2.46/2.52 MAYBE 2.46/2.52 2.46/2.52 Preprocessing Cost Relations 2.46/2.52 ===================================== 2.46/2.52 2.46/2.52 #### Computed strongly connected components 2.46/2.52 0. recursive : [f1/31] 2.46/2.52 1. non_recursive : [f10/38] 2.46/2.52 2. non_recursive : [exit_location/1] 2.46/2.52 3. recursive : [f16/34] 2.46/2.52 4. recursive : [f8/27] 2.46/2.52 5. non_recursive : [f8_loop_cont/39] 2.46/2.52 6. non_recursive : [f16_loop_cont/39] 2.46/2.52 7. non_recursive : [f1_loop_cont/39] 2.46/2.52 8. non_recursive : [f9/38] 2.46/2.52 2.46/2.52 #### Obtained direct recursion through partial evaluation 2.46/2.52 0. SCC is partially evaluated into f1/31 2.46/2.52 1. SCC is completely evaluated into other SCCs 2.46/2.52 2. SCC is completely evaluated into other SCCs 2.46/2.52 3. SCC is partially evaluated into f16/34 2.46/2.52 4. SCC is partially evaluated into f8/27 2.46/2.52 5. SCC is partially evaluated into f8_loop_cont/39 2.46/2.52 6. SCC is partially evaluated into f16_loop_cont/39 2.46/2.52 7. SCC is partially evaluated into f1_loop_cont/39 2.46/2.52 8. SCC is partially evaluated into f9/38 2.46/2.52 2.46/2.52 Control-Flow Refinement of Cost Relations 2.46/2.52 ===================================== 2.46/2.52 2.46/2.52 ### Specialization of cost equations f1/31 2.46/2.52 * CE 6 is refined into CE [24] 2.46/2.52 * CE 5 is refined into CE [25] 2.46/2.52 * CE 4 is refined into CE [26] 2.46/2.52 * CE 3 is refined into CE [27] 2.46/2.52 2.46/2.52 2.46/2.52 ### Cost equations --> "Loop" of f1/31 2.46/2.52 * CEs [27] --> Loop 23 2.46/2.52 * CEs [24] --> Loop 24 2.46/2.52 * CEs [25] --> Loop 25 2.46/2.52 * CEs [26] --> Loop 26 2.46/2.52 2.46/2.52 ### Ranking functions of CR f1(A,B,C,D,E,H,Q,R,S,T,U,V,W,X,Y,Z,E2,F2,G2,H2,I2,J2,K2,L2,M2,N2,O2,P2,Q2,R2,S2) 2.46/2.52 * RF of phase [23]: [-A+D,-A+Q] 2.46/2.52 2.46/2.52 #### Partial ranking functions of CR f1(A,B,C,D,E,H,Q,R,S,T,U,V,W,X,Y,Z,E2,F2,G2,H2,I2,J2,K2,L2,M2,N2,O2,P2,Q2,R2,S2) 2.46/2.52 * Partial RF of phase [23]: 2.46/2.52 - RF of loop [23:1]: 2.46/2.52 -A+D 2.46/2.52 -A+Q 2.46/2.52 2.46/2.52 2.46/2.52 ### Specialization of cost equations f16/34 2.46/2.52 * CE 15 is refined into CE [28] 2.46/2.52 * CE 13 is refined into CE [29] 2.46/2.52 * CE 14 is refined into CE [30] 2.46/2.52 * CE 12 is refined into CE [31] 2.46/2.52 * CE 11 is refined into CE [32] 2.46/2.52 * CE 10 is refined into CE [33] 2.46/2.52 * CE 9 is refined into CE [34] 2.46/2.52 2.46/2.52 2.46/2.52 ### Cost equations --> "Loop" of f16/34 2.46/2.52 * CEs [31] --> Loop 27 2.46/2.52 * CEs [32] --> Loop 28 2.46/2.52 * CEs [33] --> Loop 29 2.46/2.52 * CEs [34] --> Loop 30 2.46/2.52 * CEs [28] --> Loop 31 2.46/2.52 * CEs [29] --> Loop 32 2.46/2.52 * CEs [30] --> Loop 33 2.46/2.52 2.46/2.52 ### Ranking functions of CR f16(B,C,D,E,F,H,M,N,O,P,A1,B1,C1,D1,E1,F1,G1,E2,F2,G2,H2,I2,J2,K2,L2,M2,N2,O2,P2,Q2,R2,S2,T2,U2) 2.46/2.52 * RF of phase [27,28,29,30]: [H+1] 2.46/2.52 2.46/2.52 #### Partial ranking functions of CR f16(B,C,D,E,F,H,M,N,O,P,A1,B1,C1,D1,E1,F1,G1,E2,F2,G2,H2,I2,J2,K2,L2,M2,N2,O2,P2,Q2,R2,S2,T2,U2) 2.46/2.52 * Partial RF of phase [27,28,29,30]: 2.46/2.52 - RF of loop [27:1,28:1,29:1,30:1]: 2.46/2.52 H+1 2.46/2.52 2.46/2.52 2.46/2.52 ### Specialization of cost equations f8/27 2.46/2.52 * CE 21 is refined into CE [35] 2.46/2.52 * CE 20 is refined into CE [36] 2.46/2.52 * CE 19 is refined into CE [37] 2.46/2.52 * CE 18 is refined into CE [38] 2.46/2.52 2.46/2.52 2.46/2.52 ### Cost equations --> "Loop" of f8/27 2.46/2.52 * CEs [37] --> Loop 34 2.46/2.52 * CEs [38] --> Loop 35 2.46/2.52 * CEs [35] --> Loop 36 2.46/2.52 * CEs [36] --> Loop 37 2.46/2.52 2.46/2.52 ### Ranking functions of CR f8(B,D,E,F,Y,A1,C1,D1,E1,F1,G1,H1,I1,E2,F2,G2,H2,I2,J2,K2,L2,M2,N2,O2,P2,Q2,R2) 2.46/2.52 * RF of phase [34,35]: [H1+1] 2.46/2.52 2.46/2.52 #### Partial ranking functions of CR f8(B,D,E,F,Y,A1,C1,D1,E1,F1,G1,H1,I1,E2,F2,G2,H2,I2,J2,K2,L2,M2,N2,O2,P2,Q2,R2) 2.46/2.52 * Partial RF of phase [34,35]: 2.46/2.52 - RF of loop [34:1,35:1]: 2.46/2.52 H1+1 2.46/2.52 2.46/2.52 2.46/2.52 ### Specialization of cost equations f8_loop_cont/39 2.46/2.52 * CE 23 is refined into CE [39] 2.46/2.52 * CE 22 is refined into CE [40] 2.46/2.52 2.46/2.52 2.46/2.52 ### Cost equations --> "Loop" of f8_loop_cont/39 2.46/2.52 * CEs [39] --> Loop 38 2.46/2.52 * CEs [40] --> Loop 39 2.46/2.52 2.46/2.52 ### 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,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1) 2.46/2.52 2.46/2.52 #### 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,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1) 2.46/2.52 2.46/2.52 2.46/2.52 ### Specialization of cost equations f16_loop_cont/39 2.46/2.52 * CE 17 is refined into CE [41,42,43,44] 2.46/2.52 * CE 16 is refined into CE [45] 2.46/2.52 2.46/2.52 2.46/2.52 ### Cost equations --> "Loop" of f16_loop_cont/39 2.46/2.52 * CEs [44] --> Loop 40 2.46/2.52 * CEs [43] --> Loop 41 2.46/2.52 * CEs [42] --> Loop 42 2.46/2.52 * CEs [41] --> Loop 43 2.46/2.52 * CEs [45] --> Loop 44 2.46/2.52 2.46/2.52 ### Ranking functions of CR f16_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,H1,I1,J1,K1,L1,M1) 2.46/2.52 2.46/2.52 #### Partial ranking functions of CR f16_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,H1,I1,J1,K1,L1,M1) 2.46/2.52 2.46/2.52 2.46/2.52 ### Specialization of cost equations f1_loop_cont/39 2.46/2.52 * CE 8 is refined into CE [46,47,48,49,50,51,52,53,54,55] 2.46/2.52 * CE 7 is refined into CE [56] 2.46/2.52 2.46/2.52 2.46/2.52 ### Cost equations --> "Loop" of f1_loop_cont/39 2.46/2.52 * CEs [55] --> Loop 45 2.46/2.52 * CEs [54] --> Loop 46 2.46/2.52 * CEs [46,48] --> Loop 47 2.46/2.52 * CEs [47,49] --> Loop 48 2.46/2.52 * CEs [52] --> Loop 49 2.46/2.52 * CEs [53] --> Loop 50 2.46/2.52 * CEs [50] --> Loop 51 2.46/2.52 * CEs [51] --> Loop 52 2.46/2.52 * CEs [56] --> Loop 53 2.46/2.52 2.46/2.52 ### 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,E1,F1,G1,H1,I1,J1,K1,L1,M1) 2.46/2.52 2.46/2.52 #### 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,E1,F1,G1,H1,I1,J1,K1,L1,M1) 2.46/2.52 2.46/2.52 2.46/2.52 ### Specialization of cost equations f9/38 2.46/2.52 * CE 1 is refined into CE [57] 2.46/2.52 * CE 2 is refined into CE [58,59,60,61,62,63,64,65,66,67] 2.46/2.52 2.46/2.52 2.46/2.52 ### Cost equations --> "Loop" of f9/38 2.46/2.52 * CEs [58,59,60,61,62,63,64,65] --> Loop 54 2.46/2.52 * CEs [57,66,67] --> Loop 55 2.46/2.52 2.46/2.52 ### 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,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,E2) 2.46/2.52 2.46/2.52 #### 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,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,E2) 2.46/2.52 2.46/2.52 2.46/2.52 Computing Bounds 2.46/2.52 ===================================== 2.46/2.52 2.46/2.52 #### Cost of chains of f1(A,B,C,D,E,H,Q,R,S,T,U,V,W,X,Y,Z,E2,F2,G2,H2,I2,J2,K2,L2,M2,N2,O2,P2,Q2,R2,S2): 2.46/2.52 * Chain [[23],26]: 1*it(23)+0 2.46/2.52 Such that:it(23) =< -A+O2+1 2.46/2.52 2.46/2.52 with precondition: [C=0,E2=5,G2=0,D=Q,R=T,F2=I2,D=O2+1,0>=F2+1,A>=2,H2>=2,D>=A+1,H>=H2,S2>=H2] 2.46/2.52 2.46/2.52 * Chain [[23],25]: 1*it(23)+0 2.46/2.52 Such that:it(23) =< -A+O2+1 2.46/2.52 2.46/2.52 with precondition: [C=0,E2=5,G2=0,D=Q,R=T,F2=I2,D=O2+1,A>=2,F2>=1,H2>=2,D>=A+1,H>=H2,S2>=H2] 2.46/2.52 2.46/2.52 * Chain [[23],24]: 1*it(23)+0 2.46/2.52 Such that:it(23) =< -A+Q 2.46/2.52 2.46/2.52 with precondition: [E2=3,D=Q,R=T,A>=2,D>=A+1] 2.46/2.52 2.46/2.52 * Chain [26]: 0 2.46/2.52 with precondition: [C=0,E2=5,G2=0,D=A,D=Q,T=R,N2=U,O2=V,T=F2,T=I2,0>=T+1,D>=2,H2>=2,H>=H2,S2>=H2] 2.46/2.52 2.46/2.52 * Chain [25]: 0 2.46/2.52 with precondition: [C=0,E2=5,G2=0,D=A,D=Q,T=R,N2=U,O2=V,T=F2,T=I2,D>=2,T>=1,H2>=2,H>=H2,S2>=H2] 2.46/2.52 2.46/2.52 * Chain [24]: 0 2.46/2.52 with precondition: [E2=3,Q=D,T=R,A>=2,Q>=A] 2.46/2.52 2.46/2.52 2.46/2.52 #### Cost of chains of f16(B,C,D,E,F,H,M,N,O,P,A1,B1,C1,D1,E1,F1,G1,E2,F2,G2,H2,I2,J2,K2,L2,M2,N2,O2,P2,Q2,R2,S2,T2,U2): 2.46/2.52 * Chain [[27,28,29,30],33]: 4*it(27)+0 2.46/2.52 Such that:aux(2) =< -C+N2 2.46/2.52 aux(1) =< H+1 2.46/2.52 it(27) =< aux(1) 2.46/2.52 it(27) =< aux(2) 2.46/2.52 2.46/2.52 with precondition: [B=0,E2=4,F2=0,L2=0,Q2=0,S2=0,K2=O2,I2=P2,I2=R2,I2=T2,I2=U2,K2+N2=C+H,0>=I2+1,C>=0,H2>=2,K2>=0,H>=K2+1] 2.46/2.52 2.46/2.52 * Chain [[27,28,29,30],32]: 4*it(27)+0 2.46/2.52 Such that:aux(2) =< -C+N2 2.46/2.52 aux(1) =< H+1 2.46/2.52 it(27) =< aux(1) 2.46/2.52 it(27) =< aux(2) 2.46/2.52 2.46/2.52 with precondition: [B=0,E2=4,F2=0,L2=0,Q2=0,S2=0,K2=O2,I2=P2,I2=R2,I2=T2,I2=U2,K2+N2=C+H,C>=0,H2>=2,I2>=1,K2>=0,H>=K2+1] 2.46/2.52 2.46/2.52 * Chain [[27,28,29,30],31]: 4*it(27)+0 2.46/2.52 Such that:aux(3) =< H+1 2.46/2.52 it(27) =< aux(3) 2.46/2.52 2.46/2.52 with precondition: [E2=3,C>=0,H>=0] 2.46/2.52 2.46/2.52 * Chain [33]: 0 2.46/2.52 with precondition: [B=0,E2=4,F2=0,Q2=0,S2=0,J2=F,L2=M,M2=N,N2=O,O2=P,E=I2,H=K2,E=P2,E=R2,E=T2,E=U2,0>=E+1,C>=0,H>=0,H2>=2] 2.46/2.52 2.46/2.52 * Chain [32]: 0 2.46/2.52 with precondition: [B=0,E2=4,F2=0,Q2=0,S2=0,J2=F,L2=M,M2=N,N2=O,O2=P,E=I2,H=K2,E=P2,E=R2,E=T2,E=U2,C>=0,E>=1,H>=0,H2>=2] 2.46/2.52 2.46/2.52 * Chain [31]: 0 2.46/2.52 with precondition: [E2=3] 2.46/2.52 2.46/2.52 2.46/2.52 #### Cost of chains of f8(B,D,E,F,Y,A1,C1,D1,E1,F1,G1,H1,I1,E2,F2,G2,H2,I2,J2,K2,L2,M2,N2,O2,P2,Q2,R2): 2.46/2.52 * Chain [[34,35],37]: 2*it(34)+0 2.46/2.52 Such that:aux(4) =< H1+1 2.46/2.52 aux(5) =< H1-R2 2.46/2.52 it(34) =< aux(4) 2.46/2.52 it(34) =< aux(5) 2.46/2.52 2.46/2.52 with precondition: [A1=0,C1=0,E2=2,F2=0,Q2=R2,G2>=2,Q2>=0,H1>=Q2+1] 2.46/2.52 2.46/2.52 * Chain [[34,35],36]: 2*it(34)+0 2.46/2.52 Such that:aux(6) =< H1+1 2.46/2.52 it(34) =< aux(6) 2.46/2.52 2.46/2.52 with precondition: [C1=0,E2=3,H1>=0] 2.46/2.52 2.46/2.52 * Chain [37]: 0 2.46/2.52 with precondition: [E2=2,F2=B,H2=E,I2=F,C1=A1,R2=I1,H1=Q2,H1>=0,G2>=2] 2.46/2.52 2.46/2.52 * Chain [36]: 0 2.46/2.52 with precondition: [E2=3] 2.46/2.52 2.46/2.52 2.46/2.52 #### 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,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1): 2.46/2.52 * Chain [39]: 0 2.46/2.52 with precondition: [A=2] 2.46/2.52 2.46/2.52 * Chain [38]: 0 2.46/2.52 with precondition: [A=3] 2.46/2.52 2.46/2.52 2.46/2.52 #### Cost of chains of f16_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,H1,I1,J1,K1,L1,M1): 2.46/2.52 * Chain [44]: 0 2.46/2.52 with precondition: [A=3,I1=C1] 2.46/2.52 2.46/2.52 * Chain [43]: 2*s(3)+0 2.46/2.52 Such that:s(2) =< C1 2.46/2.52 s(1) =< C1+1 2.46/2.52 s(3) =< s(1) 2.46/2.52 s(3) =< s(2) 2.46/2.52 2.46/2.52 with precondition: [A=4,B1=0,D1=0,I1=C1,I1>=1] 2.46/2.52 2.46/2.52 * Chain [42]: 2*s(5)+0 2.46/2.52 Such that:s(4) =< I1+1 2.46/2.52 s(5) =< s(4) 2.46/2.52 2.46/2.52 with precondition: [A=4,D1=0,I1=C1,I1>=0] 2.46/2.52 2.46/2.52 * Chain [41]: 0 2.46/2.52 with precondition: [A=4,D1=B1,I1=C1,I1>=0] 2.46/2.52 2.46/2.52 * Chain [40]: 0 2.46/2.52 with precondition: [A=4,I1=C1] 2.46/2.52 2.46/2.52 2.46/2.52 #### 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,E1,F1,G1,H1,I1,J1,K1,L1,M1): 2.46/2.52 * Chain [53]: 0 2.46/2.52 with precondition: [A=3,I=B] 2.46/2.52 2.46/2.52 * Chain [52]: 0 2.46/2.52 with precondition: [A=5,C=0,I=B,0>=F+1,D>=0,I>=0] 2.46/2.52 2.46/2.52 * Chain [51]: 2*s(7)+0 2.46/2.52 Such that:s(6) =< I1+1 2.46/2.52 s(7) =< s(6) 2.46/2.52 2.46/2.52 with precondition: [A=5,C=0,I=B,0>=F+1,D>=0,I>=0,I1>=0] 2.46/2.52 2.46/2.52 * Chain [50]: 0 2.46/2.52 with precondition: [A=5,C=0,I=B,D>=0,F>=1,I>=0] 2.46/2.52 2.46/2.52 * Chain [49]: 2*s(9)+0 2.46/2.52 Such that:s(8) =< I1+1 2.46/2.52 s(9) =< s(8) 2.46/2.52 2.46/2.52 with precondition: [A=5,C=0,I=B,D>=0,F>=1,I>=0,I1>=0] 2.46/2.52 2.46/2.52 * Chain [48]: 8*s(12)+0 2.46/2.52 Such that:aux(7) =< I 2.46/2.52 aux(8) =< I+1 2.46/2.52 s(12) =< aux(8) 2.46/2.52 s(12) =< aux(7) 2.46/2.52 2.46/2.52 with precondition: [A=5,C=0,I=B,D>=0,I>=1] 2.46/2.52 2.46/2.52 * Chain [47]: 8*s(18)+4*s(20)+0 2.46/2.52 Such that:aux(9) =< B 2.46/2.52 aux(10) =< B+1 2.46/2.52 aux(11) =< I1+1 2.46/2.52 s(20) =< aux(11) 2.46/2.52 s(18) =< aux(10) 2.46/2.52 s(18) =< aux(9) 2.46/2.52 2.46/2.52 with precondition: [A=5,C=0,I=B,D>=0,I>=1,I1>=0] 2.46/2.52 2.46/2.52 * Chain [46]: 0 2.46/2.52 with precondition: [A=5,I=B] 2.46/2.52 2.46/2.52 * Chain [45]: 4*s(27)+0 2.46/2.52 Such that:s(26) =< I+1 2.46/2.52 s(27) =< s(26) 2.46/2.52 2.46/2.52 with precondition: [A=5,I=B,D>=0,I>=0] 2.46/2.52 2.46/2.52 2.46/2.52 #### 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,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,E2): 2.46/2.52 * Chain [55]: 1*aux(12)+0 2.46/2.52 with precondition: [] 2.46/2.52 2.46/2.52 * Chain [54]: 16*s(30)+4*s(33)+0 2.46/2.52 Such that:aux(13) =< H+1 2.46/2.52 s(30) =< aux(13) 2.46/2.52 2.46/2.52 with precondition: [C=0,H>=2] 2.46/2.52 2.46/2.52 2.46/2.52 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,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,E2): 2.46/2.52 ------------------------------------- 2.46/2.52 * Chain [55] with precondition: [] 2.46/2.52 - Upper bound: inf 2.46/2.52 - Complexity: infinity 2.46/2.52 * Chain [54] with precondition: [C=0,H>=2] 2.46/2.52 - Upper bound: inf 2.46/2.52 - Complexity: infinity 2.46/2.52 2.46/2.52 ### 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,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,E2): inf 2.46/2.52 Asymptotic class: infinity 2.46/2.52 * Total analysis performed in 2227 ms. 2.46/2.52 2.53/2.62 EOF