2.60/2.60 MAYBE 2.60/2.60 2.60/2.60 Preprocessing Cost Relations 2.60/2.60 ===================================== 2.60/2.60 2.60/2.60 #### Computed strongly connected components 2.60/2.60 0. recursive : [f1/33] 2.60/2.60 1. non_recursive : [f16/39] 2.60/2.60 2. non_recursive : [exit_location/1] 2.60/2.60 3. recursive : [f14/36] 2.60/2.60 4. recursive : [f8/25] 2.60/2.60 5. non_recursive : [f8_loop_cont/40] 2.60/2.60 6. non_recursive : [f14_loop_cont/40] 2.60/2.60 7. non_recursive : [f1_loop_cont/40] 2.60/2.60 8. non_recursive : [f15/39] 2.60/2.60 2.60/2.60 #### Obtained direct recursion through partial evaluation 2.60/2.60 0. SCC is partially evaluated into f1/33 2.60/2.60 1. SCC is completely evaluated into other SCCs 2.60/2.60 2. SCC is completely evaluated into other SCCs 2.60/2.60 3. SCC is partially evaluated into f14/36 2.60/2.60 4. SCC is partially evaluated into f8/25 2.60/2.60 5. SCC is partially evaluated into f8_loop_cont/40 2.60/2.60 6. SCC is partially evaluated into f14_loop_cont/40 2.60/2.60 7. SCC is partially evaluated into f1_loop_cont/40 2.60/2.60 8. SCC is partially evaluated into f15/39 2.60/2.60 2.60/2.60 Control-Flow Refinement of Cost Relations 2.60/2.60 ===================================== 2.60/2.60 2.60/2.60 ### Specialization of cost equations f1/33 2.60/2.60 * CE 6 is refined into CE [24] 2.60/2.60 * CE 4 is refined into CE [25] 2.60/2.60 * CE 3 is refined into CE [26] 2.60/2.60 * CE 5 is refined into CE [27] 2.60/2.60 2.60/2.60 2.60/2.60 ### Cost equations --> "Loop" of f1/33 2.60/2.60 * CEs [27] --> Loop 23 2.60/2.60 * CEs [24] --> Loop 24 2.60/2.60 * CEs [25] --> Loop 25 2.60/2.60 * CEs [26] --> Loop 26 2.60/2.60 2.60/2.60 ### Ranking functions of CR f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,H2,I2,J2,K2,L2,M2,N2,O2,P2,Q2,R2,S2,T2,U2,V2,W2) 2.60/2.60 * RF of phase [23]: [-A+B,-A+F] 2.60/2.60 2.60/2.60 #### Partial ranking functions of CR f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,H2,I2,J2,K2,L2,M2,N2,O2,P2,Q2,R2,S2,T2,U2,V2,W2) 2.60/2.60 * Partial RF of phase [23]: 2.60/2.60 - RF of loop [23:1]: 2.60/2.60 -A+B 2.60/2.60 -A+F 2.60/2.60 2.60/2.60 2.60/2.60 ### Specialization of cost equations f14/36 2.60/2.60 * CE 15 is refined into CE [28] 2.60/2.60 * CE 13 is refined into CE [29] 2.60/2.60 * CE 14 is refined into CE [30] 2.60/2.60 * CE 12 is refined into CE [31] 2.60/2.60 * CE 11 is refined into CE [32] 2.60/2.60 * CE 10 is refined into CE [33] 2.60/2.60 * CE 9 is refined into CE [34] 2.60/2.60 2.60/2.60 2.60/2.60 ### Cost equations --> "Loop" of f14/36 2.60/2.60 * CEs [31] --> Loop 27 2.60/2.60 * CEs [32] --> Loop 28 2.60/2.60 * CEs [33] --> Loop 29 2.60/2.60 * CEs [34] --> Loop 30 2.60/2.60 * CEs [28] --> Loop 31 2.60/2.60 * CEs [29] --> Loop 32 2.60/2.60 * CEs [30] --> Loop 33 2.60/2.60 2.60/2.60 ### Ranking functions of CR f14(D,E,F,L,M,N,R,X,Y,Z,A1,B1,C1,D1,E1,F1,G1,H1,H2,I2,J2,K2,L2,M2,N2,O2,P2,Q2,R2,S2,T2,U2,V2,W2,X2,Y2) 2.60/2.60 * RF of phase [27,28,29,30]: [D+1] 2.60/2.60 2.60/2.60 #### Partial ranking functions of CR f14(D,E,F,L,M,N,R,X,Y,Z,A1,B1,C1,D1,E1,F1,G1,H1,H2,I2,J2,K2,L2,M2,N2,O2,P2,Q2,R2,S2,T2,U2,V2,W2,X2,Y2) 2.60/2.60 * Partial RF of phase [27,28,29,30]: 2.60/2.60 - RF of loop [27:1,28:1,29:1,30:1]: 2.60/2.60 D+1 2.60/2.60 2.60/2.60 2.60/2.60 ### Specialization of cost equations f8/25 2.60/2.60 * CE 21 is refined into CE [35] 2.60/2.60 * CE 20 is refined into CE [36] 2.60/2.60 * CE 19 is refined into CE [37] 2.60/2.60 * CE 18 is refined into CE [38] 2.60/2.60 2.60/2.60 2.60/2.60 ### Cost equations --> "Loop" of f8/25 2.60/2.60 * CEs [37] --> Loop 34 2.60/2.60 * CEs [38] --> Loop 35 2.60/2.60 * CEs [35] --> Loop 36 2.60/2.60 * CEs [36] --> Loop 37 2.60/2.60 2.60/2.60 ### Ranking functions of CR f8(F,H,L,R,B1,D1,E1,F1,G1,H1,I1,J1,H2,I2,J2,K2,L2,M2,N2,O2,P2,Q2,R2,S2,T2) 2.60/2.60 * RF of phase [34,35]: [I1+1] 2.60/2.60 2.60/2.60 #### Partial ranking functions of CR f8(F,H,L,R,B1,D1,E1,F1,G1,H1,I1,J1,H2,I2,J2,K2,L2,M2,N2,O2,P2,Q2,R2,S2,T2) 2.60/2.60 * Partial RF of phase [34,35]: 2.60/2.60 - RF of loop [34:1,35:1]: 2.60/2.60 I1+1 2.60/2.60 2.60/2.60 2.60/2.60 ### Specialization of cost equations f8_loop_cont/40 2.60/2.60 * CE 23 is refined into CE [39] 2.60/2.60 * CE 22 is refined into CE [40] 2.60/2.60 2.60/2.60 2.60/2.60 ### Cost equations --> "Loop" of f8_loop_cont/40 2.60/2.60 * CEs [39] --> Loop 38 2.60/2.60 * CEs [40] --> Loop 39 2.60/2.60 2.60/2.60 ### 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,N1) 2.60/2.60 2.60/2.60 #### 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,N1) 2.60/2.60 2.60/2.60 2.60/2.60 ### Specialization of cost equations f14_loop_cont/40 2.60/2.60 * CE 17 is refined into CE [41,42,43,44] 2.60/2.60 * CE 16 is refined into CE [45] 2.60/2.60 2.60/2.60 2.60/2.60 ### Cost equations --> "Loop" of f14_loop_cont/40 2.60/2.60 * CEs [44] --> Loop 40 2.60/2.60 * CEs [43] --> Loop 41 2.60/2.60 * CEs [42] --> Loop 42 2.60/2.60 * CEs [41] --> Loop 43 2.60/2.60 * CEs [45] --> Loop 44 2.60/2.60 2.60/2.60 ### Ranking functions of CR f14_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,N1) 2.60/2.60 2.60/2.60 #### Partial ranking functions of CR f14_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,N1) 2.60/2.60 2.60/2.60 2.60/2.60 ### Specialization of cost equations f1_loop_cont/40 2.60/2.60 * CE 8 is refined into CE [46,47,48,49,50,51,52,53,54,55] 2.60/2.60 * CE 7 is refined into CE [56] 2.60/2.60 2.60/2.60 2.60/2.60 ### Cost equations --> "Loop" of f1_loop_cont/40 2.60/2.60 * CEs [55] --> Loop 45 2.60/2.60 * CEs [54] --> Loop 46 2.60/2.60 * CEs [46,48] --> Loop 47 2.60/2.60 * CEs [47,49] --> Loop 48 2.60/2.60 * CEs [52] --> Loop 49 2.60/2.60 * CEs [53] --> Loop 50 2.60/2.60 * CEs [50] --> Loop 51 2.60/2.60 * CEs [51] --> Loop 52 2.60/2.60 * CEs [56] --> Loop 53 2.60/2.60 2.60/2.60 ### 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,N1) 2.60/2.60 2.60/2.60 #### 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,N1) 2.60/2.60 2.60/2.60 2.60/2.60 ### Specialization of cost equations f15/39 2.60/2.60 * CE 1 is refined into CE [57] 2.60/2.60 * CE 2 is refined into CE [58,59,60,61,62,63,64,65,66,67] 2.60/2.60 2.60/2.60 2.60/2.60 ### Cost equations --> "Loop" of f15/39 2.60/2.60 * CEs [58,59,60,61,62,63,64,65] --> Loop 54 2.60/2.60 * CEs [57,66,67] --> Loop 55 2.60/2.60 2.60/2.60 ### Ranking functions of CR f15(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,H2) 2.60/2.60 2.60/2.60 #### Partial ranking functions of CR f15(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,H2) 2.60/2.60 2.60/2.60 2.60/2.60 Computing Bounds 2.60/2.60 ===================================== 2.60/2.60 2.60/2.60 #### Cost of chains of f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,H2,I2,J2,K2,L2,M2,N2,O2,P2,Q2,R2,S2,T2,U2,V2,W2): 2.60/2.60 * Chain [[23],26]: 1*it(23)+0 2.60/2.60 Such that:it(23) =< -A+B 2.60/2.60 2.60/2.60 with precondition: [E=0,H2=5,K2=0,B=F,C=J,R2=S2,R2=T2,B=W2+1,0>=R2+1,A>=2,L2>=2,B>=A+1,D>=L2,U2>=L2] 2.60/2.60 2.60/2.60 * Chain [[23],25]: 1*it(23)+0 2.60/2.60 Such that:it(23) =< -A+B 2.60/2.60 2.60/2.60 with precondition: [E=0,H2=5,K2=0,B=F,C=J,R2=S2,R2=T2,B=W2+1,A>=2,L2>=2,R2>=1,B>=A+1,D>=L2,U2>=L2] 2.60/2.60 2.60/2.60 * Chain [[23],24]: 1*it(23)+0 2.60/2.60 Such that:it(23) =< -A+B 2.60/2.60 2.60/2.60 with precondition: [H2=3,B=F,C=J,A>=2,B>=A+1] 2.60/2.60 2.60/2.60 * Chain [26]: 0 2.60/2.60 with precondition: [E=0,H2=5,K2=0,B=A,J=C,B=F,V2=P,W2=Q,J=R2,J=S2,J=T2,0>=J+1,B>=2,L2>=2,D>=L2,U2>=L2] 2.60/2.60 2.60/2.60 * Chain [25]: 0 2.60/2.60 with precondition: [E=0,H2=5,K2=0,B=A,J=C,B=F,V2=P,W2=Q,J=R2,J=S2,J=T2,B>=2,J>=1,L2>=2,D>=L2,U2>=L2] 2.60/2.60 2.60/2.60 * Chain [24]: 0 2.60/2.60 with precondition: [H2=3,F=B,J=C,A>=2,F>=A] 2.60/2.60 2.60/2.60 2.60/2.60 #### Cost of chains of f14(D,E,F,L,M,N,R,X,Y,Z,A1,B1,C1,D1,E1,F1,G1,H1,H2,I2,J2,K2,L2,M2,N2,O2,P2,Q2,R2,S2,T2,U2,V2,W2,X2,Y2): 2.60/2.60 * Chain [[27,28,29,30],33]: 4*it(27)+0 2.60/2.60 Such that:aux(1) =< D+1 2.60/2.60 aux(2) =< -E+R2 2.60/2.60 it(27) =< aux(1) 2.60/2.60 it(27) =< aux(2) 2.60/2.60 2.60/2.60 with precondition: [N=0,H2=4,P2=0,U2=0,W2=0,I2=S2,L2=T2,L2=V2,L2=X2,L2=Y2,I2+R2=D+E,0>=L2+1,E>=0,I2>=0,K2>=2,D>=I2+1] 2.60/2.60 2.60/2.60 * Chain [[27,28,29,30],32]: 4*it(27)+0 2.60/2.60 Such that:aux(1) =< D+1 2.60/2.60 aux(2) =< -E+R2 2.60/2.60 it(27) =< aux(1) 2.60/2.60 it(27) =< aux(2) 2.60/2.60 2.60/2.60 with precondition: [N=0,H2=4,P2=0,U2=0,W2=0,I2=S2,L2=T2,L2=V2,L2=X2,L2=Y2,I2+R2=D+E,E>=0,I2>=0,K2>=2,L2>=1,D>=I2+1] 2.60/2.60 2.60/2.60 * Chain [[27,28,29,30],31]: 4*it(27)+0 2.60/2.60 Such that:aux(3) =< D+1 2.60/2.60 it(27) =< aux(3) 2.60/2.60 2.60/2.60 with precondition: [H2=3,D>=0,E>=0] 2.60/2.60 2.60/2.60 * Chain [33]: 0 2.60/2.60 with precondition: [N=0,H2=4,U2=0,W2=0,O2=R,P2=X,Q2=Y,R2=Z,S2=A1,D=I2,L=L2,L=T2,L=V2,L=X2,L=Y2,0>=L+1,D>=0,E>=0,K2>=2] 2.60/2.60 2.60/2.60 * Chain [32]: 0 2.60/2.60 with precondition: [N=0,H2=4,U2=0,W2=0,O2=R,P2=X,Q2=Y,R2=Z,S2=A1,D=I2,L=L2,L=T2,L=V2,L=X2,L=Y2,D>=0,E>=0,L>=1,K2>=2] 2.60/2.60 2.60/2.60 * Chain [31]: 0 2.60/2.60 with precondition: [H2=3] 2.60/2.60 2.60/2.60 2.60/2.60 #### Cost of chains of f8(F,H,L,R,B1,D1,E1,F1,G1,H1,I1,J1,H2,I2,J2,K2,L2,M2,N2,O2,P2,Q2,R2,S2,T2): 2.60/2.60 * Chain [[34,35],37]: 2*it(34)+0 2.60/2.60 Such that:aux(4) =< I1+1 2.60/2.60 aux(5) =< I1-S2 2.60/2.60 it(34) =< aux(4) 2.60/2.60 it(34) =< aux(5) 2.60/2.60 2.60/2.60 with precondition: [B1=0,D1=0,H2=2,S2=T2,I2>=2,S2>=0,I1>=S2+1] 2.60/2.60 2.60/2.60 * Chain [[34,35],36]: 2*it(34)+0 2.60/2.60 Such that:aux(6) =< I1+1 2.60/2.60 it(34) =< aux(6) 2.60/2.60 2.60/2.60 with precondition: [D1=0,H2=3,I1>=0] 2.60/2.60 2.60/2.60 * Chain [37]: 0 2.60/2.60 with precondition: [H2=2,K2=L,L2=R,D1=B1,T2=J1,I1=S2,I1>=0,I2>=2] 2.60/2.60 2.60/2.60 * Chain [36]: 0 2.60/2.60 with precondition: [H2=3] 2.60/2.60 2.60/2.60 2.60/2.60 #### 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,N1): 2.60/2.60 * Chain [39]: 0 2.60/2.60 with precondition: [A=2] 2.60/2.60 2.60/2.60 * Chain [38]: 0 2.60/2.60 with precondition: [A=3] 2.60/2.60 2.60/2.60 2.60/2.60 #### Cost of chains of f14_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,N1): 2.60/2.60 * Chain [44]: 0 2.60/2.60 with precondition: [A=3,J1=D1] 2.60/2.60 2.60/2.60 * Chain [43]: 2*s(3)+0 2.60/2.60 Such that:s(2) =< J1 2.60/2.60 s(1) =< J1+1 2.60/2.60 s(3) =< s(1) 2.60/2.60 s(3) =< s(2) 2.60/2.60 2.60/2.60 with precondition: [A=4,C1=0,E1=0,J1=D1,J1>=1] 2.60/2.60 2.60/2.60 * Chain [42]: 2*s(5)+0 2.60/2.60 Such that:s(4) =< J1+1 2.60/2.60 s(5) =< s(4) 2.60/2.60 2.60/2.60 with precondition: [A=4,E1=0,J1=D1,J1>=0] 2.60/2.60 2.60/2.60 * Chain [41]: 0 2.60/2.60 with precondition: [A=4,E1=C1,J1=D1,J1>=0] 2.60/2.60 2.60/2.60 * Chain [40]: 0 2.60/2.60 with precondition: [A=4,J1=D1] 2.60/2.60 2.60/2.60 2.60/2.60 #### 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,N1): 2.60/2.60 * Chain [53]: 0 2.60/2.60 with precondition: [A=3,E=B] 2.60/2.60 2.60/2.60 * Chain [52]: 0 2.60/2.60 with precondition: [A=5,O=0,E=B,0>=M+1,E>=0,F>=0] 2.60/2.60 2.60/2.60 * Chain [51]: 2*s(7)+0 2.60/2.60 Such that:s(6) =< J1+1 2.60/2.60 s(7) =< s(6) 2.60/2.60 2.60/2.60 with precondition: [A=5,O=0,E=B,0>=M+1,E>=0,F>=0,J1>=0] 2.60/2.60 2.60/2.60 * Chain [50]: 0 2.60/2.60 with precondition: [A=5,O=0,E=B,E>=0,F>=0,M>=1] 2.60/2.60 2.60/2.60 * Chain [49]: 2*s(9)+0 2.60/2.60 Such that:s(8) =< J1+1 2.60/2.60 s(9) =< s(8) 2.60/2.60 2.60/2.60 with precondition: [A=5,O=0,E=B,E>=0,F>=0,M>=1,J1>=0] 2.60/2.60 2.60/2.60 * Chain [48]: 8*s(12)+0 2.60/2.60 Such that:aux(7) =< E 2.60/2.60 aux(8) =< E+1 2.60/2.60 s(12) =< aux(8) 2.60/2.60 s(12) =< aux(7) 2.60/2.60 2.60/2.60 with precondition: [A=5,O=0,E=B,E>=1,F>=0] 2.60/2.60 2.60/2.60 * Chain [47]: 8*s(18)+4*s(20)+0 2.60/2.60 Such that:aux(9) =< E 2.60/2.60 aux(10) =< E+1 2.60/2.60 aux(11) =< J1+1 2.60/2.60 s(20) =< aux(11) 2.60/2.60 s(18) =< aux(10) 2.60/2.60 s(18) =< aux(9) 2.60/2.60 2.60/2.60 with precondition: [A=5,O=0,E=B,E>=1,F>=0,J1>=0] 2.60/2.60 2.60/2.60 * Chain [46]: 0 2.60/2.60 with precondition: [A=5,E=B] 2.60/2.60 2.60/2.60 * Chain [45]: 4*s(27)+0 2.60/2.60 Such that:s(26) =< E+1 2.60/2.60 s(27) =< s(26) 2.60/2.60 2.60/2.60 with precondition: [A=5,E=B,E>=0,F>=0] 2.60/2.60 2.60/2.60 2.60/2.60 #### Cost of chains of f15(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,H2): 2.60/2.60 * Chain [55]: 1*aux(12)+0 2.60/2.60 with precondition: [] 2.60/2.60 2.60/2.60 * Chain [54]: 16*s(30)+4*s(33)+0 2.60/2.60 Such that:aux(13) =< D+1 2.60/2.60 s(30) =< aux(13) 2.60/2.60 2.60/2.60 with precondition: [E=0,D>=2] 2.60/2.60 2.60/2.60 2.60/2.60 Closed-form bounds of f15(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,H2): 2.60/2.60 ------------------------------------- 2.60/2.60 * Chain [55] with precondition: [] 2.60/2.60 - Upper bound: inf 2.60/2.60 - Complexity: infinity 2.60/2.60 * Chain [54] with precondition: [E=0,D>=2] 2.60/2.60 - Upper bound: inf 2.60/2.60 - Complexity: infinity 2.60/2.60 2.60/2.60 ### Maximum cost of f15(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,H2): inf 2.60/2.60 Asymptotic class: infinity 2.60/2.60 * Total analysis performed in 2299 ms. 2.60/2.60 2.61/2.70 EOF