1.21/1.27 MAYBE 1.21/1.27 1.21/1.27 Preprocessing Cost Relations 1.21/1.27 ===================================== 1.21/1.27 1.21/1.27 #### Computed strongly connected components 1.21/1.27 0. recursive : [f11/37] 1.21/1.27 1. non_recursive : [exit_location/1] 1.21/1.27 2. recursive : [f53/1] 1.21/1.27 3. non_recursive : [f53_loop_cont/2] 1.21/1.27 4. non_recursive : [f45/24] 1.21/1.27 5. non_recursive : [f37/24] 1.21/1.27 6. non_recursive : [f11_loop_cont/25] 1.21/1.27 7. non_recursive : [f0/24] 1.21/1.27 1.21/1.27 #### Obtained direct recursion through partial evaluation 1.21/1.27 0. SCC is partially evaluated into f11/37 1.21/1.27 1. SCC is completely evaluated into other SCCs 1.21/1.27 2. SCC is partially evaluated into f53/1 1.21/1.27 3. SCC is completely evaluated into other SCCs 1.21/1.27 4. SCC is partially evaluated into f45/24 1.21/1.27 5. SCC is partially evaluated into f37/24 1.21/1.27 6. SCC is partially evaluated into f11_loop_cont/25 1.21/1.27 7. SCC is partially evaluated into f0/24 1.21/1.27 1.21/1.27 Control-Flow Refinement of Cost Relations 1.21/1.27 ===================================== 1.21/1.27 1.21/1.27 ### Specialization of cost equations f11/37 1.21/1.27 * CE 7 is refined into CE [17] 1.21/1.27 * CE 4 is refined into CE [18] 1.21/1.27 * CE 5 is refined into CE [19] 1.21/1.27 * CE 3 is refined into CE [20] 1.21/1.27 * CE 2 is refined into CE [21] 1.21/1.27 * CE 6 is refined into CE [22] 1.21/1.27 1.21/1.27 1.21/1.27 ### Cost equations --> "Loop" of f11/37 1.21/1.27 * CEs [22] --> Loop 17 1.21/1.27 * CEs [17] --> Loop 18 1.21/1.27 * CEs [18] --> Loop 19 1.21/1.27 * CEs [19] --> Loop 20 1.21/1.27 * CEs [20] --> Loop 21 1.21/1.27 * CEs [21] --> Loop 22 1.21/1.27 1.21/1.27 ### Ranking functions of CR f11(A,B,C,D,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1) 1.21/1.27 * RF of phase [17]: [-A+B] 1.21/1.27 1.21/1.27 #### Partial ranking functions of CR f11(A,B,C,D,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1) 1.21/1.27 * Partial RF of phase [17]: 1.21/1.27 - RF of loop [17:1]: 1.21/1.27 -A+B 1.21/1.27 1.21/1.27 1.21/1.27 ### Specialization of cost equations f53/1 1.21/1.27 * CE 16 is refined into CE [23] 1.21/1.27 * CE 15 is refined into CE [24] 1.21/1.27 1.21/1.27 1.21/1.27 ### Cost equations --> "Loop" of f53/1 1.21/1.27 * CEs [24] --> Loop 23 1.21/1.27 * CEs [23] --> Loop 24 1.21/1.27 1.21/1.27 ### Ranking functions of CR f53(C1) 1.21/1.27 1.21/1.27 #### Partial ranking functions of CR f53(C1) 1.21/1.27 1.21/1.27 1.21/1.27 ### Specialization of cost equations f45/24 1.21/1.27 * CE 11 is refined into CE [25,26] 1.21/1.27 1.21/1.27 1.21/1.27 ### Cost equations --> "Loop" of f45/24 1.21/1.27 * CEs [26] --> Loop 25 1.21/1.27 * CEs [25] --> Loop 26 1.21/1.27 1.21/1.27 ### Ranking functions of CR f45(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,C1) 1.21/1.27 1.21/1.27 #### Partial ranking functions of CR f45(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,C1) 1.21/1.27 1.21/1.27 1.21/1.27 ### Specialization of cost equations f37/24 1.21/1.27 * CE 12 is refined into CE [27,28] 1.21/1.27 * CE 13 is refined into CE [29,30] 1.21/1.27 * CE 14 is refined into CE [31,32] 1.21/1.27 1.21/1.27 1.21/1.27 ### Cost equations --> "Loop" of f37/24 1.21/1.27 * CEs [28] --> Loop 27 1.21/1.27 * CEs [30] --> Loop 28 1.21/1.27 * CEs [32] --> Loop 29 1.21/1.27 * CEs [27] --> Loop 30 1.21/1.27 * CEs [29] --> Loop 31 1.21/1.27 * CEs [31] --> Loop 32 1.21/1.27 1.21/1.27 ### Ranking functions of CR f37(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,C1) 1.21/1.27 1.21/1.27 #### Partial ranking functions of CR f37(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,C1) 1.21/1.27 1.21/1.27 1.21/1.27 ### Specialization of cost equations f11_loop_cont/25 1.21/1.27 * CE 10 is refined into CE [33] 1.21/1.27 * CE 9 is refined into CE [34,35,36,37,38,39] 1.21/1.27 * CE 8 is refined into CE [40,41] 1.21/1.27 1.21/1.27 1.21/1.27 ### Cost equations --> "Loop" of f11_loop_cont/25 1.21/1.27 * CEs [39] --> Loop 33 1.21/1.27 * CEs [38] --> Loop 34 1.21/1.27 * CEs [37] --> Loop 35 1.21/1.27 * CEs [41] --> Loop 36 1.21/1.27 * CEs [33] --> Loop 37 1.21/1.27 * CEs [36] --> Loop 38 1.21/1.27 * CEs [35] --> Loop 39 1.21/1.27 * CEs [34] --> Loop 40 1.21/1.27 * CEs [40] --> Loop 41 1.21/1.27 1.21/1.27 ### Ranking functions of CR f11_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) 1.21/1.27 1.21/1.27 #### Partial ranking functions of CR f11_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) 1.21/1.27 1.21/1.27 1.21/1.27 ### Specialization of cost equations f0/24 1.21/1.27 * CE 1 is refined into CE [42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63] 1.21/1.27 1.21/1.27 1.21/1.27 ### Cost equations --> "Loop" of f0/24 1.21/1.27 * CEs [48] --> Loop 42 1.21/1.27 * CEs [44,56,58,59] --> Loop 43 1.21/1.27 * CEs [42,46,50,52,53,63] --> Loop 44 1.21/1.27 * CEs [62] --> Loop 45 1.21/1.27 * CEs [49] --> Loop 46 1.21/1.27 * CEs [45,57,60,61] --> Loop 47 1.21/1.27 * CEs [43,47,51,54,55] --> Loop 48 1.21/1.27 1.21/1.27 ### Ranking functions of CR f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,C1) 1.21/1.27 1.21/1.27 #### Partial ranking functions of CR f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,C1) 1.21/1.27 1.21/1.27 1.21/1.27 Computing Bounds 1.21/1.27 ===================================== 1.21/1.27 1.21/1.27 #### Cost of chains of f11(A,B,C,D,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1): 1.21/1.27 * Chain [[17],22]: 1*it(17)+0 1.21/1.27 Such that:it(17) =< -A+B 1.21/1.27 1.21/1.27 with precondition: [C1=2,E1=1,Q1=1,R1=1,S1=1,T1=0,B=D1,D=J1,F1=K1,F1=L1,F1=M1,F1=N1,R=O1,R=P1,0>=F1,B>=A+1] 1.21/1.27 1.21/1.27 * Chain [[17],21]: 1*it(17)+0 1.21/1.27 Such that:it(17) =< -A+D1 1.21/1.27 1.21/1.27 with precondition: [C1=2,E1=1,Q1=1,R1=1,S1=1,T1=0,D=J1,F1=K1,F1=L1,F1=M1,R=O1,R=P1,0>=N1,F1>=1,D1>=A+1,B>=D1+1] 1.21/1.27 1.21/1.27 * Chain [[17],20]: 1*it(17)+0 1.21/1.27 Such that:it(17) =< -A+D1 1.21/1.27 1.21/1.27 with precondition: [C1=3,P1=0,T1=0,D=J1,F1=K1,F1=L1,F1=M1,F1=N1,R=O1,E1=Q1,E1=R1,E1=S1,0>=E1,0>=F1,D1>=A+1,B>=D1+1] 1.21/1.27 1.21/1.27 * Chain [[17],19]: 1*it(17)+0 1.21/1.27 Such that:it(17) =< -A+D1 1.21/1.27 1.21/1.27 with precondition: [C1=3,P1=0,T1=0,D=J1,F1=K1,F1=L1,F1=M1,F1=N1,R=O1,E1=Q1,E1=R1,E1=S1,0>=F1,E1>=2,D1>=A+1,B>=D1+1] 1.21/1.27 1.21/1.27 * Chain [[17],18]: 1*it(17)+0 1.21/1.27 Such that:it(17) =< -A+B 1.21/1.27 1.21/1.27 with precondition: [C1=4,B>=A+1] 1.21/1.27 1.21/1.27 * Chain [22]: 0 1.21/1.27 with precondition: [C1=2,E1=C,F1=H,G1=I,H1=J,I1=K,J1=L,K1=M,L1=N,M1=O,N1=P,O1=Q,P1=R,Q1=S,R1=T,S1=U,T1=V,A=D1,A>=B] 1.21/1.27 1.21/1.27 * Chain [21]: 0 1.21/1.27 with precondition: [C1=2,E1=C,J1=D,N1=P,O1=Q,P1=R,Q1=S,R1=T,S1=U,T1=V,A=D1,F1=K1,F1=L1,F1=M1,F1>=1,B>=A+1] 1.21/1.27 1.21/1.27 * Chain [20]: 0 1.21/1.27 with precondition: [C1=3,P1=0,T1=0,J1=D,O1=R,A=D1,F1=K1,F1=L1,F1=M1,F1=N1,E1=Q1,E1=R1,E1=S1,0>=E1,0>=F1,B>=A+1] 1.21/1.27 1.21/1.27 * Chain [19]: 0 1.21/1.27 with precondition: [C1=3,P1=0,T1=0,J1=D,O1=R,A=D1,F1=K1,F1=L1,F1=M1,F1=N1,E1=Q1,E1=R1,E1=S1,0>=F1,E1>=2,B>=A+1] 1.21/1.27 1.21/1.27 * Chain [18]: 0 1.21/1.27 with precondition: [C1=4] 1.21/1.27 1.21/1.27 1.21/1.27 #### Cost of chains of f53(C1): 1.21/1.27 * Chain [[23]]...: 1*it(23)+0 1.21/1.27 with precondition: [C1=4] 1.21/1.27 1.21/1.27 * Chain [[23],24]: 1*it(23)+0 1.21/1.27 with precondition: [C1=4] 1.21/1.27 1.21/1.27 * Chain [24]: 0 1.21/1.27 with precondition: [C1=4] 1.21/1.27 1.21/1.27 1.21/1.27 #### Cost of chains of f45(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,C1): 1.21/1.27 * Chain [26]: 1*s(2)+0 1.21/1.27 with precondition: [F=0,W=0] 1.21/1.27 1.21/1.27 * Chain [25]...: 1*s(3)+0 1.21/1.27 with precondition: [F=0,W=0] 1.21/1.27 1.21/1.27 1.21/1.27 #### Cost of chains of f37(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,C1): 1.21/1.27 * Chain [32]: 1*s(4)+0 1.21/1.27 with precondition: [C=2,F=0,W=0] 1.21/1.27 1.21/1.27 * Chain [31]: 1*s(5)+0 1.21/1.27 with precondition: [F=0,W=0,1>=C] 1.21/1.27 1.21/1.27 * Chain [30]: 1*s(6)+0 1.21/1.27 with precondition: [F=0,W=0,C>=3] 1.21/1.27 1.21/1.27 * Chain [29]...: 1*s(7)+0 1.21/1.27 with precondition: [C=2,F=0,W=0] 1.21/1.27 1.21/1.27 * Chain [28]...: 1*s(8)+0 1.21/1.27 with precondition: [F=0,W=0,1>=C] 1.21/1.27 1.21/1.27 * Chain [27]...: 1*s(9)+0 1.21/1.27 with precondition: [F=0,W=0,C>=3] 1.21/1.27 1.21/1.27 1.21/1.27 #### Cost of chains of f11_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): 1.21/1.27 * Chain [41]: 1*s(10)+0 1.21/1.27 with precondition: [A=2,G=0,X=0] 1.21/1.27 1.21/1.27 * Chain [40]: 1*s(11)+0 1.21/1.27 with precondition: [A=3,D=2,G=0,X=0] 1.21/1.27 1.21/1.27 * Chain [39]: 1*s(12)+0 1.21/1.27 with precondition: [A=3,G=0,X=0,1>=D] 1.21/1.27 1.21/1.27 * Chain [38]: 1*s(13)+0 1.21/1.27 with precondition: [A=3,G=0,X=0,D>=3] 1.21/1.27 1.21/1.27 * Chain [37]: 0 1.21/1.27 with precondition: [A=4,G=0,X=0] 1.21/1.27 1.21/1.27 * Chain [36]...: 1*s(14)+0 1.21/1.27 with precondition: [A=2,G=0,X=0] 1.21/1.27 1.21/1.27 * Chain [35]...: 1*s(15)+0 1.21/1.27 with precondition: [A=3,D=2,G=0,X=0] 1.21/1.27 1.21/1.27 * Chain [34]...: 1*s(16)+0 1.21/1.27 with precondition: [A=3,G=0,X=0,1>=D] 1.21/1.27 1.21/1.27 * Chain [33]...: 1*s(17)+0 1.21/1.27 with precondition: [A=3,G=0,X=0,D>=3] 1.21/1.27 1.21/1.27 1.21/1.27 #### Cost of chains of f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,C1): 1.21/1.27 * Chain [48]...: 1*s(18)+5*s(19)+0 1.21/1.27 Such that:s(18) =< -A+B 1.21/1.27 1.21/1.27 with precondition: [B>=A+1] 1.21/1.27 1.21/1.27 * Chain [47]...: 4*s(24)+4*s(25)+0 1.21/1.27 Such that:aux(2) =< -A+B 1.21/1.27 s(24) =< aux(2) 1.21/1.27 1.21/1.27 with precondition: [B>=A+2] 1.21/1.27 1.21/1.27 * Chain [46]...: 1*s(32)+0 1.21/1.27 with precondition: [A>=B] 1.21/1.27 1.21/1.27 * Chain [45]: 0 1.21/1.27 with precondition: [] 1.21/1.27 1.21/1.27 * Chain [44]: 2*s(33)+5*s(34)+0 1.21/1.27 Such that:aux(3) =< -A+B 1.21/1.27 s(33) =< aux(3) 1.21/1.27 1.21/1.27 with precondition: [B>=A+1] 1.21/1.27 1.21/1.27 * Chain [43]: 4*s(40)+4*s(41)+0 1.21/1.27 Such that:aux(4) =< -A+B 1.21/1.27 s(40) =< aux(4) 1.21/1.27 1.21/1.27 with precondition: [B>=A+2] 1.21/1.27 1.21/1.27 * Chain [42]: 1*s(48)+0 1.21/1.27 with precondition: [A>=B] 1.21/1.27 1.21/1.27 1.21/1.27 Closed-form bounds of f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,C1): 1.21/1.27 ------------------------------------- 1.21/1.27 * Chain [48]... with precondition: [B>=A+1] 1.21/1.27 - Upper bound: inf 1.21/1.27 - Complexity: infinity 1.21/1.27 * Chain [47]... with precondition: [B>=A+2] 1.21/1.27 - Upper bound: inf 1.21/1.27 - Complexity: infinity 1.21/1.27 * Chain [46]... with precondition: [A>=B] 1.21/1.27 - Upper bound: inf 1.21/1.27 - Complexity: infinity 1.21/1.27 * Chain [45] with precondition: [] 1.21/1.27 - Upper bound: 0 1.21/1.27 - Complexity: constant 1.21/1.27 * Chain [44] with precondition: [B>=A+1] 1.21/1.27 - Upper bound: inf 1.21/1.27 - Complexity: infinity 1.21/1.27 * Chain [43] with precondition: [B>=A+2] 1.21/1.27 - Upper bound: inf 1.21/1.27 - Complexity: infinity 1.21/1.27 * Chain [42] with precondition: [A>=B] 1.21/1.27 - Upper bound: inf 1.21/1.27 - Complexity: infinity 1.21/1.27 1.21/1.27 ### Maximum cost of f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,C1): inf 1.21/1.27 Asymptotic class: infinity 1.21/1.27 * Total analysis performed in 1143 ms. 1.21/1.27 1.26/1.37 EOF