0.99/1.00 MAYBE 0.99/1.00 0.99/1.00 Preprocessing Cost Relations 0.99/1.00 ===================================== 0.99/1.00 0.99/1.00 #### Computed strongly connected components 0.99/1.00 0. recursive : [f2/32] 0.99/1.00 1. non_recursive : [exit_location/1] 0.99/1.00 2. recursive : [f8/5] 0.99/1.00 3. non_recursive : [f8_loop_cont/2] 0.99/1.00 4. non_recursive : [f2_loop_cont/29] 0.99/1.00 5. non_recursive : [f23/28] 0.99/1.00 0.99/1.00 #### Obtained direct recursion through partial evaluation 0.99/1.00 0. SCC is partially evaluated into f2/32 0.99/1.00 1. SCC is completely evaluated into other SCCs 0.99/1.00 2. SCC is partially evaluated into f8/5 0.99/1.00 3. SCC is completely evaluated into other SCCs 0.99/1.00 4. SCC is partially evaluated into f2_loop_cont/29 0.99/1.00 5. SCC is partially evaluated into f23/28 0.99/1.00 0.99/1.00 Control-Flow Refinement of Cost Relations 0.99/1.00 ===================================== 0.99/1.00 0.99/1.00 ### Specialization of cost equations f2/32 0.99/1.00 * CE 4 is refined into CE [12] 0.99/1.00 * CE 5 is refined into CE [13] 0.99/1.00 * CE 6 is refined into CE [14] 0.99/1.00 * CE 2 is refined into CE [15] 0.99/1.00 * CE 3 is refined into CE [16] 0.99/1.00 0.99/1.00 0.99/1.00 ### Cost equations --> "Loop" of f2/32 0.99/1.00 * CEs [15] --> Loop 12 0.99/1.00 * CEs [16] --> Loop 13 0.99/1.00 * CEs [12] --> Loop 14 0.99/1.00 * CEs [13] --> Loop 15 0.99/1.00 * CEs [14] --> Loop 16 0.99/1.00 0.99/1.00 ### Ranking functions of CR f2(A,B,C,D,E,F,G,H,I,J,K,L,M,Q,U,A1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1,V1,W1,X1,Y1,Z1) 0.99/1.00 * RF of phase [12,13]: [G,-H+3,-I+3,J] 0.99/1.00 0.99/1.00 #### Partial ranking functions of CR f2(A,B,C,D,E,F,G,H,I,J,K,L,M,Q,U,A1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1,V1,W1,X1,Y1,Z1) 0.99/1.00 * Partial RF of phase [12,13]: 0.99/1.00 - RF of loop [12:1,13:1]: 0.99/1.00 G 0.99/1.00 -H+3 0.99/1.00 -I+3 0.99/1.00 J 0.99/1.00 0.99/1.00 0.99/1.00 ### Specialization of cost equations f8/5 0.99/1.00 * CE 11 is refined into CE [17] 0.99/1.00 * CE 9 is refined into CE [18] 0.99/1.00 * CE 10 is refined into CE [19] 0.99/1.00 0.99/1.00 0.99/1.00 ### Cost equations --> "Loop" of f8/5 0.99/1.00 * CEs [18] --> Loop 17 0.99/1.00 * CEs [19] --> Loop 18 0.99/1.00 * CEs [17] --> Loop 19 0.99/1.00 0.99/1.00 ### Ranking functions of CR f8(A,B,C,D,K1) 0.99/1.00 0.99/1.00 #### Partial ranking functions of CR f8(A,B,C,D,K1) 0.99/1.00 0.99/1.00 0.99/1.00 ### Specialization of cost equations f2_loop_cont/29 0.99/1.00 * CE 8 is refined into CE [20,21,22,23,24] 0.99/1.00 * CE 7 is refined into CE [25] 0.99/1.00 0.99/1.00 0.99/1.00 ### Cost equations --> "Loop" of f2_loop_cont/29 0.99/1.00 * CEs [22] --> Loop 20 0.99/1.00 * CEs [21] --> Loop 21 0.99/1.00 * CEs [20] --> Loop 22 0.99/1.00 * CEs [25] --> Loop 23 0.99/1.00 * CEs [24] --> Loop 24 0.99/1.00 * CEs [23] --> Loop 25 0.99/1.00 0.99/1.00 ### Ranking functions of CR f2_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) 0.99/1.00 0.99/1.00 #### Partial ranking functions of CR f2_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) 0.99/1.00 0.99/1.00 0.99/1.00 ### Specialization of cost equations f23/28 0.99/1.00 * CE 1 is refined into CE [26,27,28,29,30,31,32,33,34,35,36,37,38,39] 0.99/1.00 0.99/1.00 0.99/1.00 ### Cost equations --> "Loop" of f23/28 0.99/1.00 * CEs [28,31,36,39] --> Loop 26 0.99/1.00 * CEs [26,27,29,30,32,33,34,35,37,38] --> Loop 27 0.99/1.00 0.99/1.00 ### Ranking functions of CR f23(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,K1) 0.99/1.00 0.99/1.00 #### Partial ranking functions of CR f23(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,K1) 0.99/1.00 0.99/1.00 0.99/1.00 Computing Bounds 0.99/1.00 ===================================== 0.99/1.00 0.99/1.00 #### Cost of chains of f2(A,B,C,D,E,F,G,H,I,J,K,L,M,Q,U,A1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1,V1,W1,X1,Y1,Z1): 0.99/1.00 * Chain [[12,13],16]: 2*it(12)+0 0.99/1.00 Such that:aux(9) =< J 0.99/1.00 it(12) =< aux(9) 0.99/1.00 0.99/1.00 with precondition: [K1=2,G=J,G+H=3,G+I=3,2>=G,G>=1] 0.99/1.00 0.99/1.00 * Chain [[12,13],15]: 2*it(12)+0 0.99/1.00 Such that:aux(10) =< 1 0.99/1.00 aux(11) =< 2 0.99/1.00 it(12) =< aux(11) 0.99/1.00 it(12) =< aux(10) 0.99/1.00 0.99/1.00 with precondition: [G=2,H=1,I=1,J=2,K1=3,Q1=1,R1=2,S1=2,T1=1,W1=1,L1=M1,L1=N1,E=O1,E=P1,L1>=A+1] 0.99/1.00 0.99/1.00 * Chain [[12,13],14]: 2*it(12)+0 0.99/1.00 Such that:aux(12) =< 1 0.99/1.00 aux(13) =< 2 0.99/1.00 it(12) =< aux(13) 0.99/1.00 it(12) =< aux(12) 0.99/1.00 0.99/1.00 with precondition: [G=2,H=1,I=1,J=2,K1=3,Q1=1,R1=2,S1=2,T1=1,W1=1,L1=M1,L1=N1,E=O1,E=P1,A>=L1+1] 0.99/1.00 0.99/1.00 * Chain [16]: 0 0.99/1.00 with precondition: [K1=2,J=G,H+J=3,I+J=3,2>=J] 0.99/1.00 0.99/1.00 * Chain [15]: 0 0.99/1.00 with precondition: [K1=3,E=F,I=H,U1=K,V1=L,W1=M,L1=M1,L1=N1,E=O1,E=P1,I=R1,I=S1,G+I=3,I+J=3,I+Q1=3,I+T1=3,2>=I,I>=1,L1>=A+1] 0.99/1.00 0.99/1.00 * Chain [14]: 0 0.99/1.00 with precondition: [K1=3,E=F,I=H,U1=K,V1=L,W1=M,L1=M1,L1=N1,E=O1,E=P1,I=R1,I=S1,G+I=3,I+J=3,I+Q1=3,I+T1=3,2>=I,I>=1,A>=L1+1] 0.99/1.00 0.99/1.00 0.99/1.00 #### Cost of chains of f8(A,B,C,D,K1): 0.99/1.00 * Chain [[18]]...: 1*it(18)+0 0.99/1.00 with precondition: [B>=A+1,K1=2] 0.99/1.00 0.99/1.00 * Chain [[18],19]: 1*it(18)+0 0.99/1.00 with precondition: [K1=2,B>=A+1] 0.99/1.00 0.99/1.00 * Chain [[17]]...: 1*it(17)+0 0.99/1.00 with precondition: [A>=B+1,K1=2] 0.99/1.00 0.99/1.00 * Chain [[17],19]: 1*it(17)+0 0.99/1.00 with precondition: [K1=2,A>=B+1] 0.99/1.00 0.99/1.00 * Chain [19]: 0 0.99/1.00 with precondition: [K1=2] 0.99/1.00 0.99/1.00 0.99/1.00 #### Cost of chains of f2_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): 0.99/1.00 * Chain [25]...: 1*s(1)+0 0.99/1.00 with precondition: [A=3,O=2,Y=2,A1=0,T=S,T=U,C>=B+1] 0.99/1.00 0.99/1.00 * Chain [24]...: 1*s(2)+0 0.99/1.00 with precondition: [A=3,O=2,Y=2,A1=0,T=S,T=U,B>=C+1] 0.99/1.00 0.99/1.00 * Chain [23]: 0 0.99/1.00 with precondition: [A=2,O=2,Y=2,A1=0,T=S,T=U] 0.99/1.00 0.99/1.00 * Chain [22]: 0 0.99/1.00 with precondition: [A=3,O=2,Y=2,A1=0,T=S,T=U] 0.99/1.00 0.99/1.00 * Chain [21]: 1*s(3)+0 0.99/1.00 with precondition: [A=3,O=2,Y=2,A1=0,T=S,T=U,C>=B+1] 0.99/1.00 0.99/1.00 * Chain [20]: 1*s(4)+0 0.99/1.00 with precondition: [A=3,O=2,Y=2,A1=0,T=S,T=U,B>=C+1] 0.99/1.00 0.99/1.00 0.99/1.00 #### Cost of chains of f23(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,K1): 0.99/1.00 * Chain [27]: 1*aux(16)+0 0.99/1.00 with precondition: [] 0.99/1.00 0.99/1.00 * Chain [26]...: 1*aux(19)+0 0.99/1.00 with precondition: [] 0.99/1.00 0.99/1.00 0.99/1.00 Closed-form bounds of f23(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,K1): 0.99/1.00 ------------------------------------- 0.99/1.00 * Chain [27] with precondition: [] 0.99/1.00 - Upper bound: inf 0.99/1.00 - Complexity: infinity 0.99/1.00 * Chain [26]... with precondition: [] 0.99/1.00 - Upper bound: inf 0.99/1.00 - Complexity: infinity 0.99/1.00 0.99/1.00 ### Maximum cost of f23(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,K1): inf 0.99/1.00 Asymptotic class: infinity 0.99/1.00 * Total analysis performed in 886 ms. 0.99/1.00 1.00/1.10 EOF