0.03/0.34 WORST_CASE(?,O(n^1)) 0.03/0.34 0.03/0.34 Preprocessing Cost Relations 0.03/0.34 ===================================== 0.03/0.34 0.03/0.34 #### Computed strongly connected components 0.03/0.34 0. recursive : [lbl101/7] 0.03/0.34 1. non_recursive : [exit_location/1] 0.03/0.34 2. non_recursive : [stop/7] 0.03/0.34 3. non_recursive : [lbl101_loop_cont/8] 0.03/0.34 4. non_recursive : [start/7] 0.03/0.34 5. non_recursive : [start0/7] 0.03/0.34 0.03/0.34 #### Obtained direct recursion through partial evaluation 0.03/0.34 0. SCC is partially evaluated into lbl101/7 0.03/0.34 1. SCC is completely evaluated into other SCCs 0.03/0.34 2. SCC is completely evaluated into other SCCs 0.03/0.34 3. SCC is partially evaluated into lbl101_loop_cont/8 0.03/0.34 4. SCC is partially evaluated into start/7 0.03/0.34 5. SCC is partially evaluated into start0/7 0.03/0.34 0.03/0.34 Control-Flow Refinement of Cost Relations 0.03/0.34 ===================================== 0.03/0.34 0.03/0.34 ### Specialization of cost equations lbl101/7 0.03/0.34 * CE 8 is refined into CE [11] 0.03/0.34 * CE 5 is refined into CE [12] 0.03/0.34 * CE 7 is refined into CE [13] 0.03/0.34 * CE 6 is refined into CE [14] 0.03/0.34 0.03/0.34 0.03/0.34 ### Cost equations --> "Loop" of lbl101/7 0.03/0.34 * CEs [13] --> Loop 10 0.03/0.34 * CEs [14] --> Loop 11 0.03/0.34 * CEs [11] --> Loop 12 0.03/0.34 * CEs [12] --> Loop 13 0.03/0.34 0.03/0.34 ### Ranking functions of CR lbl101(A,B,D,E,G,H,I) 0.03/0.34 * RF of phase [10,11]: [A-B+1,-B+D+1] 0.03/0.34 0.03/0.34 #### Partial ranking functions of CR lbl101(A,B,D,E,G,H,I) 0.03/0.34 * Partial RF of phase [10,11]: 0.03/0.34 - RF of loop [10:1]: 0.03/0.34 A+E depends on loops [11:1] 0.03/0.34 D+E depends on loops [11:1] 0.03/0.34 - RF of loop [10:1,11:1]: 0.03/0.34 A-B+1 0.03/0.34 -B+D+1 0.03/0.34 - RF of loop [11:1]: 0.03/0.34 A-E depends on loops [10:1] 0.03/0.34 D-E depends on loops [10:1] 0.03/0.34 0.03/0.34 0.03/0.34 ### Specialization of cost equations lbl101_loop_cont/8 0.03/0.34 * CE 10 is refined into CE [15] 0.03/0.34 * CE 9 is refined into CE [16] 0.03/0.34 0.03/0.34 0.03/0.34 ### Cost equations --> "Loop" of lbl101_loop_cont/8 0.03/0.34 * CEs [15] --> Loop 14 0.03/0.34 * CEs [16] --> Loop 15 0.03/0.34 0.03/0.34 ### Ranking functions of CR lbl101_loop_cont(A,B,C,D,E,F,G,H) 0.03/0.34 0.03/0.34 #### Partial ranking functions of CR lbl101_loop_cont(A,B,C,D,E,F,G,H) 0.03/0.34 0.03/0.34 0.03/0.34 ### Specialization of cost equations start/7 0.03/0.34 * CE 3 is refined into CE [17,18,19,20] 0.03/0.34 * CE 4 is refined into CE [21,22,23,24] 0.03/0.34 * CE 2 is refined into CE [25] 0.03/0.34 0.03/0.34 0.03/0.34 ### Cost equations --> "Loop" of start/7 0.03/0.34 * CEs [18,20,22,24] --> Loop 16 0.03/0.34 * CEs [19,23] --> Loop 17 0.03/0.34 * CEs [25] --> Loop 18 0.03/0.34 * CEs [17,21] --> Loop 19 0.03/0.34 0.03/0.34 ### Ranking functions of CR start(A,B,C,D,E,F,G) 0.03/0.34 0.03/0.34 #### Partial ranking functions of CR start(A,B,C,D,E,F,G) 0.03/0.34 0.03/0.34 0.03/0.34 ### Specialization of cost equations start0/7 0.03/0.34 * CE 1 is refined into CE [26,27,28,29] 0.03/0.34 0.03/0.34 0.03/0.34 ### Cost equations --> "Loop" of start0/7 0.03/0.34 * CEs [29] --> Loop 20 0.03/0.34 * CEs [28] --> Loop 21 0.03/0.34 * CEs [27] --> Loop 22 0.03/0.34 * CEs [26] --> Loop 23 0.03/0.34 0.03/0.34 ### Ranking functions of CR start0(A,B,C,D,E,F,G) 0.03/0.34 0.03/0.34 #### Partial ranking functions of CR start0(A,B,C,D,E,F,G) 0.03/0.34 0.03/0.34 0.03/0.34 Computing Bounds 0.03/0.34 ===================================== 0.03/0.34 0.03/0.34 #### Cost of chains of lbl101(A,B,D,E,G,H,I): 0.03/0.34 * Chain [[10,11],13]: 2*it(10)+0 0.03/0.34 Such that:aux(13) =< -B+D+1 0.03/0.34 it(10) =< aux(13) 0.03/0.34 0.03/0.34 with precondition: [G=2,A=D,A+1=H,B>=2,A>=B,B>=E+1,B+E>=1,A+I+1>=B+E,A+E+1>=B+I] 0.03/0.34 0.03/0.34 * Chain [[10,11],12]: 2*it(10)+0 0.03/0.34 Such that:aux(14) =< A-B+1 0.03/0.34 it(10) =< aux(14) 0.03/0.34 0.03/0.34 with precondition: [G=3,A=D,B>=2,A>=B,B>=E+1,B+E>=1] 0.03/0.34 0.03/0.34 * Chain [13]: 0 0.03/0.34 with precondition: [G=2,A+1=B,A=D,A+1=H,E=I,A>=1,A>=E,A+E>=0] 0.03/0.34 0.03/0.34 * Chain [12]: 0 0.03/0.34 with precondition: [G=3,D=A,B>=2,D+1>=B,B>=E+1,B+E>=1] 0.03/0.34 0.03/0.34 0.03/0.34 #### Cost of chains of lbl101_loop_cont(A,B,C,D,E,F,G,H): 0.03/0.34 * Chain [15]: 0 0.03/0.34 with precondition: [A=2,E=B,E>=1] 0.03/0.34 0.03/0.34 * Chain [14]: 0 0.03/0.34 with precondition: [A=3,E=B,E>=1] 0.03/0.34 0.03/0.34 0.03/0.34 #### Cost of chains of start(A,B,C,D,E,F,G): 0.03/0.34 * Chain [19]: 0 0.03/0.34 with precondition: [A=1,D=1,C=B,F=E] 0.03/0.34 0.03/0.34 * Chain [18]: 0 0.03/0.34 with precondition: [D=A,C=B,F=E,0>=D] 0.03/0.34 0.03/0.34 * Chain [17]: 0 0.03/0.34 with precondition: [D=A,C=B,F=E,D>=1] 0.03/0.34 0.03/0.34 * Chain [16]: 8*s(2)+0 0.03/0.34 Such that:aux(15) =< D 0.03/0.34 s(2) =< aux(15) 0.03/0.34 0.03/0.34 with precondition: [D=A,C=B,F=E,D>=2] 0.03/0.34 0.03/0.34 0.03/0.34 #### Cost of chains of start0(A,B,C,D,E,F,G): 0.03/0.34 * Chain [23]: 0 0.03/0.34 with precondition: [A=1] 0.03/0.34 0.03/0.34 * Chain [22]: 0 0.03/0.34 with precondition: [0>=A] 0.03/0.34 0.03/0.34 * Chain [21]: 0 0.03/0.34 with precondition: [A>=1] 0.03/0.34 0.03/0.34 * Chain [20]: 8*s(10)+0 0.03/0.34 Such that:s(9) =< A 0.03/0.34 s(10) =< s(9) 0.03/0.34 0.03/0.34 with precondition: [A>=2] 0.03/0.34 0.03/0.34 0.03/0.34 Closed-form bounds of start0(A,B,C,D,E,F,G): 0.03/0.34 ------------------------------------- 0.03/0.34 * Chain [23] with precondition: [A=1] 0.03/0.34 - Upper bound: 0 0.03/0.34 - Complexity: constant 0.03/0.34 * Chain [22] with precondition: [0>=A] 0.03/0.34 - Upper bound: 0 0.03/0.34 - Complexity: constant 0.03/0.34 * Chain [21] with precondition: [A>=1] 0.03/0.34 - Upper bound: 0 0.03/0.34 - Complexity: constant 0.03/0.34 * Chain [20] with precondition: [A>=2] 0.03/0.34 - Upper bound: 8*A 0.03/0.34 - Complexity: n 0.03/0.34 0.03/0.34 ### Maximum cost of start0(A,B,C,D,E,F,G): nat(A)*8 0.03/0.34 Asymptotic class: n 0.03/0.34 * Total analysis performed in 272 ms. 0.03/0.34 0.03/0.44 EOF