondition: [A=2] 1.03/1.04 1.03/1.04 * Chain [20]: 0 1.03/1.04 with precondition: [A=3] 1.03/1.04 1.03/1.04 1.03/1.04 #### 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): 1.03/1.04 * Chain [26]: 0 1.03/1.04 with precondition: [A=3,S=J] 1.03/1.04 1.03/1.04 * Chain [25]: 1*s(1)+0 1.03/1.04 Such that:s(1) =< J 1.03/1.04 1.03/1.04 with precondition: [A=4,I=0,K=0,S=J,S>=1] 1.03/1.04 1.03/1.04 * Chain [24]: 1*s(2)+0 1.03/1.04 Such that:s(2) =< J+1 1.03/1.04 1.03/1.04 with precondition: [A=4,K=0,S=J,S>=0] 1.03/1.04 1.03/1.04 * Chain [23]: 0 1.03/1.04 with precondition: [A=4,K=I,S=J,S>=0] 1.03/1.04 1.03/1.04 * Chain [22]: 0 1.03/1.04 with precondition: [A=4,S=J] 1.03/1.04 1.03/1.04 1.03/1.04 #### 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,R1): 1.03/1.04 * Chain [28]: 1*aux(1)+0 1.03/1.04 with precondition: [] 1.03/1.04 1.03/1.04 * Chain [27]: 4*s(6)+2*s(8)+0 1.03/1.04 Such that:aux(2) =< R+1 1.03/1.04 s(6) =< aux(2) 1.03/1.04 1.03/1.04 with precondition: [R>=0] 1.03/1.04 1.03/1.04 1.03/1.04 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,R1): 1.03/1.04 ------------------------------------- 1.03/1.04 * Chain [28] with precondition: [] 1.03/1.04 - Upper bound: inf 1.03/1.04 - Complexity: infinity 1.03/1.04 * Chain [27] with precondition: [R>=0] 1.03/1.04 - Upper bound: inf 1.03/1.04 - Complexity: infinity 1.03/1.04 1.03/1.04 ### 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,R1): inf 1.03/1.04 Asymptotic class: infinity 1.03/1.04 * Total analysis performed in 888 ms. 1.03/1.04 1.03/1.14 EOF