0.03/0.21 WORST_CASE(?,O(n^1)) 0.03/0.21 0.03/0.21 Preprocessing Cost Relations 0.03/0.21 ===================================== 0.03/0.21 0.03/0.21 #### Computed strongly connected components 0.03/0.21 0. recursive : [evalterminatebb1in/7,evalterminatebbin/7] 0.03/0.21 1. non_recursive : [evalterminatestop/4] 0.03/0.21 2. non_recursive : [evalterminatereturnin/4] 0.03/0.21 3. non_recursive : [exit_location/1] 0.03/0.21 4. non_recursive : [evalterminatebb1in_loop_cont/5] 0.03/0.21 5. non_recursive : [evalterminateentryin/4] 0.03/0.21 6. non_recursive : [evalterminatestart/4] 0.03/0.21 0.03/0.21 #### Obtained direct recursion through partial evaluation 0.03/0.21 0. SCC is partially evaluated into evalterminatebb1in/7 0.03/0.21 1. SCC is completely evaluated into other SCCs 0.03/0.21 2. SCC is completely evaluated into other SCCs 0.03/0.21 3. SCC is completely evaluated into other SCCs 0.03/0.21 4. SCC is partially evaluated into evalterminatebb1in_loop_cont/5 0.03/0.21 5. SCC is partially evaluated into evalterminateentryin/4 0.03/0.21 6. SCC is partially evaluated into evalterminatestart/4 0.03/0.21 0.03/0.21 Control-Flow Refinement of Cost Relations 0.03/0.21 ===================================== 0.03/0.21 0.03/0.21 ### Specialization of cost equations evalterminatebb1in/7 0.03/0.21 * CE 6 is refined into CE [9] 0.03/0.21 * CE 5 is refined into CE [10] 0.03/0.21 * CE 4 is refined into CE [11] 0.03/0.21 * CE 3 is refined into CE [12] 0.03/0.21 0.03/0.21 0.03/0.21 ### Cost equations --> "Loop" of evalterminatebb1in/7 0.03/0.21 * CEs [12] --> Loop 9 0.03/0.21 * CEs [9] --> Loop 10 0.03/0.21 * CEs [10] --> Loop 11 0.03/0.21 * CEs [11] --> Loop 12 0.03/0.21 0.03/0.21 ### Ranking functions of CR evalterminatebb1in(A,B,C,D,E,F,G) 0.03/0.21 * RF of phase [9]: [A/2-B/2-C/2+101/2] 0.03/0.21 0.03/0.21 #### Partial ranking functions of CR evalterminatebb1in(A,B,C,D,E,F,G) 0.03/0.21 * Partial RF of phase [9]: 0.03/0.21 - RF of loop [9:1]: 0.03/0.21 A/2-B/2-C/2+101/2 0.03/0.21 0.03/0.21 0.03/0.21 ### Specialization of cost equations evalterminatebb1in_loop_cont/5 0.03/0.21 * CE 8 is refined into CE [13] 0.03/0.21 * CE 7 is refined into CE [14] 0.03/0.21 0.03/0.21 0.03/0.21 ### Cost equations --> "Loop" of evalterminatebb1in_loop_cont/5 0.03/0.21 * CEs [13] --> Loop 13 0.03/0.21 * CEs [14] --> Loop 14 0.03/0.21 0.03/0.21 ### Ranking functions of CR evalterminatebb1in_loop_cont(A,B,C,D,E) 0.03/0.21 0.03/0.21 #### Partial ranking functions of CR evalterminatebb1in_loop_cont(A,B,C,D,E) 0.03/0.21 0.03/0.21 0.03/0.21 ### Specialization of cost equations evalterminateentryin/4 0.03/0.21 * CE 2 is refined into CE [15,16,17,18,19,20] 0.03/0.21 0.03/0.21 0.03/0.21 ### Cost equations --> "Loop" of evalterminateentryin/4 0.03/0.21 * CEs [16] --> Loop 15 0.03/0.21 * CEs [15] --> Loop 16 0.03/0.21 * CEs [18] --> Loop 17 0.03/0.21 * CEs [20] --> Loop 18 0.03/0.21 * CEs [17] --> Loop 19 0.03/0.21 * CEs [19] --> Loop 20 0.03/0.21 0.03/0.21 ### Ranking functions of CR evalterminateentryin(A,B,C,D) 0.03/0.21 0.03/0.21 #### Partial ranking functions of CR evalterminateentryin(A,B,C,D) 0.03/0.21 0.03/0.21 0.03/0.21 ### Specialization of cost equations evalterminatestart/4 0.03/0.21 * CE 1 is refined into CE [21,22,23,24,25,26] 0.03/0.21 0.03/0.21 0.03/0.21 ### Cost equations --> "Loop" of evalterminatestart/4 0.03/0.21 * CEs [26] --> Loop 21 0.03/0.21 * CEs [25] --> Loop 22 0.03/0.21 * CEs [24] --> Loop 23 0.03/0.21 * CEs [23] --> Loop 24 0.03/0.21 * CEs [22] --> Loop 25 0.03/0.21 * CEs [21] --> Loop 26 0.03/0.21 0.03/0.21 ### Ranking functions of CR evalterminatestart(A,B,C,D) 0.03/0.21 0.03/0.21 #### Partial ranking functions of CR evalterminatestart(A,B,C,D) 0.03/0.21 0.03/0.21 0.03/0.21 Computing Bounds 0.03/0.21 ===================================== 0.03/0.21 0.03/0.21 #### Cost of chains of evalterminatebb1in(A,B,C,D,E,F,G): 0.03/0.21 * Chain [[9],12]: 1*it(9)+0 0.03/0.21 Such that:it(9) =< A/2-B/2-C/2+101/2 0.03/0.21 it(9) =< -B-C+F+G 0.03/0.21 0.03/0.21 with precondition: [D=2,A+B+C=E+F+G,100>=B,F>=101,A>=C,A>=E+1,E+1>=F] 0.03/0.21 0.03/0.21 * Chain [[9],11]: 1*it(9)+0 0.03/0.21 Such that:it(9) =< A/2-B/2-C/2+101/2 0.03/0.21 it(9) =< -B-C+F+G 0.03/0.21 0.03/0.21 with precondition: [D=2,A+B+C=E+F+G,100>=B,A>=C,A>=E+1,E+1>=F,C+2*A>=2*E+F+2,A+B+C>=2*E+F+1,E+F+101>=A+B+C] 0.03/0.21 0.03/0.21 * Chain [[9],10]: 1*it(9)+0 0.03/0.21 Such that:it(9) =< A/2-B/2-C/2+101/2 0.03/0.21 0.03/0.21 with precondition: [D=3,100>=B,A>=C] 0.03/0.21 0.03/0.21 * Chain [12]: 0 0.03/0.21 with precondition: [D=2,E=A,G=C,B=F,B>=101] 0.03/0.21 0.03/0.21 * Chain [11]: 0 0.03/0.21 with precondition: [D=2,F=B,A=E,C=G,C>=A+1] 0.03/0.21 0.03/0.21 * Chain [10]: 0 0.03/0.21 with precondition: [D=3] 0.03/0.21 0.03/0.21 0.03/0.21 #### Cost of chains of evalterminatebb1in_loop_cont(A,B,C,D,E): 0.03/0.21 * Chain [14]: 0 0.03/0.21 with precondition: [A=2] 0.03/0.21 0.03/0.21 * Chain [13]: 0 0.03/0.21 with precondition: [A=3] 0.03/0.21 0.03/0.21 0.03/0.21 #### Cost of chains of evalterminateentryin(A,B,C,D): 0.03/0.21 * Chain [20]: 0 0.03/0.21 with precondition: [] 0.03/0.21 0.03/0.21 * Chain [19]: 1*s(1)+0 0.03/0.21 Such that:s(1) =< -A/2+B/2-C/2+101/2 0.03/0.21 s(1) =< B 0.03/0.21 0.03/0.21 with precondition: [100>=A,B>=101,B>=C] 0.03/0.21 0.03/0.21 * Chain [18]: 1*s(2)+0 0.03/0.21 Such that:s(2) =< -A/2+B/2-C/2+101/2 0.03/0.21 0.03/0.21 with precondition: [100>=A,B>=C] 0.03/0.21 0.03/0.21 * Chain [17]: 1*s(3)+0 0.03/0.21 Such that:s(3) =< -A/2+B/2-C/2+101/2 0.03/0.21 0.03/0.21 with precondition: [100>=A,B>=C,302>=A+B+C] 0.03/0.21 0.03/0.21 * Chain [16]: 0 0.03/0.21 with precondition: [A>=101] 0.03/0.21 0.03/0.21 * Chain [15]: 0 0.03/0.21 with precondition: [C>=B+1] 0.03/0.21 0.03/0.21 0.03/0.21 #### Cost of chains of evalterminatestart(A,B,C,D): 0.03/0.21 * Chain [26]: 0 0.03/0.21 with precondition: [] 0.03/0.21 0.03/0.21 * Chain [25]: 1*s(4)+0 0.03/0.21 Such that:s(4) =< -A/2+B/2-C/2+101/2 0.03/0.21 s(4) =< B 0.03/0.21 0.03/0.21 with precondition: [100>=A,B>=101,B>=C] 0.03/0.21 0.03/0.21 * Chain [24]: 1*s(5)+0 0.03/0.21 Such that:s(5) =< -A/2+B/2-C/2+101/2 0.03/0.21 0.03/0.21 with precondition: [100>=A,B>=C] 0.03/0.21 0.03/0.21 * Chain [23]: 1*s(6)+0 0.03/0.21 Such that:s(6) =< -A/2+B/2-C/2+101/2 0.03/0.21 0.03/0.21 with precondition: [100>=A,B>=C,302>=A+B+C] 0.03/0.21 0.03/0.21 * Chain [22]: 0 0.03/0.21 with precondition: [A>=101] 0.03/0.21 0.03/0.21 * Chain [21]: 0 0.03/0.21 with precondition: [C>=B+1] 0.03/0.21 0.03/0.21 0.03/0.21 Closed-form bounds of evalterminatestart(A,B,C,D): 0.03/0.21 ------------------------------------- 0.03/0.21 * Chain [26] with precondition: [] 0.03/0.21 - Upper bound: 0 0.03/0.21 - Complexity: constant 0.03/0.21 * Chain [25] with precondition: [100>=A,B>=101,B>=C] 0.03/0.21 - Upper bound: -A/2+B/2-C/2+101/2 0.03/0.21 - Complexity: n 0.03/0.21 * Chain [24] with precondition: [100>=A,B>=C] 0.03/0.21 - Upper bound: -A/2+B/2-C/2+101/2 0.03/0.21 - Complexity: n 0.03/0.21 * Chain [23] with precondition: [100>=A,B>=C,302>=A+B+C] 0.03/0.21 - Upper bound: -A/2+B/2-C/2+101/2 0.03/0.21 - Complexity: n 0.03/0.21 * Chain [22] with precondition: [A>=101] 0.03/0.21 - Upper bound: 0 0.03/0.21 - Complexity: constant 0.03/0.21 * Chain [21] with precondition: [C>=B+1] 0.03/0.21 - Upper bound: 0 0.03/0.21 - Complexity: constant 0.03/0.21 0.03/0.21 ### Maximum cost of evalterminatestart(A,B,C,D): nat(-A/2+B/2-C/2+101/2) 0.03/0.21 Asymptotic class: n 0.03/0.21 * Total analysis performed in 153 ms. 0.03/0.21 0.03/0.31 EOF