0.91/0.92 WORST_CASE(?,O(n^1)) 0.91/0.92 0.91/0.92 Preprocessing Cost Relations 0.91/0.92 ===================================== 0.91/0.92 0.91/0.92 #### Computed strongly connected components 0.91/0.92 0. recursive : [lZZ1/9] 0.91/0.92 1. recursive : [lM1/17,lZZ1_loop_cont/18] 0.91/0.92 2. non_recursive : [exit_location/1] 0.91/0.92 3. non_recursive : [stop/9] 0.91/0.92 4. non_recursive : [lM1_loop_cont/10] 0.91/0.92 5. non_recursive : [start/9] 0.91/0.92 6. non_recursive : [start0/9] 0.91/0.92 0.91/0.92 #### Obtained direct recursion through partial evaluation 0.91/0.92 0. SCC is partially evaluated into lZZ1/9 0.91/0.92 1. SCC is partially evaluated into lM1/17 0.91/0.92 2. SCC is completely evaluated into other SCCs 0.91/0.92 3. SCC is completely evaluated into other SCCs 0.91/0.92 4. SCC is partially evaluated into lM1_loop_cont/10 0.91/0.92 5. SCC is partially evaluated into start/9 0.91/0.92 6. SCC is partially evaluated into start0/9 0.91/0.92 0.91/0.92 Control-Flow Refinement of Cost Relations 0.91/0.92 ===================================== 0.91/0.92 0.91/0.92 ### Specialization of cost equations lZZ1/9 0.91/0.92 * CE 14 is refined into CE [15] 0.91/0.92 * CE 13 is refined into CE [16] 0.91/0.92 0.91/0.92 0.91/0.92 ### Cost equations --> "Loop" of lZZ1/9 0.91/0.92 * CEs [15] --> Loop 15 0.91/0.92 * CEs [16] --> Loop 16 0.91/0.92 0.91/0.92 ### Ranking functions of CR lZZ1(A,B,D,F,G,H,I,J,K) 0.91/0.92 0.91/0.92 #### Partial ranking functions of CR lZZ1(A,B,D,F,G,H,I,J,K) 0.91/0.92 0.91/0.92 0.91/0.92 ### Specialization of cost equations lM1/17 0.91/0.92 * CE 6 is refined into CE [17] 0.91/0.92 * CE 10 is refined into CE [18] 0.91/0.92 * CE 8 is refined into CE [19] 0.91/0.92 * CE 9 is refined into CE [20] 0.91/0.92 * CE 7 is refined into CE [21] 0.91/0.92 0.91/0.92 0.91/0.92 ### Cost equations --> "Loop" of lM1/17 0.91/0.92 * CEs [20] --> Loop 17 0.91/0.92 * CEs [21] --> Loop 18 0.91/0.92 * CEs [18] --> Loop 19 0.91/0.92 * CEs [17] --> Loop 20 0.91/0.92 * CEs [19] --> Loop 21 0.91/0.92 0.91/0.92 ### Ranking functions of CR lM1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q) 0.91/0.92 * RF of phase [17,18]: [D] 0.91/0.92 0.91/0.92 #### Partial ranking functions of CR lM1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q) 0.91/0.92 * Partial RF of phase [17,18]: 0.91/0.92 - RF of loop [17:1]: 0.91/0.92 A-B depends on loops [18:1] 0.91/0.92 -B+F depends on loops [18:1] 0.91/0.92 -B+G depends on loops [18:1] 0.91/0.92 -B+H depends on loops [18:1] 0.91/0.92 - RF of loop [17:1,18:1]: 0.91/0.92 D 0.91/0.92 - RF of loop [18:1]: 0.91/0.92 -A+B+1 depends on loops [17:1] 0.91/0.92 B-1 depends on loops [17:1] 0.91/0.92 B-H+1 depends on loops [17:1] 0.91/0.92 0.91/0.92 0.91/0.92 ### Specialization of cost equations lM1_loop_cont/10 0.91/0.92 * CE 12 is refined into CE [22] 0.91/0.92 * CE 11 is refined into CE [23] 0.91/0.92 0.91/0.92 0.91/0.92 ### Cost equations --> "Loop" of lM1_loop_cont/10 0.91/0.92 * CEs [22] --> Loop 22 0.91/0.92 * CEs [23] --> Loop 23 0.91/0.92 0.91/0.92 ### Ranking functions of CR lM1_loop_cont(A,B,C,D,E,F,G,H,I,J) 0.91/0.92 0.91/0.92 #### Partial ranking functions of CR lM1_loop_cont(A,B,C,D,E,F,G,H,I,J) 0.91/0.92 0.91/0.92 0.91/0.92 ### Specialization of cost equations start/9 0.91/0.92 * CE 5 is refined into CE [24,25,26,27,28,29] 0.91/0.92 * CE 3 is refined into CE [30] 0.91/0.92 * CE 2 is refined into CE [31] 0.91/0.92 * CE 4 is refined into CE [32] 0.91/0.92 0.91/0.92 0.91/0.92 ### Cost equations --> "Loop" of start/9 0.91/0.92 * CEs [29] --> Loop 24 0.91/0.92 * CEs [25,28] --> Loop 25 0.91/0.92 * CEs [26] --> Loop 26 0.91/0.92 * CEs [30] --> Loop 27 0.91/0.92 * CEs [31] --> Loop 28 0.91/0.92 * CEs [24] --> Loop 29 0.91/0.92 * CEs [32] --> Loop 30 0.91/0.92 * CEs [27] --> Loop 31 0.91/0.92 0.91/0.92 ### Ranking functions of CR start(A,B,C,D,E,F,G,H,I) 0.91/0.92 0.91/0.92 #### Partial ranking functions of CR start(A,B,C,D,E,F,G,H,I) 0.91/0.92 0.91/0.92 0.91/0.92 ### Specialization of cost equations start0/9 0.91/0.92 * CE 1 is refined into CE [33,34,35,36,37,38,39,40] 0.91/0.92 0.91/0.92 0.91/0.92 ### Cost equations --> "Loop" of start0/9 0.91/0.92 * CEs [40] --> Loop 32 0.91/0.92 * CEs [39] --> Loop 33 0.91/0.92 * CEs [38] --> Loop 34 0.91/0.92 * CEs [36] --> Loop 35 0.91/0.92 * CEs [37] --> Loop 36 0.91/0.92 * CEs [35] --> Loop 37 0.91/0.92 * CEs [34] --> Loop 38 0.91/0.92 * CEs [33] --> Loop 39 0.91/0.92 0.91/0.92 ### Ranking functions of CR start0(A,B,C,D,E,F,G,H,I) 0.91/0.92 0.91/0.92 #### Partial ranking functions of CR start0(A,B,C,D,E,F,G,H,I) 0.91/0.92 0.91/0.92 0.91/0.92 Computing Bounds 0.91/0.92 ===================================== 0.91/0.92 0.91/0.92 #### Cost of chains of lZZ1(A,B,D,F,G,H,I,J,K): 0.91/0.92 * Chain [16]: 0 0.91/0.92 with precondition: [B=0,I=3,J=1,H=A,G=F,D=K+1,D>=1,H>=2,G>=D+H] 0.91/0.92 0.91/0.92 * Chain [15]: 0 0.91/0.92 with precondition: [B=0,I=4,H=A,G=F,D>=1,H>=1,G>=D+H] 0.91/0.92 0.91/0.92 0.91/0.92 #### Cost of chains of lM1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q): 0.91/0.92 * Chain [[17,18],21]: 2*it(17)+0 0.91/0.92 Such that:aux(59) =< D 0.91/0.92 it(17) =< aux(59) 0.91/0.92 0.91/0.92 with precondition: [I=2,M=0,F=G,A=H,A=J,C=L,E=N,F=O,F=P,A=Q,A>=2,B>=1,D>=1,K>=1,A>=B,A>=K,F>=B+D,B+D>=K,B+D+K>=4,D+2*A>=B+K+2] 0.91/0.92 0.91/0.92 * Chain [[17,18],20]: 2*it(17)+0 0.91/0.92 Such that:aux(60) =< D 0.91/0.92 it(17) =< aux(60) 0.91/0.92 0.91/0.92 with precondition: [I=4,F=G,A=H,A>=2,B>=1,A>=B,B+D>=A+1,F>=B+D,A+D>=B+3] 0.91/0.92 0.91/0.92 * Chain [[17,18],19]: 2*it(17)+0 0.91/0.92 Such that:aux(61) =< D 0.91/0.92 it(17) =< aux(61) 0.91/0.92 0.91/0.92 with precondition: [I=4,F=G,A=H,A>=2,B>=1,D>=1,A>=B,F>=B+D] 0.91/0.92 0.91/0.92 * Chain [21]: 0 0.91/0.92 with precondition: [D=0,I=2,M=0,H=A,L=C,N=E,G=F,H=J,B=K,G=O,G=P,H=Q,B>=1,G>=B,H>=B] 0.91/0.92 0.91/0.92 * Chain [20]: 0 0.91/0.92 with precondition: [I=4,A=B,G=F,A=H,A>=1,D>=1,G>=A+D] 0.91/0.92 0.91/0.92 * Chain [19]: 0 0.91/0.92 with precondition: [I=4,H=A,G=F,B>=1,D>=0,H>=B,G>=B+D] 0.91/0.92 0.91/0.92 0.91/0.92 #### Cost of chains of lM1_loop_cont(A,B,C,D,E,F,G,H,I,J): 0.91/0.92 * Chain [23]: 0 0.91/0.92 with precondition: [A=2] 0.91/0.92 0.91/0.92 * Chain [22]: 0 0.91/0.92 with precondition: [A=4] 0.91/0.92 0.91/0.92 0.91/0.92 #### Cost of chains of start(A,B,C,D,E,F,G,H,I): 0.91/0.92 * Chain [31]: 0 0.91/0.92 with precondition: [A=1,H=1,C=B,E=D,G=F,G>=2] 0.91/0.92 0.91/0.92 * Chain [30]: 0 0.91/0.92 with precondition: [F=0,G=0,H=A,C=B,E=D,H>=1] 0.91/0.92 0.91/0.92 * Chain [29]: 0 0.91/0.92 with precondition: [F=1,G=1,H=A,C=B,E=D,H>=1] 0.91/0.92 0.91/0.92 * Chain [28]: 0 0.91/0.92 with precondition: [H=A,C=B,E=D,G=F,0>=H] 0.91/0.92 0.91/0.92 * Chain [27]: 0 0.91/0.92 with precondition: [H=A,C=B,E=D,G=F,0>=G+1] 0.91/0.92 0.91/0.92 * Chain [26]: 0 0.91/0.92 with precondition: [H=A,C=B,E=D,G=F,G>=1,H>=1] 0.91/0.92 0.91/0.92 * Chain [25]: 4*s(2)+0 0.91/0.92 Such that:aux(62) =< F 0.91/0.92 s(2) =< aux(62) 0.91/0.92 0.91/0.92 with precondition: [H=A,C=B,E=D,G=F,G>=2,H>=2] 0.91/0.92 0.91/0.92 * Chain [24]: 2*s(6)+0 0.91/0.92 Such that:s(5) =< F 0.91/0.92 s(6) =< s(5) 0.91/0.92 0.91/0.92 with precondition: [H=A,C=B,E=D,G=F,H>=2,G>=H+1] 0.91/0.92 0.91/0.92 0.91/0.92 #### Cost of chains of start0(A,B,C,D,E,F,G,H,I): 0.91/0.92 * Chain [39]: 0 0.91/0.92 with precondition: [A=1,G>=2] 0.91/0.92 0.91/0.92 * Chain [38]: 0 0.91/0.92 with precondition: [G=0,A>=1] 0.91/0.92 0.91/0.92 * Chain [37]: 0 0.91/0.92 with precondition: [G=1,A>=1] 0.91/0.92 0.91/0.92 * Chain [36]: 0 0.91/0.92 with precondition: [0>=A] 0.91/0.92 0.91/0.92 * Chain [35]: 0 0.91/0.92 with precondition: [0>=G+1] 0.91/0.92 0.91/0.92 * Chain [34]: 0 0.91/0.92 with precondition: [A>=1,G>=1] 0.91/0.92 0.91/0.92 * Chain [33]: 4*s(8)+0 0.91/0.92 Such that:s(7) =< G 0.91/0.92 s(8) =< s(7) 0.91/0.92 0.91/0.92 with precondition: [A>=2,G>=2] 0.91/0.92 0.91/0.92 * Chain [32]: 2*s(10)+0 0.91/0.92 Such that:s(9) =< G 0.91/0.92 s(10) =< s(9) 0.91/0.92 0.91/0.92 with precondition: [A>=2,G>=A+1] 0.91/0.92 0.91/0.92 0.91/0.92 Closed-form bounds of start0(A,B,C,D,E,F,G,H,I): 0.91/0.92 ------------------------------------- 0.91/0.92 * Chain [39] with precondition: [A=1,G>=2] 0.91/0.92 - Upper bound: 0 0.91/0.92 - Complexity: constant 0.91/0.92 * Chain [38] with precondition: [G=0,A>=1] 0.91/0.92 - Upper bound: 0 0.91/0.92 - Complexity: constant 0.91/0.92 * Chain [37] with precondition: [G=1,A>=1] 0.91/0.92 - Upper bound: 0 0.91/0.92 - Complexity: constant 0.91/0.92 * Chain [36] with precondition: [0>=A] 0.91/0.92 - Upper bound: 0 0.91/0.92 - Complexity: constant 0.91/0.92 * Chain [35] with precondition: [0>=G+1] 0.91/0.92 - Upper bound: 0 0.91/0.92 - Complexity: constant 0.91/0.92 * Chain [34] with precondition: [A>=1,G>=1] 0.91/0.92 - Upper bound: 0 0.91/0.92 - Complexity: constant 0.91/0.92 * Chain [33] with precondition: [A>=2,G>=2] 0.91/0.92 - Upper bound: 4*G 0.91/0.92 - Complexity: n 0.91/0.92 * Chain [32] with precondition: [A>=2,G>=A+1] 0.91/0.92 - Upper bound: 2*G 0.91/0.92 - Complexity: n 0.91/0.92 0.91/0.92 ### Maximum cost of start0(A,B,C,D,E,F,G,H,I): nat(G)*4 0.91/0.92 Asymptotic class: n 0.91/0.92 * Total analysis performed in 770 ms. 0.91/0.92 0.91/1.02 EOF