0.03/0.29 WORST_CASE(?,O(n^1)) 0.03/0.29 0.03/0.29 Preprocessing Cost Relations 0.03/0.29 ===================================== 0.03/0.29 0.03/0.29 #### Computed strongly connected components 0.03/0.29 0. recursive : [evalfbb1in/6,evalfbb3in/6,evalfbb4in/6,evalfbbin/6] 0.03/0.29 1. non_recursive : [evalfstop/4] 0.03/0.29 2. non_recursive : [evalfreturnin/4] 0.03/0.29 3. non_recursive : [exit_location/1] 0.03/0.29 4. non_recursive : [evalfbb3in_loop_cont/5] 0.03/0.29 5. non_recursive : [evalfentryin/4] 0.03/0.29 6. non_recursive : [evalfstart/4] 0.03/0.29 0.03/0.29 #### Obtained direct recursion through partial evaluation 0.03/0.29 0. SCC is partially evaluated into evalfbb3in/6 0.03/0.29 1. SCC is completely evaluated into other SCCs 0.03/0.29 2. SCC is completely evaluated into other SCCs 0.03/0.29 3. SCC is completely evaluated into other SCCs 0.03/0.29 4. SCC is partially evaluated into evalfbb3in_loop_cont/5 0.03/0.29 5. SCC is partially evaluated into evalfentryin/4 0.03/0.29 6. SCC is partially evaluated into evalfstart/4 0.03/0.29 0.03/0.29 Control-Flow Refinement of Cost Relations 0.03/0.29 ===================================== 0.03/0.29 0.03/0.29 ### Specialization of cost equations evalfbb3in/6 0.03/0.29 * CE 7 is refined into CE [10] 0.03/0.29 * CE 3 is refined into CE [11] 0.03/0.29 * CE 6 is refined into CE [12] 0.03/0.29 * CE 4 is refined into CE [13] 0.03/0.29 * CE 5 is refined into CE [14] 0.03/0.29 0.03/0.29 0.03/0.29 ### Cost equations --> "Loop" of evalfbb3in/6 0.03/0.29 * CEs [13] --> Loop 10 0.03/0.29 * CEs [14] --> Loop 11 0.03/0.29 * CEs [10] --> Loop 12 0.03/0.29 * CEs [11] --> Loop 13 0.03/0.29 * CEs [12] --> Loop 14 0.03/0.29 0.03/0.29 ### Ranking functions of CR evalfbb3in(A,B,C,E,F,G) 0.03/0.29 * RF of phase [10,11]: [2*B+C-1] 0.03/0.29 0.03/0.29 #### Partial ranking functions of CR evalfbb3in(A,B,C,E,F,G) 0.03/0.29 * Partial RF of phase [10,11]: 0.03/0.29 - RF of loop [10:1]: 0.03/0.29 A-C depends on loops [11:1] 0.03/0.29 B 0.03/0.29 - RF of loop [11:1]: 0.03/0.29 -A+C+1 depends on loops [10:1] 0.03/0.29 C depends on loops [10:1] 0.03/0.29 0.03/0.29 0.03/0.29 ### Specialization of cost equations evalfbb3in_loop_cont/5 0.03/0.29 * CE 9 is refined into CE [15] 0.03/0.29 * CE 8 is refined into CE [16] 0.03/0.29 0.03/0.29 0.03/0.29 ### Cost equations --> "Loop" of evalfbb3in_loop_cont/5 0.03/0.29 * CEs [15] --> Loop 15 0.03/0.29 * CEs [16] --> Loop 16 0.03/0.29 0.03/0.29 ### Ranking functions of CR evalfbb3in_loop_cont(A,B,C,D,E) 0.03/0.29 0.03/0.29 #### Partial ranking functions of CR evalfbb3in_loop_cont(A,B,C,D,E) 0.03/0.29 0.03/0.29 0.03/0.29 ### Specialization of cost equations evalfentryin/4 0.03/0.29 * CE 2 is refined into CE [17,18,19,20,21] 0.03/0.29 0.03/0.29 0.03/0.29 ### Cost equations --> "Loop" of evalfentryin/4 0.03/0.29 * CEs [19] --> Loop 17 0.03/0.29 * CEs [17,18,20,21] --> Loop 18 0.03/0.29 0.03/0.29 ### Ranking functions of CR evalfentryin(A,B,C,E) 0.03/0.29 0.03/0.29 #### Partial ranking functions of CR evalfentryin(A,B,C,E) 0.03/0.29 0.03/0.29 0.03/0.29 ### Specialization of cost equations evalfstart/4 0.03/0.29 * CE 1 is refined into CE [22,23] 0.03/0.29 0.03/0.29 0.03/0.29 ### Cost equations --> "Loop" of evalfstart/4 0.03/0.29 * CEs [23] --> Loop 19 0.03/0.29 * CEs [22] --> Loop 20 0.03/0.29 0.03/0.29 ### Ranking functions of CR evalfstart(A,B,C,E) 0.03/0.29 0.03/0.29 #### Partial ranking functions of CR evalfstart(A,B,C,E) 0.03/0.29 0.03/0.29 0.03/0.29 Computing Bounds 0.03/0.29 ===================================== 0.03/0.29 0.03/0.29 #### Cost of chains of evalfbb3in(A,B,C,E,F,G): 0.03/0.29 * Chain [[10,11],14]: 1*it(10)+1*it(11)+0 0.03/0.29 Such that:it(10) =< B 0.03/0.29 aux(16) =< 2*B+C 0.03/0.29 aux(17) =< 2*B+C-G 0.03/0.29 it(10) =< aux(16) 0.03/0.29 it(11) =< aux(16) 0.03/0.29 it(10) =< aux(17) 0.03/0.29 it(11) =< aux(17) 0.03/0.29 0.03/0.29 with precondition: [E=2,F=0,A>=1,B>=1,C>=0,A>=G,B+C>=G] 0.03/0.29 0.03/0.29 * Chain [[10,11],13]: 1*it(10)+1*it(11)+0 0.03/0.29 Such that:it(10) =< B-F 0.03/0.29 aux(16) =< 2*B+C 0.03/0.29 aux(17) =< 2*B+C-2*F-G 0.03/0.29 it(10) =< aux(16) 0.03/0.29 it(11) =< aux(16) 0.03/0.30 it(10) =< aux(17) 0.03/0.30 it(11) =< aux(17) 0.03/0.30 0.03/0.30 with precondition: [E=2,A>=1,C>=0,F>=1,G>=0,B>=F,A>=G,B+C>=F+1,C+2*B>=2*F+G+1,A+B>=F+G+1,B+C>=F+G] 0.03/0.30 0.03/0.30 * Chain [[10,11],12]: 1*it(10)+1*it(11)+0 0.03/0.30 Such that:it(10) =< B 0.03/0.30 aux(20) =< 2*B+C 0.03/0.30 it(10) =< aux(20) 0.03/0.30 it(11) =< aux(20) 0.03/0.30 0.03/0.30 with precondition: [E=3,A>=1,B>=1,C>=0] 0.03/0.30 0.03/0.30 * Chain [13]: 0 0.03/0.30 with precondition: [E=2,B=F,C=G,A>=1,B>=1,C>=0] 0.03/0.30 0.03/0.30 * Chain [12]: 0 0.03/0.30 with precondition: [E=3,A>=1,C>=0,B+C>=1] 0.03/0.30 0.03/0.30 0.03/0.30 #### Cost of chains of evalfbb3in_loop_cont(A,B,C,D,E): 0.03/0.30 * Chain [16]: 0 0.03/0.30 with precondition: [A=2,B>=1] 0.03/0.30 0.03/0.30 * Chain [15]: 0 0.03/0.30 with precondition: [A=3,B>=1] 0.03/0.30 0.03/0.30 0.03/0.30 #### Cost of chains of evalfentryin(A,B,C,E): 0.03/0.30 * Chain [18]: 2*s(1)+2*s(4)+0 0.03/0.30 Such that:aux(21) =< A 0.03/0.30 aux(22) =< 2*A 0.03/0.30 s(1) =< aux(21) 0.03/0.30 s(1) =< aux(22) 0.03/0.30 s(4) =< aux(22) 0.03/0.30 0.03/0.30 with precondition: [A>=1,B>=1] 0.03/0.30 0.03/0.30 * Chain [17]: 1*s(8)+1*s(11)+0 0.03/0.30 Such that:s(8) =< A 0.03/0.30 aux(23) =< 2*A 0.03/0.30 s(8) =< aux(23) 0.03/0.30 s(11) =< aux(23) 0.03/0.30 0.03/0.30 with precondition: [A>=2,B>=1] 0.03/0.30 0.03/0.30 0.03/0.30 #### Cost of chains of evalfstart(A,B,C,E): 0.03/0.30 * Chain [20]: 2*s(14)+2*s(15)+0 0.03/0.30 Such that:s(12) =< A 0.03/0.30 s(13) =< 2*A 0.03/0.30 s(14) =< s(12) 0.03/0.30 s(14) =< s(13) 0.03/0.30 s(15) =< s(13) 0.03/0.30 0.03/0.30 with precondition: [A>=1,B>=1] 0.03/0.30 0.03/0.30 * Chain [19]: 1*s(16)+1*s(18)+0 0.03/0.30 Such that:s(16) =< A 0.03/0.30 s(17) =< 2*A 0.03/0.30 s(16) =< s(17) 0.03/0.30 s(18) =< s(17) 0.03/0.30 0.03/0.30 with precondition: [A>=2,B>=1] 0.03/0.30 0.03/0.30 0.03/0.30 Closed-form bounds of evalfstart(A,B,C,E): 0.03/0.30 ------------------------------------- 0.03/0.30 * Chain [20] with precondition: [A>=1,B>=1] 0.03/0.30 - Upper bound: 6*A 0.03/0.30 - Complexity: n 0.03/0.30 * Chain [19] with precondition: [A>=2,B>=1] 0.03/0.30 - Upper bound: 3*A 0.03/0.30 - Complexity: n 0.03/0.30 0.03/0.30 ### Maximum cost of evalfstart(A,B,C,E): 6*A 0.03/0.30 Asymptotic class: n 0.03/0.30 * Total analysis performed in 224 ms. 0.03/0.30 0.03/0.40 EOF