0.03/0.38 WORST_CASE(?,O(n^2)) 0.03/0.38 0.03/0.38 Preprocessing Cost Relations 0.03/0.38 ===================================== 0.03/0.38 0.03/0.38 #### Computed strongly connected components 0.03/0.38 0. recursive : [evalfbb1in/7,evalfbb2in/7,evalfbb3in/7,evalfbb4in/7,evalfbbin/7] 0.03/0.38 1. non_recursive : [evalfstop/5] 0.03/0.38 2. non_recursive : [evalfreturnin/5] 0.03/0.38 3. non_recursive : [exit_location/1] 0.03/0.38 4. non_recursive : [evalfbb3in_loop_cont/6] 0.03/0.38 5. non_recursive : [evalfentryin/5] 0.03/0.38 6. non_recursive : [evalfstart/5] 0.03/0.38 0.03/0.38 #### Obtained direct recursion through partial evaluation 0.03/0.38 0. SCC is partially evaluated into evalfbb3in/7 0.03/0.38 1. SCC is completely evaluated into other SCCs 0.03/0.38 2. SCC is completely evaluated into other SCCs 0.03/0.38 3. SCC is completely evaluated into other SCCs 0.03/0.38 4. SCC is partially evaluated into evalfbb3in_loop_cont/6 0.03/0.38 5. SCC is partially evaluated into evalfentryin/5 0.03/0.38 6. SCC is partially evaluated into evalfstart/5 0.03/0.38 0.03/0.38 Control-Flow Refinement of Cost Relations 0.03/0.38 ===================================== 0.03/0.38 0.03/0.38 ### Specialization of cost equations evalfbb3in/7 0.03/0.38 * CE 7 is refined into CE [10] 0.03/0.38 * CE 3 is refined into CE [11] 0.03/0.38 * CE 6 is refined into CE [12] 0.03/0.38 * CE 5 is refined into CE [13] 0.03/0.38 * CE 4 is refined into CE [14] 0.03/0.38 0.03/0.38 0.03/0.38 ### Cost equations --> "Loop" of evalfbb3in/7 0.03/0.38 * CEs [13] --> Loop 10 0.03/0.38 * CEs [14] --> Loop 11 0.03/0.38 * CEs [10] --> Loop 12 0.03/0.38 * CEs [12] --> Loop 13 0.03/0.38 * CEs [11] --> Loop 14 0.03/0.38 0.03/0.38 ### Ranking functions of CR evalfbb3in(A,B,C,D,F,G,H) 0.03/0.38 0.03/0.38 #### Partial ranking functions of CR evalfbb3in(A,B,C,D,F,G,H) 0.03/0.38 * Partial RF of phase [10,11]: 0.03/0.38 - RF of loop [10:1]: 0.03/0.38 A-C depends on loops [11:1] 0.03/0.38 B-C-1 depends on loops [11:1] 0.03/0.38 - RF of loop [11:1]: 0.03/0.38 -A+C+1 depends on loops [10:1] 0.03/0.38 B-D 0.03/0.38 C depends on loops [10:1] 0.03/0.38 0.03/0.38 0.03/0.38 ### Specialization of cost equations evalfbb3in_loop_cont/6 0.03/0.38 * CE 9 is refined into CE [15] 0.03/0.38 * CE 8 is refined into CE [16] 0.03/0.38 0.03/0.38 0.03/0.38 ### Cost equations --> "Loop" of evalfbb3in_loop_cont/6 0.03/0.38 * CEs [15] --> Loop 15 0.03/0.38 * CEs [16] --> Loop 16 0.03/0.38 0.03/0.38 ### Ranking functions of CR evalfbb3in_loop_cont(A,B,C,D,E,F) 0.03/0.38 0.03/0.38 #### Partial ranking functions of CR evalfbb3in_loop_cont(A,B,C,D,E,F) 0.03/0.38 0.03/0.38 0.03/0.38 ### Specialization of cost equations evalfentryin/5 0.03/0.38 * CE 2 is refined into CE [17,18,19,20,21] 0.03/0.38 0.03/0.38 0.03/0.38 ### Cost equations --> "Loop" of evalfentryin/5 0.03/0.38 * CEs [17,18,19,20,21] --> Loop 17 0.03/0.38 0.03/0.38 ### Ranking functions of CR evalfentryin(A,B,C,D,F) 0.03/0.38 0.03/0.38 #### Partial ranking functions of CR evalfentryin(A,B,C,D,F) 0.03/0.38 0.03/0.38 0.03/0.38 ### Specialization of cost equations evalfstart/5 0.03/0.38 * CE 1 is refined into CE [22] 0.03/0.38 0.03/0.38 0.03/0.38 ### Cost equations --> "Loop" of evalfstart/5 0.03/0.38 * CEs [22] --> Loop 18 0.03/0.38 0.03/0.38 ### Ranking functions of CR evalfstart(A,B,C,D,F) 0.03/0.38 0.03/0.38 #### Partial ranking functions of CR evalfstart(A,B,C,D,F) 0.03/0.38 0.03/0.38 0.03/0.38 Computing Bounds 0.03/0.38 ===================================== 0.03/0.38 0.03/0.38 #### Cost of chains of evalfbb3in(A,B,C,D,F,G,H): 0.03/0.38 * Chain [[10,11],14]: 1*it(10)+1*it(11)+0 0.03/0.38 Such that:aux(19) =< B 0.03/0.38 aux(4) =< B-C 0.03/0.38 it(11) =< -D+H 0.03/0.38 aux(3) =< it(11)*aux(19) 0.03/0.38 it(10) =< aux(3)+aux(4) 0.03/0.38 0.03/0.38 with precondition: [F=2,A>=1,C>=0,D>=0,B>=A+1,H>=D,A>=G,B>=H+1,G+H>=D+1] 0.03/0.38 0.03/0.38 * Chain [[10,11],13]: 1*it(10)+1*it(11)+0 0.03/0.38 Such that:aux(19) =< B 0.03/0.38 aux(4) =< B-C 0.03/0.38 it(11) =< B-D 0.03/0.38 aux(3) =< it(11)*aux(19) 0.03/0.38 it(10) =< aux(3)+aux(4) 0.03/0.38 0.03/0.38 with precondition: [F=2,G=0,B=H,A>=1,C>=0,D>=0,B>=A+1,B>=D+1] 0.03/0.38 0.03/0.38 * Chain [[10,11],12]: 1*it(10)+1*it(11)+0 0.03/0.38 Such that:aux(19) =< B 0.03/0.38 aux(4) =< B-C 0.03/0.38 it(11) =< B-D 0.03/0.38 aux(3) =< it(11)*aux(19) 0.03/0.38 it(10) =< aux(3)+aux(4) 0.03/0.38 0.03/0.38 with precondition: [F=3,A>=1,C>=0,D>=0,B>=A+1,B>=D+1] 0.03/0.38 0.03/0.38 * Chain [14]: 0 0.03/0.38 with precondition: [F=2,C=G,D=H,A>=1,C>=0,D>=0,B>=A+1,B>=D+1] 0.03/0.38 0.03/0.38 * Chain [12]: 0 0.03/0.38 with precondition: [F=3,A>=1,C>=0,D>=0,B>=A+1] 0.03/0.38 0.03/0.38 0.03/0.38 #### Cost of chains of evalfbb3in_loop_cont(A,B,C,D,E,F): 0.03/0.38 * Chain [16]: 0 0.03/0.38 with precondition: [A=2,B>=1,C>=B+1] 0.03/0.38 0.03/0.38 * Chain [15]: 0 0.03/0.38 with precondition: [A=3,B>=1,C>=B+1] 0.03/0.38 0.03/0.38 0.03/0.38 #### Cost of chains of evalfentryin(A,B,C,D,F): 0.03/0.38 * Chain [17]: 3*s(3)+3*s(5)+0 0.03/0.38 Such that:aux(25) =< B 0.03/0.38 s(3) =< aux(25) 0.03/0.38 s(4) =< s(3)*aux(25) 0.03/0.38 s(5) =< s(4)+aux(25) 0.03/0.38 0.03/0.38 with precondition: [A>=1,B>=A+1] 0.03/0.38 0.03/0.38 0.03/0.38 #### Cost of chains of evalfstart(A,B,C,D,F): 0.03/0.38 * Chain [18]: 3*s(17)+3*s(19)+0 0.03/0.38 Such that:s(16) =< B 0.03/0.38 s(17) =< s(16) 0.03/0.38 s(18) =< s(17)*s(16) 0.03/0.38 s(19) =< s(18)+s(16) 0.03/0.38 0.03/0.38 with precondition: [A>=1,B>=A+1] 0.03/0.38 0.03/0.38 0.03/0.38 Closed-form bounds of evalfstart(A,B,C,D,F): 0.03/0.38 ------------------------------------- 0.03/0.38 * Chain [18] with precondition: [A>=1,B>=A+1] 0.03/0.38 - Upper bound: 3*B*B+6*B 0.03/0.38 - Complexity: n^2 0.03/0.38 0.03/0.38 ### Maximum cost of evalfstart(A,B,C,D,F): 3*B*B+6*B 0.03/0.38 Asymptotic class: n^2 0.03/0.38 * Total analysis performed in 296 ms. 0.03/0.38 0.03/0.48 EOF