1.25/1.30 WORST_CASE(?,O(n^1)) 1.25/1.30 1.25/1.30 Preprocessing Cost Relations 1.25/1.30 ===================================== 1.25/1.30 1.25/1.30 #### Computed strongly connected components 1.25/1.30 0. recursive : [lbl71/12] 1.25/1.30 1. non_recursive : [exit_location/1] 1.25/1.30 2. non_recursive : [stop/9] 1.25/1.30 3. non_recursive : [lbl71_loop_cont/10] 1.25/1.30 4. non_recursive : [start/9] 1.25/1.30 5. non_recursive : [start0/9] 1.25/1.30 1.25/1.30 #### Obtained direct recursion through partial evaluation 1.25/1.30 0. SCC is partially evaluated into lbl71/12 1.25/1.30 1. SCC is completely evaluated into other SCCs 1.25/1.30 2. SCC is completely evaluated into other SCCs 1.25/1.30 3. SCC is partially evaluated into lbl71_loop_cont/10 1.25/1.30 4. SCC is partially evaluated into start/9 1.25/1.30 5. SCC is partially evaluated into start0/9 1.25/1.30 1.25/1.30 Control-Flow Refinement of Cost Relations 1.25/1.30 ===================================== 1.25/1.30 1.25/1.30 ### Specialization of cost equations lbl71/12 1.25/1.30 * CE 8 is refined into CE [11] 1.25/1.30 * CE 6 is refined into CE [12] 1.25/1.30 * CE 5 is refined into CE [13] 1.25/1.30 * CE 7 is refined into CE [14] 1.25/1.30 1.25/1.30 1.25/1.30 ### Cost equations --> "Loop" of lbl71/12 1.25/1.30 * CEs [14] --> Loop 11 1.25/1.30 * CEs [11] --> Loop 12 1.25/1.30 * CEs [12] --> Loop 13 1.25/1.30 * CEs [13] --> Loop 14 1.25/1.30 1.25/1.30 ### Ranking functions of CR lbl71(A,B,D,E,F,G,H,I,J,K,L,M) 1.25/1.30 * RF of phase [11]: [-A+D-E-G+202,-A+D-2*G+202,-A+D-G+100,-A/2+D-E/2-G/2+101/2,-A/2+D-G+101/2,-A/2+D-G/2+1/2,-A/3+D-E/3-G/3+2/3,-A/3+D-2/3*G+2/3,A/2-B+E-H+99/2,A/2-B+E/2+G/2-H+99/2,A/2+E-F-H+101/2,A/2+E/2-F+G/2-H+101/2,2/3*A-B+2/3*E+2/3*G-H-1/3,2/3*A-B+4/3*E-H-1/3,2/3*A+2/3*E-F+2/3*G-H+2/3,2/3*A+4/3*E-F-H+2/3,-B+E-H+99,-B+2*E-H-1,-B+E/2+G/2-H+199/2,-B+2/3*E+2/3*G-H+199/3,-B+4/3*E-H+65,-B-H+201,-B/2+D/2-H/2+50,-B/3+2/3*D-H/3+1/3,D/2-F/2-H/2+101/2,2/3*D-F/3-H/3+2/3,E-F-H+100,2*E-F-H,E/2-F+G/2-H+201/2,2/3*E-F+2/3*G-H+202/3,4/3*E-F-H+66,-F-H+202] 1.25/1.30 1.25/1.30 #### Partial ranking functions of CR lbl71(A,B,D,E,F,G,H,I,J,K,L,M) 1.25/1.30 * Partial RF of phase [11]: 1.25/1.30 - RF of loop [11:1]: 1.25/1.30 -A+D-E-G+202 1.25/1.30 -A+D-2*G+202 1.25/1.30 -A+D-G+100 1.25/1.30 -A/2+D-E/2-G/2+101/2 1.25/1.30 -A/2+D-G+101/2 1.25/1.30 -A/2+D-G/2+1/2 1.25/1.30 -A/3+D-E/3-G/3+2/3 1.25/1.30 -A/3+D-2/3*G+2/3 1.25/1.30 A/2-B+E-H+99/2 1.25/1.30 A/2-B+E/2+G/2-H+99/2 1.25/1.30 A/2+E-F-H+101/2 1.25/1.30 A/2+E/2-F+G/2-H+101/2 1.25/1.30 2/3*A-B+2/3*E+2/3*G-H-1/3 1.25/1.30 2/3*A-B+4/3*E-H-1/3 1.25/1.30 2/3*A+2/3*E-F+2/3*G-H+2/3 1.25/1.30 2/3*A+4/3*E-F-H+2/3 1.25/1.30 -B+E-H+99 1.25/1.30 -B+2*E-H-1 1.25/1.30 -B+E/2+G/2-H+199/2 1.25/1.30 -B+2/3*E+2/3*G-H+199/3 1.25/1.30 -B+4/3*E-H+65 1.25/1.30 -B-H+201 1.25/1.30 -B/2+D/2-H/2+50 1.25/1.30 -B/3+2/3*D-H/3+1/3 1.25/1.30 D/2-F/2-H/2+101/2 1.25/1.30 2/3*D-F/3-H/3+2/3 1.25/1.30 E-F-H+100 1.25/1.30 2*E-F-H 1.25/1.30 E/2-F+G/2-H+201/2 1.25/1.30 2/3*E-F+2/3*G-H+202/3 1.25/1.30 4/3*E-F-H+66 1.25/1.30 -F-H+202 1.25/1.30 1.25/1.30 1.25/1.30 ### Specialization of cost equations lbl71_loop_cont/10 1.25/1.30 * CE 10 is refined into CE [15] 1.25/1.30 * CE 9 is refined into CE [16] 1.25/1.30 1.25/1.30 1.25/1.30 ### Cost equations --> "Loop" of lbl71_loop_cont/10 1.25/1.30 * CEs [15] --> Loop 15 1.25/1.30 * CEs [16] --> Loop 16 1.25/1.30 1.25/1.30 ### Ranking functions of CR lbl71_loop_cont(A,B,C,D,E,F,G,H,I,J) 1.25/1.30 1.25/1.30 #### Partial ranking functions of CR lbl71_loop_cont(A,B,C,D,E,F,G,H,I,J) 1.25/1.30 1.25/1.30 1.25/1.30 ### Specialization of cost equations start/9 1.25/1.30 * CE 3 is refined into CE [17] 1.25/1.30 * CE 2 is refined into CE [18] 1.25/1.30 * CE 4 is refined into CE [19,20,21,22,23,24] 1.25/1.30 1.25/1.30 1.25/1.30 ### Cost equations --> "Loop" of start/9 1.25/1.30 * CEs [17] --> Loop 17 1.25/1.30 * CEs [18] --> Loop 18 1.25/1.30 * CEs [23] --> Loop 19 1.25/1.30 * CEs [21] --> Loop 20 1.25/1.30 * CEs [20] --> Loop 21 1.25/1.30 * CEs [22] --> Loop 22 1.25/1.30 * CEs [24] --> Loop 23 1.25/1.30 * CEs [19] --> Loop 24 1.25/1.30 1.25/1.30 ### Ranking functions of CR start(A,B,C,D,E,F,G,H,I) 1.25/1.30 1.25/1.30 #### Partial ranking functions of CR start(A,B,C,D,E,F,G,H,I) 1.25/1.30 1.25/1.30 1.25/1.30 ### Specialization of cost equations start0/9 1.25/1.30 * CE 1 is refined into CE [25,26,27,28,29,30,31,32] 1.25/1.30 1.25/1.30 1.25/1.30 ### Cost equations --> "Loop" of start0/9 1.25/1.30 * CEs [32] --> Loop 25 1.25/1.30 * CEs [31] --> Loop 26 1.25/1.30 * CEs [30] --> Loop 27 1.25/1.30 * CEs [29] --> Loop 28 1.25/1.30 * CEs [28] --> Loop 29 1.25/1.30 * CEs [27] --> Loop 30 1.25/1.30 * CEs [26] --> Loop 31 1.25/1.30 * CEs [25] --> Loop 32 1.25/1.30 1.25/1.30 ### Ranking functions of CR start0(A,B,C,D,E,F,G,H,I) 1.25/1.30 1.25/1.30 #### Partial ranking functions of CR start0(A,B,C,D,E,F,G,H,I) 1.25/1.30 1.25/1.30 1.25/1.30 Computing Bounds 1.25/1.30 ===================================== 1.25/1.30 1.25/1.30 #### Cost of chains of lbl71(A,B,D,E,F,G,H,I,J,K,L,M): 1.25/1.30 * Chain [[11],14]: 1*it(11)+0 1.25/1.30 Such that:it(11) =< D-K 1.25/1.30 it(11) =< D-K/2-L/2 1.25/1.30 1.25/1.30 with precondition: [I=2,M=101,J+1=L,J+K+102=A+E+G,A+E+G=B+D+H+1,A+E+G=D+F+H,100>=A,100>=H,E>=D+1,E>=G,A+E+G>=J+202,D+H+101>=A+E+G,D+J+101>=A+E+G] 1.25/1.30 1.25/1.30 * Chain [[11],13]: 1*it(11)+0 1.25/1.30 Such that:it(11) =< D-J/2-K/2-M/2+50 1.25/1.30 it(11) =< D-J/3-K/3-M/3+1/3 1.25/1.30 1.25/1.30 with precondition: [I=2,J+1=L,A+E+G=B+D+H+1,A+E+G=D+F+H,A+E+G=J+K+M+1,100>=A,100>=H,100>=J,E>=D+1,E>=G,K+2>=J,D>=K+1,J>=K,D+J>=H+K+1,D+H+101>=A+E+G,H+2*D>=A+E+G,J+2*K+2>=A+E+G] 1.25/1.30 1.25/1.30 * Chain [[11],12]: 1*it(11)+0 1.25/1.30 Such that:it(11) =< A/2+E/2-F+G/2-H+101/2 1.25/1.30 it(11) =< 2/3*A+2/3*E-F+2/3*G-H+2/3 1.25/1.30 1.25/1.30 with precondition: [I=3,A+E+G=B+D+H+1,A+E+G=D+F+H,100>=A,100>=H,E>=D+1,E>=G,D+1>=H,D+H+101>=A+E+G,H+2*D>=A+E+G] 1.25/1.30 1.25/1.30 * Chain [14]: 0 1.25/1.30 with precondition: [I=2,B+1=F,B=J,D=K,B+1=L,H=M,B+D+H+1=A+E+G,100>=A,100>=B,H>=101,E>=D+1,D+1>=H,A+2*E>=B+D+H+1] 1.25/1.30 1.25/1.30 * Chain [13]: 0 1.25/1.30 with precondition: [I=2,B+1=F,B=J,D=K,B+1=L,H=M,B+D+H+1=A+E+G,100>=A,100>=B,B>=D,E>=D+1,D+1>=H,A+2*E>=B+D+H+1] 1.25/1.30 1.25/1.30 * Chain [12]: 0 1.25/1.30 with precondition: [I=3,B+1=F,B+D+H+1=A+E+G,100>=A,100>=B,E>=D+1,D+1>=H,A+2*E>=B+D+H+1] 1.25/1.30 1.25/1.30 1.25/1.30 #### Cost of chains of lbl71_loop_cont(A,B,C,D,E,F,G,H,I,J): 1.25/1.30 * Chain [16]: 0 1.25/1.30 with precondition: [A=2,100>=B,F>=H] 1.25/1.30 1.25/1.30 * Chain [15]: 0 1.25/1.30 with precondition: [A=3,100>=B,F>=H] 1.25/1.30 1.25/1.30 1.25/1.30 #### Cost of chains of start(A,B,C,D,E,F,G,H,I): 1.25/1.30 * Chain [24]: 1*s(1)+0 1.25/1.30 Such that:s(1) =< -A/2+E/2-G/2+99/2 1.25/1.30 s(1) =< E 1.25/1.30 1.25/1.30 with precondition: [H=A,C=B,E=D,G=F,100>=G,100>=H,E>=102] 1.25/1.30 1.25/1.30 * Chain [23]: 1*s(2)+0 1.25/1.30 Such that:s(2) =< -A/2+E/2-G/2+99/2 1.25/1.30 s(2) =< -A/3+2/3*E-G/3 1.25/1.30 1.25/1.30 with precondition: [H=A,C=B,E=D,G=F,100>=G,100>=H,E>=G,E>=H+2] 1.25/1.30 1.25/1.30 * Chain [22]: 1*s(3)+0 1.25/1.30 Such that:s(3) =< -A/2+E/2-G/2+99/2 1.25/1.30 s(3) =< -A/3+2/3*E-G/3 1.25/1.30 1.25/1.30 with precondition: [H=A,C=B,E=D,G=F,100>=G,100>=H,E>=G,E>=H+2,302>=E+G+H] 1.25/1.30 1.25/1.30 * Chain [21]: 0 1.25/1.30 with precondition: [H=A,C=B,E=D,G=F,100>=H,G>=101,E>=G] 1.25/1.30 1.25/1.30 * Chain [20]: 0 1.25/1.30 with precondition: [H=A,C=B,E=D,G=F,100>=H,H+1>=E,E>=G] 1.25/1.30 1.25/1.30 * Chain [19]: 0 1.25/1.30 with precondition: [H=A,C=B,E=D,G=F,100>=H,E>=G] 1.25/1.30 1.25/1.30 * Chain [18]: 0 1.25/1.30 with precondition: [H=A,C=B,E=D,G=F,H>=101] 1.25/1.30 1.25/1.30 * Chain [17]: 0 1.25/1.30 with precondition: [H=A,C=B,E=D,G=F,G>=E+1] 1.25/1.30 1.25/1.30 1.25/1.30 #### Cost of chains of start0(A,B,C,D,E,F,G,H,I): 1.25/1.30 * Chain [32]: 1*s(4)+0 1.25/1.30 Such that:s(4) =< -A/2+E/2-G/2+99/2 1.25/1.30 s(4) =< E 1.25/1.30 1.25/1.30 with precondition: [100>=A,100>=G,E>=102] 1.25/1.30 1.25/1.30 * Chain [31]: 1*s(5)+0 1.25/1.30 Such that:s(5) =< -A/2+E/2-G/2+99/2 1.25/1.30 s(5) =< -A/3+2/3*E-G/3 1.25/1.30 1.25/1.30 with precondition: [100>=A,100>=G,E>=A+2,E>=G] 1.25/1.30 1.25/1.30 * Chain [30]: 1*s(6)+0 1.25/1.30 Such that:s(6) =< -A/2+E/2-G/2+99/2 1.25/1.30 s(6) =< -A/3+2/3*E-G/3 1.25/1.30 1.25/1.30 with precondition: [100>=A,100>=G,E>=A+2,E>=G,302>=A+E+G] 1.25/1.30 1.25/1.30 * Chain [29]: 0 1.25/1.30 with precondition: [100>=A,G>=101,E>=G] 1.25/1.30 1.25/1.30 * Chain [28]: 0 1.25/1.30 with precondition: [100>=A,A+1>=E,E>=G] 1.25/1.30 1.25/1.30 * Chain [27]: 0 1.25/1.30 with precondition: [100>=A,E>=G] 1.25/1.30 1.25/1.30 * Chain [26]: 0 1.25/1.30 with precondition: [A>=101] 1.25/1.30 1.25/1.30 * Chain [25]: 0 1.25/1.30 with precondition: [G>=E+1] 1.25/1.30 1.25/1.30 1.25/1.30 Closed-form bounds of start0(A,B,C,D,E,F,G,H,I): 1.25/1.30 ------------------------------------- 1.25/1.30 * Chain [32] with precondition: [100>=A,100>=G,E>=102] 1.25/1.30 - Upper bound: -A/2+E/2-G/2+99/2 1.25/1.30 - Complexity: n 1.25/1.30 * Chain [31] with precondition: [100>=A,100>=G,E>=A+2,E>=G] 1.25/1.30 - Upper bound: -A/2+E/2-G/2+99/2 1.25/1.30 - Complexity: n 1.25/1.30 * Chain [30] with precondition: [100>=A,100>=G,E>=A+2,E>=G,302>=A+E+G] 1.25/1.30 - Upper bound: -A/2+E/2-G/2+99/2 1.25/1.30 - Complexity: n 1.25/1.30 * Chain [29] with precondition: [100>=A,G>=101,E>=G] 1.25/1.30 - Upper bound: 0 1.25/1.30 - Complexity: constant 1.25/1.30 * Chain [28] with precondition: [100>=A,A+1>=E,E>=G] 1.25/1.30 - Upper bound: 0 1.25/1.30 - Complexity: constant 1.25/1.30 * Chain [27] with precondition: [100>=A,E>=G] 1.25/1.30 - Upper bound: 0 1.25/1.30 - Complexity: constant 1.25/1.30 * Chain [26] with precondition: [A>=101] 1.25/1.30 - Upper bound: 0 1.25/1.30 - Complexity: constant 1.25/1.30 * Chain [25] with precondition: [G>=E+1] 1.25/1.30 - Upper bound: 0 1.25/1.30 - Complexity: constant 1.25/1.30 1.25/1.30 ### Maximum cost of start0(A,B,C,D,E,F,G,H,I): nat(-A/2+E/2-G/2+99/2) 1.25/1.30 Asymptotic class: n 1.25/1.30 * Total analysis performed in 1211 ms. 1.25/1.30 1.30/1.40 EOF