0.62/0.65 WORST_CASE(?,O(n^1)) 0.62/0.65 0.62/0.65 Preprocessing Cost Relations 0.62/0.65 ===================================== 0.62/0.65 0.62/0.65 #### Computed strongly connected components 0.62/0.65 0. recursive : [cut/9] 0.62/0.65 1. non_recursive : [exit_location/1] 0.62/0.65 2. non_recursive : [stop/9] 0.62/0.65 3. non_recursive : [cut_loop_cont/10] 0.62/0.65 4. non_recursive : [start/9] 0.62/0.65 5. non_recursive : [start0/9] 0.62/0.65 0.62/0.65 #### Obtained direct recursion through partial evaluation 0.62/0.65 0. SCC is partially evaluated into cut/9 0.62/0.65 1. SCC is completely evaluated into other SCCs 0.62/0.65 2. SCC is completely evaluated into other SCCs 0.62/0.65 3. SCC is partially evaluated into cut_loop_cont/10 0.62/0.65 4. SCC is partially evaluated into start/9 0.62/0.65 5. SCC is partially evaluated into start0/9 0.62/0.65 0.62/0.65 Control-Flow Refinement of Cost Relations 0.62/0.65 ===================================== 0.62/0.65 0.62/0.65 ### Specialization of cost equations cut/9 0.62/0.65 * CE 13 is refined into CE [16] 0.62/0.65 * CE 11 is refined into CE [17] 0.62/0.65 * CE 7 is refined into CE [18] 0.62/0.65 * CE 9 is refined into CE [19] 0.62/0.65 * CE 12 is refined into CE [20] 0.62/0.65 * CE 10 is refined into CE [21] 0.62/0.65 * CE 6 is refined into CE [22] 0.62/0.65 * CE 8 is refined into CE [23] 0.62/0.65 0.62/0.65 0.62/0.65 ### Cost equations --> "Loop" of cut/9 0.62/0.65 * CEs [21] --> Loop 15 0.62/0.65 * CEs [22] --> Loop 16 0.62/0.65 * CEs [23] --> Loop 17 0.62/0.65 * CEs [16] --> Loop 18 0.62/0.65 * CEs [17] --> Loop 19 0.62/0.65 * CEs [18] --> Loop 20 0.62/0.65 * CEs [19] --> Loop 21 0.62/0.65 * CEs [20] --> Loop 22 0.62/0.65 0.62/0.65 ### Ranking functions of CR cut(A,B,D,E,G,I,J,K,L) 0.62/0.65 * RF of phase [15,16,17]: [G-1] 0.62/0.65 0.62/0.65 #### Partial ranking functions of CR cut(A,B,D,E,G,I,J,K,L) 0.62/0.65 * Partial RF of phase [15,16,17]: 0.62/0.65 - RF of loop [15:1]: 0.62/0.65 A-E-1 depends on loops [16:1,17:1] 0.62/0.65 D-E-1 depends on loops [16:1,17:1] 0.62/0.65 - RF of loop [15:1,16:1,17:1]: 0.62/0.65 G-1 0.62/0.65 - RF of loop [16:1]: 0.62/0.65 E-1 depends on loops [15:1] 0.62/0.65 0.62/0.65 0.62/0.65 ### Specialization of cost equations cut_loop_cont/10 0.62/0.65 * CE 15 is refined into CE [24] 0.62/0.65 * CE 14 is refined into CE [25] 0.62/0.65 0.62/0.65 0.62/0.65 ### Cost equations --> "Loop" of cut_loop_cont/10 0.62/0.65 * CEs [24] --> Loop 23 0.62/0.65 * CEs [25] --> Loop 24 0.62/0.65 0.62/0.65 ### Ranking functions of CR cut_loop_cont(A,B,C,D,E,F,G,H,I,J) 0.62/0.65 0.62/0.65 #### Partial ranking functions of CR cut_loop_cont(A,B,C,D,E,F,G,H,I,J) 0.62/0.65 0.62/0.65 0.62/0.65 ### Specialization of cost equations start/9 0.62/0.65 * CE 4 is refined into CE [26,27,28,29,30,31,32] 0.62/0.65 * CE 5 is refined into CE [33,34,35,36,37,38,39,40] 0.62/0.65 * CE 2 is refined into CE [41] 0.62/0.65 * CE 3 is refined into CE [42] 0.62/0.65 0.62/0.65 0.62/0.65 ### Cost equations --> "Loop" of start/9 0.62/0.65 * CEs [30] --> Loop 25 0.62/0.65 * CEs [28,29,32,35,36,37,38,40] --> Loop 26 0.62/0.65 * CEs [31,39] --> Loop 27 0.62/0.65 * CEs [41] --> Loop 28 0.62/0.65 * CEs [26,27,33,34] --> Loop 29 0.62/0.65 * CEs [42] --> Loop 30 0.62/0.65 0.62/0.65 ### Ranking functions of CR start(A,B,C,D,E,F,G,H,I) 0.62/0.65 0.62/0.65 #### Partial ranking functions of CR start(A,B,C,D,E,F,G,H,I) 0.62/0.65 0.62/0.65 0.62/0.65 ### Specialization of cost equations start0/9 0.62/0.65 * CE 1 is refined into CE [43,44,45,46,47,48] 0.62/0.65 0.62/0.65 0.62/0.65 ### Cost equations --> "Loop" of start0/9 0.62/0.65 * CEs [48] --> Loop 31 0.62/0.65 * CEs [47] --> Loop 32 0.62/0.65 * CEs [46] --> Loop 33 0.62/0.65 * CEs [45] --> Loop 34 0.62/0.65 * CEs [44] --> Loop 35 0.62/0.65 * CEs [43] --> Loop 36 0.62/0.65 0.62/0.65 ### Ranking functions of CR start0(A,B,C,D,E,F,G,H,I) 0.62/0.65 0.62/0.65 #### Partial ranking functions of CR start0(A,B,C,D,E,F,G,H,I) 0.62/0.65 0.62/0.65 0.62/0.65 Computing Bounds 0.62/0.65 ===================================== 0.62/0.65 0.62/0.65 #### Cost of chains of cut(A,B,D,E,G,I,J,K,L): 0.62/0.65 * Chain [[15,16,17],22]: 3*it(15)+0 0.62/0.65 Such that:aux(8) =< -E+J 0.62/0.65 aux(7) =< -E+J+1 0.62/0.65 it(15) =< aux(7) 0.62/0.65 it(15) =< aux(8) 0.62/0.65 0.62/0.65 with precondition: [I=2,K=0,L=0,A=D,A=J+1,A=E+G,G>=2,A>=G+1] 0.62/0.65 0.62/0.65 * Chain [[15,16,17],21]: 3*it(15)+0 0.62/0.65 Such that:aux(9) =< G 0.62/0.65 it(15) =< aux(9) 0.62/0.65 0.62/0.65 with precondition: [I=2,K=0,L=0,A=D,E>=0,G>=2,G>=E,A>=G+1,A>=E+G] 0.62/0.65 0.62/0.65 * Chain [[15,16,17],20]: 3*it(15)+0 0.62/0.65 Such that:aux(10) =< G 0.62/0.65 it(15) =< aux(10) 0.62/0.65 0.62/0.65 with precondition: [I=2,L=0,A=D,E>=0,G>=2,K>=1,A>=G+1,A>=E+G,G+K>=E,E+G>=K+2] 0.62/0.65 0.62/0.65 * Chain [[15,16,17],19]: 3*it(15)+0 0.62/0.65 Such that:aux(11) =< G 0.62/0.65 it(15) =< aux(11) 0.62/0.65 0.62/0.65 with precondition: [I=2,L=0,A=D,J+1=K,E>=0,G>=2,J>=0,A>=G+1,A>=E+G,G+J>=E+1,E+G>=J+1,2*A>=E+G+J+3] 0.62/0.65 0.62/0.65 * Chain [[15,16,17],18]: 3*it(15)+0 0.62/0.65 Such that:aux(12) =< G 0.62/0.65 it(15) =< aux(12) 0.62/0.65 0.62/0.65 with precondition: [I=3,A=D,E>=0,G>=2,A>=G+1,A>=E+G] 0.62/0.65 0.62/0.65 * Chain [22]: 0 0.62/0.65 with precondition: [G=1,I=2,K=0,L=0,A=D,A=E+1,A=J+1,A>=2] 0.62/0.65 0.62/0.65 * Chain [21]: 0 0.62/0.65 with precondition: [G=1,I=2,K=0,L=0,D=A,J=B,1>=E,D>=2,E>=0] 0.62/0.65 0.62/0.65 * Chain [19]: 0 0.62/0.65 with precondition: [G=1,I=2,L=0,D=A,E=J,E+1=K,E>=0,D>=E+2] 0.62/0.65 0.62/0.65 * Chain [18]: 0 0.62/0.65 with precondition: [I=3,D=A,E>=0,G>=1,D>=G+1,D>=E+G] 0.62/0.65 0.62/0.65 0.62/0.65 #### Cost of chains of cut_loop_cont(A,B,C,D,E,F,G,H,I,J): 0.62/0.65 * Chain [24]: 0 0.62/0.65 with precondition: [A=2,E=B,E>=2] 0.62/0.65 0.62/0.65 * Chain [23]: 0 0.62/0.65 with precondition: [A=3,E=B,E>=2] 0.62/0.65 0.62/0.65 0.62/0.65 #### Cost of chains of start(A,B,C,D,E,F,G,H,I): 0.62/0.65 * Chain [30]: 0 0.62/0.65 with precondition: [A=1,D=1,C=B,F=E,H=G] 0.62/0.65 0.62/0.65 * Chain [29]: 0 0.62/0.65 with precondition: [A=2,D=2,C=B,F=E,H=G] 0.62/0.65 0.62/0.65 * Chain [28]: 0 0.62/0.65 with precondition: [D=A,C=B,F=E,H=G,0>=D] 0.62/0.65 0.62/0.65 * Chain [27]: 0 0.62/0.65 with precondition: [D=A,C=B,F=E,H=G,D>=2] 0.62/0.65 0.62/0.65 * Chain [26]: 21*s(2)+3*s(9)+0 0.62/0.65 Such that:aux(13) =< D 0.62/0.65 aux(14) =< A 0.62/0.65 s(2) =< aux(14) 0.62/0.65 s(9) =< aux(13) 0.62/0.65 0.62/0.65 with precondition: [D=A,C=B,F=E,H=G,D>=3] 0.62/0.65 0.62/0.65 * Chain [25]: 3*s(19)+0 0.62/0.65 Such that:s(18) =< A 0.62/0.65 s(19) =< s(18) 0.62/0.65 0.62/0.65 with precondition: [D=A,C=B,F=E,H=G,D>=4] 0.62/0.65 0.62/0.65 0.62/0.65 #### Cost of chains of start0(A,B,C,D,E,F,G,H,I): 0.62/0.65 * Chain [36]: 0 0.62/0.65 with precondition: [A=1] 0.62/0.65 0.62/0.65 * Chain [35]: 0 0.62/0.65 with precondition: [A=2] 0.62/0.65 0.62/0.65 * Chain [34]: 0 0.62/0.65 with precondition: [0>=A] 0.62/0.65 0.62/0.65 * Chain [33]: 0 0.62/0.65 with precondition: [A>=2] 0.62/0.65 0.62/0.65 * Chain [32]: 24*s(22)+0 0.62/0.65 Such that:aux(15) =< A 0.62/0.65 s(22) =< aux(15) 0.62/0.65 0.62/0.65 with precondition: [A>=3] 0.62/0.65 0.62/0.65 * Chain [31]: 3*s(25)+0 0.62/0.65 Such that:s(24) =< A 0.62/0.65 s(25) =< s(24) 0.62/0.65 0.62/0.65 with precondition: [A>=4] 0.62/0.65 0.62/0.65 0.62/0.65 Closed-form bounds of start0(A,B,C,D,E,F,G,H,I): 0.62/0.65 ------------------------------------- 0.62/0.65 * Chain [36] with precondition: [A=1] 0.62/0.65 - Upper bound: 0 0.62/0.65 - Complexity: constant 0.62/0.65 * Chain [35] with precondition: [A=2] 0.62/0.65 - Upper bound: 0 0.62/0.65 - Complexity: constant 0.62/0.65 * Chain [34] with precondition: [0>=A] 0.62/0.65 - Upper bound: 0 0.62/0.65 - Complexity: constant 0.62/0.65 * Chain [33] with precondition: [A>=2] 0.62/0.65 - Upper bound: 0 0.62/0.65 - Complexity: constant 0.62/0.65 * Chain [32] with precondition: [A>=3] 0.62/0.65 - Upper bound: 24*A 0.62/0.65 - Complexity: n 0.62/0.65 * Chain [31] with precondition: [A>=4] 0.62/0.65 - Upper bound: 3*A 0.62/0.65 - Complexity: n 0.62/0.65 0.62/0.65 ### Maximum cost of start0(A,B,C,D,E,F,G,H,I): nat(A)*24 0.62/0.65 Asymptotic class: n 0.62/0.65 * Total analysis performed in 554 ms. 0.62/0.65 0.65/0.75 EOF