1.06/1.09 MAYBE 1.06/1.09 1.06/1.09 Preprocessing Cost Relations 1.06/1.09 ===================================== 1.06/1.09 1.06/1.09 #### Computed strongly connected components 1.06/1.09 0. recursive : [f11/36] 1.06/1.09 1. non_recursive : [exit_location/1] 1.06/1.09 2. recursive : [f49/1] 1.06/1.09 3. non_recursive : [f49_loop_cont/2] 1.06/1.09 4. non_recursive : [f35/21] 1.06/1.09 5. non_recursive : [f11_loop_cont/22] 1.06/1.09 6. non_recursive : [f0/21] 1.06/1.09 1.06/1.09 #### Obtained direct recursion through partial evaluation 1.06/1.09 0. SCC is partially evaluated into f11/36 1.06/1.09 1. SCC is completely evaluated into other SCCs 1.06/1.09 2. SCC is partially evaluated into f49/1 1.06/1.09 3. SCC is completely evaluated into other SCCs 1.06/1.09 4. SCC is partially evaluated into f35/21 1.06/1.09 5. SCC is partially evaluated into f11_loop_cont/22 1.06/1.09 6. SCC is partially evaluated into f0/21 1.06/1.09 1.06/1.09 Control-Flow Refinement of Cost Relations 1.06/1.09 ===================================== 1.06/1.09 1.06/1.09 ### Specialization of cost equations f11/36 1.06/1.09 * CE 4 is refined into CE [16] 1.06/1.09 * CE 5 is refined into CE [17] 1.06/1.09 * CE 3 is refined into CE [18] 1.06/1.09 * CE 2 is refined into CE [19] 1.06/1.09 * CE 7 is refined into CE [20] 1.06/1.09 * CE 6 is refined into CE [21] 1.06/1.09 1.06/1.09 1.06/1.09 ### Cost equations --> "Loop" of f11/36 1.06/1.09 * CEs [21] --> Loop 16 1.06/1.09 * CEs [16] --> Loop 17 1.06/1.09 * CEs [17] --> Loop 18 1.06/1.09 * CEs [18] --> Loop 19 1.06/1.09 * CEs [19] --> Loop 20 1.06/1.09 * CEs [20] --> Loop 21 1.06/1.09 1.06/1.09 ### Ranking functions of CR f11(A,B,C,D,E,G,H,I,J,K,L,M,N,O,P,Q,R,S,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1,P1,Q1) 1.06/1.09 * RF of phase [16]: [-A+B] 1.06/1.09 1.06/1.09 #### Partial ranking functions of CR f11(A,B,C,D,E,G,H,I,J,K,L,M,N,O,P,Q,R,S,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1,P1,Q1) 1.06/1.09 * Partial RF of phase [16]: 1.06/1.09 - RF of loop [16:1]: 1.06/1.09 -A+B 1.06/1.09 1.06/1.09 1.06/1.09 ### Specialization of cost equations f49/1 1.06/1.09 * CE 15 is refined into CE [22] 1.06/1.09 * CE 14 is refined into CE [23] 1.06/1.09 1.06/1.09 1.06/1.09 ### Cost equations --> "Loop" of f49/1 1.06/1.09 * CEs [23] --> Loop 22 1.06/1.09 * CEs [22] --> Loop 23 1.06/1.09 1.06/1.09 ### Ranking functions of CR f49(Z) 1.06/1.09 1.06/1.09 #### Partial ranking functions of CR f49(Z) 1.06/1.09 1.06/1.09 1.06/1.09 ### Specialization of cost equations f35/21 1.06/1.09 * CE 11 is refined into CE [24,25] 1.06/1.09 * CE 12 is refined into CE [26,27] 1.06/1.09 * CE 13 is refined into CE [28,29] 1.06/1.09 1.06/1.09 1.06/1.09 ### Cost equations --> "Loop" of f35/21 1.06/1.09 * CEs [25] --> Loop 24 1.06/1.09 * CEs [27] --> Loop 25 1.06/1.09 * CEs [29] --> Loop 26 1.06/1.09 * CEs [24] --> Loop 27 1.06/1.09 * CEs [26] --> Loop 28 1.06/1.09 * CEs [28] --> Loop 29 1.06/1.09 1.06/1.09 ### Ranking functions of CR f35(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,Z) 1.06/1.09 1.06/1.09 #### Partial ranking functions of CR f35(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,Z) 1.06/1.09 1.06/1.09 1.06/1.09 ### Specialization of cost equations f11_loop_cont/22 1.06/1.09 * CE 8 is refined into CE [30,31,32,33,34,35] 1.06/1.09 * CE 10 is refined into CE [36,37] 1.06/1.09 * CE 9 is refined into CE [38] 1.06/1.09 1.06/1.09 1.06/1.09 ### Cost equations --> "Loop" of f11_loop_cont/22 1.06/1.09 * CEs [32] --> Loop 30 1.06/1.09 * CEs [31] --> Loop 31 1.06/1.09 * CEs [30] --> Loop 32 1.06/1.09 * CEs [36] --> Loop 33 1.06/1.09 * CEs [38] --> Loop 34 1.06/1.09 * CEs [35] --> Loop 35 1.06/1.09 * CEs [34] --> Loop 36 1.06/1.09 * CEs [33] --> Loop 37 1.06/1.09 * CEs [37] --> Loop 38 1.06/1.09 1.06/1.09 ### 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) 1.06/1.09 1.06/1.09 #### 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) 1.06/1.09 1.06/1.09 1.06/1.09 ### Specialization of cost equations f0/21 1.06/1.09 * CE 1 is refined into CE [39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60] 1.06/1.09 1.06/1.09 1.06/1.09 ### Cost equations --> "Loop" of f0/21 1.06/1.09 * CEs [48] --> Loop 39 1.06/1.09 * CEs [44,56,59,60] --> Loop 40 1.06/1.09 * CEs [42,46,50,53,54] --> Loop 41 1.06/1.09 * CEs [47] --> Loop 42 1.06/1.09 * CEs [43,55,57,58] --> Loop 43 1.06/1.09 * CEs [40,41,45,49,51,52] --> Loop 44 1.06/1.09 * CEs [39] --> Loop 45 1.06/1.09 1.06/1.09 ### 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,Z) 1.06/1.09 1.06/1.09 #### 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,Z) 1.06/1.09 1.06/1.09 1.06/1.09 Computing Bounds 1.06/1.09 ===================================== 1.06/1.09 1.06/1.09 #### Cost of chains of f11(A,B,C,D,E,G,H,I,J,K,L,M,N,O,P,Q,R,S,Z,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1,N1,O1,P1,Q1): 1.06/1.09 * Chain [[16],21]: 1*it(16)+0 1.06/1.09 Such that:it(16) =< -A+B 1.06/1.09 1.06/1.09 with precondition: [C=0,Z=2,B>=A+1] 1.06/1.09 1.06/1.09 * Chain [[16],20]: 1*it(16)+0 1.06/1.09 Such that:it(16) =< -A+B 1.06/1.09 1.06/1.09 with precondition: [C=0,Z=3,B1=0,C1=0,D1=1,O1=1,P1=1,Q1=0,B=A1,D=I1,E1=J1,E1=K1,E1=L1,P=M1,P=N1,0>=E1,B>=A+1] 1.06/1.09 1.06/1.09 * Chain [[16],19]: 1*it(16)+0 1.06/1.09 Such that:it(16) =< -A+A1 1.06/1.09 1.06/1.09 with precondition: [C=0,Z=3,B1=0,C1=0,D1=1,O1=1,P1=1,Q1=0,D=I1,E1=J1,E1=K1,P=M1,P=N1,0>=L1,E1>=1,A1>=A+1,B>=A1+1] 1.06/1.09 1.06/1.09 * Chain [[16],18]: 1*it(16)+0 1.06/1.09 Such that:it(16) =< -A+A1 1.06/1.09 1.06/1.09 with precondition: [C=0,Z=4,B1=0,N1=0,Q1=0,D=C1,D=I1,E1=J1,E1=K1,E1=L1,P=M1,D1=O1,D1=P1,0>=D1,0>=E1,A1>=A+1,B>=A1+1] 1.06/1.09 1.06/1.09 * Chain [[16],17]: 1*it(16)+0 1.06/1.09 Such that:it(16) =< -A+A1 1.06/1.09 1.06/1.09 with precondition: [C=0,Z=4,B1=0,N1=0,Q1=0,D=C1,D=I1,E1=J1,E1=K1,E1=L1,P=M1,D1=O1,D1=P1,0>=E1,D1>=2,A1>=A+1,B>=A1+1] 1.06/1.09 1.06/1.09 * Chain [21]: 0 1.06/1.09 with precondition: [C=0,Z=2] 1.06/1.09 1.06/1.09 * Chain [20]: 0 1.06/1.09 with precondition: [C=0,Z=3,B1=0,C1=0,D1=E,E1=G,F1=H,G1=I,H1=J,I1=K,J1=L,K1=M,L1=N,M1=O,N1=P,O1=Q,P1=R,Q1=S,A=A1,A>=B] 1.06/1.09 1.06/1.09 * Chain [19]: 0 1.06/1.09 with precondition: [C=0,Z=3,B1=0,C1=0,I1=D,D1=E,L1=N,M1=O,N1=P,O1=Q,P1=R,Q1=S,A=A1,E1=J1,E1=K1,E1>=1,B>=A+1] 1.06/1.09 1.06/1.09 * Chain [18]: 0 1.06/1.09 with precondition: [C=0,Z=4,B1=0,N1=0,Q1=0,M1=P,A=A1,D=C1,D=I1,E1=J1,E1=K1,E1=L1,D1=O1,D1=P1,0>=D1,0>=E1,B>=A+1] 1.06/1.09 1.06/1.09 * Chain [17]: 0 1.06/1.09 with precondition: [C=0,Z=4,B1=0,N1=0,Q1=0,M1=P,A=A1,D=C1,D=I1,E1=J1,E1=K1,E1=L1,D1=O1,D1=P1,0>=E1,D1>=2,B>=A+1] 1.06/1.09 1.06/1.09 1.06/1.09 #### Cost of chains of f49(Z): 1.06/1.09 * Chain [[22]]...: 1*it(22)+0 1.06/1.09 with precondition: [Z=2] 1.06/1.09 1.06/1.09 * Chain [[22],23]: 1*it(22)+0 1.06/1.09 with precondition: [Z=2] 1.06/1.09 1.06/1.09 * Chain [23]: 0 1.06/1.09 with precondition: [Z=2] 1.06/1.09 1.06/1.09 1.06/1.09 #### Cost of chains of f35(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,Z): 1.06/1.09 * Chain [29]: 1*s(2)+0 1.06/1.09 with precondition: [E=2,T=0] 1.06/1.09 1.06/1.09 * Chain [28]: 1*s(3)+0 1.06/1.09 with precondition: [T=0,1>=E] 1.06/1.09 1.06/1.09 * Chain [27]: 1*s(4)+0 1.06/1.09 with precondition: [T=0,E>=3] 1.06/1.09 1.06/1.09 * Chain [26]...: 1*s(5)+0 1.06/1.09 with precondition: [E=2,T=0] 1.06/1.09 1.06/1.09 * Chain [25]...: 1*s(6)+0 1.06/1.09 with precondition: [T=0,1>=E] 1.06/1.09 1.06/1.09 * Chain [24]...: 1*s(7)+0 1.06/1.09 with precondition: [T=0,E>=3] 1.06/1.09 1.06/1.09 1.06/1.09 #### 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): 1.06/1.09 * Chain [38]...: 1*s(8)+0 1.06/1.09 with precondition: [A=3,U=0] 1.06/1.09 1.06/1.09 * Chain [37]...: 1*s(9)+0 1.06/1.09 with precondition: [A=4,F=2,U=0] 1.06/1.09 1.06/1.09 * Chain [36]...: 1*s(10)+0 1.06/1.09 with precondition: [A=4,U=0,1>=F] 1.06/1.09 1.06/1.09 * Chain [35]...: 1*s(11)+0 1.06/1.09 with precondition: [A=4,U=0,F>=3] 1.06/1.09 1.06/1.09 * Chain [34]: 0 1.06/1.09 with precondition: [A=2,U=0] 1.06/1.09 1.06/1.09 * Chain [33]: 1*s(12)+0 1.06/1.09 with precondition: [A=3,U=0] 1.06/1.09 1.06/1.09 * Chain [32]: 1*s(13)+0 1.06/1.09 with precondition: [A=4,F=2,U=0] 1.06/1.09 1.06/1.09 * Chain [31]: 1*s(14)+0 1.06/1.09 with precondition: [A=4,U=0,1>=F] 1.06/1.09 1.06/1.09 * Chain [30]: 1*s(15)+0 1.06/1.09 with precondition: [A=4,U=0,F>=3] 1.06/1.09 1.06/1.09 1.06/1.09 #### 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,Z): 1.06/1.09 * Chain [45]: 0 1.06/1.09 with precondition: [] 1.06/1.09 1.06/1.09 * Chain [44]: 2*s(16)+5*s(18)+0 1.06/1.09 Such that:aux(2) =< -A+B 1.06/1.09 s(16) =< aux(2) 1.06/1.09 1.06/1.09 with precondition: [B>=A+1] 1.06/1.09 1.06/1.09 * Chain [43]: 4*s(23)+4*s(24)+0 1.06/1.09 Such that:aux(3) =< -A+B 1.06/1.09 s(23) =< aux(3) 1.06/1.09 1.06/1.09 with precondition: [B>=A+2] 1.06/1.09 1.06/1.09 * Chain [42]: 1*s(31)+0 1.06/1.09 with precondition: [A>=B] 1.06/1.09 1.06/1.09 * Chain [41]...: 1*s(32)+5*s(33)+0 1.06/1.09 Such that:s(32) =< -A+B 1.06/1.09 1.06/1.09 with precondition: [B>=A+1] 1.06/1.09 1.06/1.09 * Chain [40]...: 4*s(38)+4*s(39)+0 1.06/1.09 Such that:aux(4) =< -A+B 1.06/1.09 s(38) =< aux(4) 1.06/1.09 1.06/1.09 with precondition: [B>=A+2] 1.06/1.09 1.06/1.09 * Chain [39]...: 1*s(46)+0 1.06/1.09 with precondition: [A>=B] 1.06/1.09 1.06/1.09 1.06/1.09 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,Z): 1.06/1.09 ------------------------------------- 1.06/1.09 * Chain [45] with precondition: [] 1.06/1.09 - Upper bound: 0 1.06/1.09 - Complexity: constant 1.06/1.09 * Chain [44] with precondition: [B>=A+1] 1.06/1.09 - Upper bound: inf 1.06/1.09 - Complexity: infinity 1.06/1.09 * Chain [43] with precondition: [B>=A+2] 1.06/1.09 - Upper bound: inf 1.06/1.09 - Complexity: infinity 1.06/1.09 * Chain [42] with precondition: [A>=B] 1.06/1.09 - Upper bound: inf 1.06/1.09 - Complexity: infinity 1.06/1.09 * Chain [41]... with precondition: [B>=A+1] 1.06/1.09 - Upper bound: inf 1.06/1.09 - Complexity: infinity 1.06/1.09 * Chain [40]... with precondition: [B>=A+2] 1.06/1.09 - Upper bound: inf 1.06/1.09 - Complexity: infinity 1.06/1.09 * Chain [39]... with precondition: [A>=B] 1.06/1.09 - Upper bound: inf 1.06/1.09 - Complexity: infinity 1.06/1.09 1.06/1.09 ### Maximum cost of f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,Z): inf 1.06/1.09 Asymptotic class: infinity 1.06/1.10 * Total analysis performed in 982 ms. 1.06/1.10 1.09/1.20 EOF