0.72/0.74 WORST_CASE(?,O(n^1)) 0.72/0.74 0.72/0.74 Preprocessing Cost Relations 0.72/0.74 ===================================== 0.72/0.74 0.72/0.74 #### Computed strongly connected components 0.72/0.74 0. recursive : [lbl81/21] 0.72/0.74 1. recursive : [lbl71/21,lbl81_loop_cont/22] 0.72/0.74 2. non_recursive : [exit_location/1] 0.72/0.74 3. non_recursive : [stop/11] 0.72/0.74 4. non_recursive : [lbl71_loop_cont/12] 0.72/0.74 5. non_recursive : [start/11] 0.72/0.74 6. non_recursive : [start0/11] 0.72/0.74 0.72/0.74 #### Obtained direct recursion through partial evaluation 0.72/0.74 0. SCC is partially evaluated into lbl81/21 0.72/0.74 1. SCC is partially evaluated into lbl71/21 0.72/0.74 2. SCC is completely evaluated into other SCCs 0.72/0.74 3. SCC is completely evaluated into other SCCs 0.72/0.74 4. SCC is partially evaluated into lbl71_loop_cont/12 0.72/0.74 5. SCC is partially evaluated into start/11 0.72/0.74 6. SCC is partially evaluated into start0/11 0.72/0.74 0.72/0.74 Control-Flow Refinement of Cost Relations 0.72/0.74 ===================================== 0.72/0.74 0.72/0.74 ### Specialization of cost equations lbl81/21 0.72/0.74 * CE 9 is refined into CE [15] 0.72/0.74 * CE 7 is refined into CE [16] 0.72/0.74 * CE 8 is refined into CE [17] 0.72/0.74 0.72/0.74 0.72/0.74 ### Cost equations --> "Loop" of lbl81/21 0.72/0.74 * CEs [17] --> Loop 14 0.72/0.74 * CEs [15] --> Loop 15 0.72/0.74 * CEs [16] --> Loop 16 0.72/0.74 0.72/0.74 ### Ranking functions of CR lbl81(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U) 0.72/0.74 * RF of phase [14]: [C-D+1,-D+G+1] 0.72/0.74 0.72/0.74 #### Partial ranking functions of CR lbl81(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U) 0.72/0.74 * Partial RF of phase [14]: 0.72/0.74 - RF of loop [14:1]: 0.72/0.74 C-D+1 0.72/0.74 -D+G+1 0.72/0.74 0.72/0.74 0.72/0.74 ### Specialization of cost equations lbl71/21 0.72/0.74 * CE 14 is refined into CE [18] 0.72/0.74 * CE 12 is refined into CE [19] 0.72/0.74 * CE 13 is refined into CE [20] 0.72/0.74 0.72/0.74 0.72/0.75 ### Cost equations --> "Loop" of lbl71/21 0.72/0.75 * CEs [20] --> Loop 17 0.72/0.75 * CEs [18] --> Loop 18 0.72/0.75 * CEs [19] --> Loop 19 0.72/0.75 0.72/0.75 ### Ranking functions of CR lbl71(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U) 0.72/0.75 * RF of phase [17]: [C-D+1,-D+G+1] 0.72/0.75 0.72/0.75 #### Partial ranking functions of CR lbl71(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U) 0.72/0.75 * Partial RF of phase [17]: 0.72/0.75 - RF of loop [17:1]: 0.72/0.75 C-D+1 0.72/0.75 -D+G+1 0.72/0.75 0.72/0.75 0.72/0.75 ### Specialization of cost equations lbl71_loop_cont/12 0.72/0.75 * CE 11 is refined into CE [21] 0.72/0.75 * CE 10 is refined into CE [22] 0.72/0.75 0.72/0.75 0.72/0.75 ### Cost equations --> "Loop" of lbl71_loop_cont/12 0.72/0.75 * CEs [21] --> Loop 20 0.72/0.75 * CEs [22] --> Loop 21 0.72/0.75 0.72/0.75 ### Ranking functions of CR lbl71_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L) 0.72/0.75 0.72/0.75 #### Partial ranking functions of CR lbl71_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L) 0.72/0.75 0.72/0.75 0.72/0.75 ### Specialization of cost equations start/11 0.72/0.75 * CE 4 is refined into CE [23] 0.72/0.75 * CE 5 is refined into CE [24,25,26,27] 0.72/0.75 * CE 6 is refined into CE [28] 0.72/0.75 * CE 2 is refined into CE [29,30] 0.72/0.75 * CE 3 is refined into CE [31,32] 0.72/0.75 0.72/0.75 0.72/0.75 ### Cost equations --> "Loop" of start/11 0.72/0.75 * CEs [23] --> Loop 22 0.72/0.75 * CEs [25,27] --> Loop 23 0.72/0.75 * CEs [26] --> Loop 24 0.72/0.75 * CEs [28] --> Loop 25 0.72/0.75 * CEs [30,32] --> Loop 26 0.72/0.75 * CEs [29] --> Loop 27 0.72/0.75 * CEs [24] --> Loop 28 0.72/0.75 * CEs [31] --> Loop 29 0.72/0.75 0.72/0.75 ### Ranking functions of CR start(A,B,C,D,E,F,G,H,I,J,K) 0.72/0.75 0.72/0.75 #### Partial ranking functions of CR start(A,B,C,D,E,F,G,H,I,J,K) 0.72/0.75 0.72/0.75 0.72/0.75 ### Specialization of cost equations start0/11 0.72/0.75 * CE 1 is refined into CE [33,34,35,36,37,38,39,40] 0.72/0.75 0.72/0.75 0.72/0.75 ### Cost equations --> "Loop" of start0/11 0.72/0.75 * CEs [38] --> Loop 30 0.72/0.75 * CEs [37] --> Loop 31 0.72/0.75 * CEs [36] --> Loop 32 0.72/0.75 * CEs [35] --> Loop 33 0.72/0.75 * CEs [34] --> Loop 34 0.72/0.75 * CEs [33] --> Loop 35 0.72/0.75 * CEs [40] --> Loop 36 0.72/0.75 * CEs [39] --> Loop 37 0.72/0.75 0.72/0.75 ### Ranking functions of CR start0(A,B,C,D,E,F,G,H,I,J,K) 0.72/0.75 0.72/0.75 #### Partial ranking functions of CR start0(A,B,C,D,E,F,G,H,I,J,K) 0.72/0.75 0.72/0.75 0.72/0.75 Computing Bounds 0.72/0.75 ===================================== 0.72/0.75 0.72/0.75 #### Cost of chains of lbl81(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U): 0.72/0.75 * Chain [[14],16]: 1*it(14)+0 0.72/0.75 Such that:it(14) =< -D+R+1 0.72/0.75 0.72/0.75 with precondition: [E+1=0,K=2,P+1=0,C=G,H=I,A=J,A=L,B=M,C=N,C+1=O,F=Q,C=R,H=S,H=T,A=U,0>=A,D>=B+1,C>=D] 0.72/0.75 0.72/0.75 * Chain [[14],15]: 1*it(14)+0 0.72/0.75 Such that:it(14) =< -D+G+1 0.72/0.75 0.72/0.75 with precondition: [E+1=0,K=4,C=G,H=I,A=J,0>=A,D>=B+1,C>=D] 0.72/0.75 0.72/0.75 * Chain [16]: 0 0.72/0.75 with precondition: [E+1=0,K=2,P+1=0,J=A,C+1=D,Q=F,C=G,I=H,J=L,B=M,C=N,C+1=O,C=R,I=S,I=T,J=U,0>=J,C>=B] 0.72/0.75 0.72/0.75 * Chain [15]: 0 0.72/0.75 with precondition: [E+1=0,K=4,J=A,G=C,I=H,0>=J,D>=B+1,G+1>=D] 0.72/0.75 0.72/0.75 0.72/0.75 #### Cost of chains of lbl71(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U): 0.72/0.75 * Chain [[17],19]: 1*it(17)+0 0.72/0.75 Such that:it(17) =< -D+R+1 0.72/0.75 0.72/0.75 with precondition: [E=1,K=2,P=1,C=G,H=I,A=J,A=L,B=M,C=N,C+1=O,F=Q,C=R,H=S,H=T,A=U,A>=1,D>=B+1,C>=D] 0.72/0.75 0.72/0.75 * Chain [[17],18]: 1*it(17)+0 0.72/0.75 Such that:it(17) =< C-D+1 0.72/0.75 0.72/0.75 with precondition: [E=1,K=4,C=G,H=I,A=J,A>=1,D>=B+1,C>=D] 0.72/0.75 0.72/0.75 * Chain [19]: 0 0.72/0.75 with precondition: [E=1,K=2,P=1,J=A,C+1=D,Q=F,C=G,I=H,J=L,B=M,C=N,C+1=O,C=R,I=S,I=T,J=U,J>=1,C>=B] 0.72/0.75 0.72/0.75 * Chain [18]: 0 0.72/0.75 with precondition: [E=1,K=4,J=A,G=C,I=H,J>=1,D>=B+1,G+1>=D] 0.72/0.75 0.72/0.75 0.72/0.75 #### Cost of chains of lbl71_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L): 0.72/0.75 * Chain [21]: 0 0.72/0.75 with precondition: [A=2] 0.72/0.75 0.72/0.75 * Chain [20]: 0 0.72/0.75 with precondition: [A=4] 0.72/0.75 0.72/0.75 0.72/0.75 #### Cost of chains of start(A,B,C,D,E,F,G,H,I,J,K): 0.72/0.75 * Chain [29]: 0 0.72/0.75 with precondition: [J=A,B=C,B=D,F=E,B=G,I=H,0>=J] 0.72/0.75 0.72/0.75 * Chain [28]: 0 0.72/0.75 with precondition: [J=A,B=C,B=D,F=E,B=G,I=H,J>=1] 0.72/0.75 0.72/0.75 * Chain [27]: 0 0.72/0.75 with precondition: [J=A,D=B,G=C,F=E,I=H,0>=J,G>=D] 0.72/0.75 0.72/0.75 * Chain [26]: 2*s(1)+0 0.72/0.75 Such that:aux(1) =< -B+G 0.72/0.75 s(1) =< aux(1) 0.72/0.75 0.72/0.75 with precondition: [J=A,D=B,G=C,F=E,I=H,0>=J,G>=D+1] 0.72/0.75 0.72/0.75 * Chain [25]: 0 0.72/0.75 with precondition: [J=A,D=B,G=C,F=E,I=H,0>=J,D>=G+1] 0.72/0.75 0.72/0.75 * Chain [24]: 0 0.72/0.75 with precondition: [J=A,D=B,G=C,F=E,I=H,J>=1,G>=D] 0.72/0.75 0.72/0.75 * Chain [23]: 2*s(3)+0 0.72/0.75 Such that:aux(2) =< -B+G 0.72/0.75 s(3) =< aux(2) 0.72/0.75 0.72/0.75 with precondition: [J=A,D=B,G=C,F=E,I=H,J>=1,G>=D+1] 0.72/0.75 0.72/0.75 * Chain [22]: 0 0.72/0.75 with precondition: [J=A,D=B,G=C,F=E,I=H,J>=1,D>=G+1] 0.72/0.75 0.72/0.75 0.72/0.75 #### Cost of chains of start0(A,B,C,D,E,F,G,H,I,J,K): 0.72/0.75 * Chain [37]: 0 0.72/0.75 with precondition: [C=B,0>=A] 0.72/0.75 0.72/0.75 * Chain [36]: 0 0.72/0.75 with precondition: [C=B,A>=1] 0.72/0.75 0.72/0.75 * Chain [35]: 0 0.72/0.75 with precondition: [0>=A,C>=B] 0.72/0.75 0.72/0.75 * Chain [34]: 2*s(6)+0 0.72/0.75 Such that:s(5) =< -B+C 0.72/0.75 s(6) =< s(5) 0.72/0.75 0.72/0.75 with precondition: [0>=A,C>=B+1] 0.72/0.75 0.72/0.75 * Chain [33]: 0 0.72/0.75 with precondition: [0>=A,B>=C+1] 0.72/0.75 0.72/0.75 * Chain [32]: 0 0.72/0.75 with precondition: [A>=1,C>=B] 0.72/0.75 0.72/0.75 * Chain [31]: 2*s(8)+0 0.72/0.75 Such that:s(7) =< -B+C 0.72/0.75 s(8) =< s(7) 0.72/0.75 0.72/0.75 with precondition: [A>=1,C>=B+1] 0.72/0.75 0.72/0.75 * Chain [30]: 0 0.72/0.75 with precondition: [A>=1,B>=C+1] 0.72/0.75 0.72/0.75 0.72/0.75 Closed-form bounds of start0(A,B,C,D,E,F,G,H,I,J,K): 0.72/0.75 ------------------------------------- 0.72/0.75 * Chain [37] with precondition: [C=B,0>=A] 0.72/0.75 - Upper bound: 0 0.72/0.75 - Complexity: constant 0.72/0.75 * Chain [36] with precondition: [C=B,A>=1] 0.72/0.75 - Upper bound: 0 0.72/0.75 - Complexity: constant 0.72/0.75 * Chain [35] with precondition: [0>=A,C>=B] 0.72/0.75 - Upper bound: 0 0.72/0.75 - Complexity: constant 0.72/0.75 * Chain [34] with precondition: [0>=A,C>=B+1] 0.72/0.75 - Upper bound: -2*B+2*C 0.72/0.75 - Complexity: n 0.72/0.75 * Chain [33] with precondition: [0>=A,B>=C+1] 0.72/0.75 - Upper bound: 0 0.72/0.75 - Complexity: constant 0.72/0.75 * Chain [32] with precondition: [A>=1,C>=B] 0.72/0.75 - Upper bound: 0 0.72/0.75 - Complexity: constant 0.72/0.75 * Chain [31] with precondition: [A>=1,C>=B+1] 0.72/0.75 - Upper bound: -2*B+2*C 0.72/0.75 - Complexity: n 0.72/0.75 * Chain [30] with precondition: [A>=1,B>=C+1] 0.72/0.75 - Upper bound: 0 0.72/0.75 - Complexity: constant 0.72/0.75 0.72/0.75 ### Maximum cost of start0(A,B,C,D,E,F,G,H,I,J,K): nat(-B+C)*2 0.72/0.75 Asymptotic class: n 0.72/0.75 * Total analysis performed in 660 ms. 0.72/0.75 0.75/0.85 EOF