0.03/0.22 WORST_CASE(?,O(n^1)) 0.03/0.22 0.03/0.22 Preprocessing Cost Relations 0.03/0.22 ===================================== 0.03/0.22 0.03/0.22 #### Computed strongly connected components 0.03/0.22 0. recursive : [evalfbb1in/5,evalfbb2in/5,evalfbb3in/5,evalfbbin/5] 0.03/0.22 1. non_recursive : [evalfstop/4] 0.03/0.22 2. non_recursive : [evalfreturnin/4] 0.03/0.22 3. non_recursive : [exit_location/1] 0.03/0.22 4. non_recursive : [evalfbb3in_loop_cont/5] 0.03/0.22 5. non_recursive : [evalfentryin/4] 0.03/0.22 6. non_recursive : [evalfstart/4] 0.03/0.22 0.03/0.22 #### Obtained direct recursion through partial evaluation 0.03/0.22 0. SCC is partially evaluated into evalfbb3in/5 0.03/0.22 1. SCC is completely evaluated into other SCCs 0.03/0.22 2. SCC is completely evaluated into other SCCs 0.03/0.22 3. SCC is completely evaluated into other SCCs 0.03/0.22 4. SCC is partially evaluated into evalfbb3in_loop_cont/5 0.03/0.22 5. SCC is partially evaluated into evalfentryin/4 0.03/0.22 6. SCC is partially evaluated into evalfstart/4 0.03/0.22 0.03/0.22 Control-Flow Refinement of Cost Relations 0.03/0.22 ===================================== 0.03/0.22 0.03/0.22 ### Specialization of cost equations evalfbb3in/5 0.03/0.22 * CE 7 is refined into CE [10] 0.03/0.22 * CE 6 is refined into CE [11] 0.03/0.22 * CE 5 is refined into CE [12] 0.03/0.22 * CE 4 is refined into CE [13] 0.03/0.22 * CE 3 is refined into CE [14] 0.03/0.22 0.03/0.22 0.03/0.22 ### Cost equations --> "Loop" of evalfbb3in/5 0.03/0.22 * CEs [13] --> Loop 10 0.03/0.22 * CEs [14] --> Loop 11 0.03/0.22 * CEs [10] --> Loop 12 0.03/0.22 * CEs [11] --> Loop 13 0.03/0.22 * CEs [12] --> Loop 14 0.03/0.22 0.03/0.22 ### Ranking functions of CR evalfbb3in(A,B,C,D,E) 0.03/0.22 * RF of phase [10]: [C] 0.03/0.22 * RF of phase [11]: [B-C] 0.03/0.22 0.03/0.22 #### Partial ranking functions of CR evalfbb3in(A,B,C,D,E) 0.03/0.22 * Partial RF of phase [10]: 0.03/0.22 - RF of loop [10:1]: 0.03/0.22 C 0.03/0.22 * Partial RF of phase [11]: 0.03/0.22 - RF of loop [11:1]: 0.03/0.22 B-C 0.03/0.22 0.03/0.22 0.03/0.22 ### Specialization of cost equations evalfbb3in_loop_cont/5 0.03/0.22 * CE 9 is refined into CE [15] 0.03/0.22 * CE 8 is refined into CE [16] 0.03/0.22 0.03/0.22 0.03/0.22 ### Cost equations --> "Loop" of evalfbb3in_loop_cont/5 0.03/0.22 * CEs [15] --> Loop 15 0.03/0.22 * CEs [16] --> Loop 16 0.03/0.22 0.03/0.22 ### Ranking functions of CR evalfbb3in_loop_cont(A,B,C,D,E) 0.03/0.22 0.03/0.22 #### Partial ranking functions of CR evalfbb3in_loop_cont(A,B,C,D,E) 0.03/0.22 0.03/0.22 0.03/0.22 ### Specialization of cost equations evalfentryin/4 0.03/0.22 * CE 2 is refined into CE [17,18,19,20,21] 0.03/0.22 0.03/0.22 0.03/0.22 ### Cost equations --> "Loop" of evalfentryin/4 0.03/0.22 * CEs [21] --> Loop 17 0.03/0.22 * CEs [18,20] --> Loop 18 0.03/0.22 * CEs [17,19] --> Loop 19 0.03/0.22 0.03/0.22 ### Ranking functions of CR evalfentryin(A,B,C,D) 0.03/0.22 0.03/0.22 #### Partial ranking functions of CR evalfentryin(A,B,C,D) 0.03/0.22 0.03/0.22 0.03/0.22 ### Specialization of cost equations evalfstart/4 0.03/0.22 * CE 1 is refined into CE [22,23,24] 0.03/0.22 0.03/0.22 0.03/0.22 ### Cost equations --> "Loop" of evalfstart/4 0.03/0.22 * CEs [24] --> Loop 20 0.03/0.22 * CEs [23] --> Loop 21 0.03/0.22 * CEs [22] --> Loop 22 0.03/0.22 0.03/0.22 ### Ranking functions of CR evalfstart(A,B,C,D) 0.03/0.22 0.03/0.22 #### Partial ranking functions of CR evalfstart(A,B,C,D) 0.03/0.22 0.03/0.22 0.03/0.22 Computing Bounds 0.03/0.22 ===================================== 0.03/0.22 0.03/0.22 #### Cost of chains of evalfbb3in(A,B,C,D,E): 0.03/0.22 * Chain [[11],13]: 1*it(11)+0 0.03/0.22 Such that:it(11) =< -C+E 0.03/0.22 0.03/0.22 with precondition: [D=2,B=E,A>=1,C>=1,B>=C+1] 0.03/0.22 0.03/0.22 * Chain [[11],12]: 1*it(11)+0 0.03/0.22 Such that:it(11) =< B-C 0.03/0.22 0.03/0.22 with precondition: [D=3,A>=1,C>=1,B>=C+1] 0.03/0.22 0.03/0.22 * Chain [[10],14]: 1*it(10)+0 0.03/0.22 Such that:it(10) =< C 0.03/0.22 0.03/0.22 with precondition: [D=2,E=0,0>=A,C>=1,B>=C+1] 0.03/0.22 0.03/0.22 * Chain [[10],12]: 1*it(10)+0 0.03/0.22 Such that:it(10) =< C 0.03/0.22 0.03/0.22 with precondition: [D=3,0>=A,C>=1,B>=C+1] 0.03/0.22 0.03/0.22 * Chain [12]: 0 0.03/0.22 with precondition: [D=3,B>=2,C>=0,B>=C] 0.03/0.22 0.03/0.22 0.03/0.22 #### Cost of chains of evalfbb3in_loop_cont(A,B,C,D,E): 0.03/0.22 * Chain [16]: 0 0.03/0.22 with precondition: [A=2,C>=2] 0.03/0.22 0.03/0.22 * Chain [15]: 0 0.03/0.22 with precondition: [A=3,C>=2] 0.03/0.22 0.03/0.22 0.03/0.22 #### Cost of chains of evalfentryin(A,B,C,D): 0.03/0.22 * Chain [19]: 2*s(1)+0 0.03/0.22 Such that:aux(1) =< A 0.03/0.22 s(1) =< aux(1) 0.03/0.22 0.03/0.22 with precondition: [0>=C,A>=1,B>=A+1] 0.03/0.22 0.03/0.22 * Chain [18]: 2*s(3)+0 0.03/0.22 Such that:aux(2) =< -A+B 0.03/0.22 s(3) =< aux(2) 0.03/0.22 0.03/0.22 with precondition: [A>=1,C>=1,B>=A+1] 0.03/0.22 0.03/0.22 * Chain [17]: 0 0.03/0.22 with precondition: [A>=1,B>=A+1] 0.03/0.22 0.03/0.22 0.03/0.22 #### Cost of chains of evalfstart(A,B,C,D): 0.03/0.22 * Chain [22]: 2*s(6)+0 0.03/0.22 Such that:s(5) =< A 0.03/0.22 s(6) =< s(5) 0.03/0.22 0.03/0.22 with precondition: [0>=C,A>=1,B>=A+1] 0.03/0.22 0.03/0.22 * Chain [21]: 2*s(8)+0 0.03/0.22 Such that:s(7) =< -A+B 0.03/0.22 s(8) =< s(7) 0.03/0.22 0.03/0.22 with precondition: [A>=1,C>=1,B>=A+1] 0.03/0.22 0.03/0.22 * Chain [20]: 0 0.03/0.22 with precondition: [A>=1,B>=A+1] 0.03/0.22 0.03/0.22 0.03/0.22 Closed-form bounds of evalfstart(A,B,C,D): 0.03/0.22 ------------------------------------- 0.03/0.22 * Chain [22] with precondition: [0>=C,A>=1,B>=A+1] 0.03/0.22 - Upper bound: 2*A 0.03/0.22 - Complexity: n 0.03/0.22 * Chain [21] with precondition: [A>=1,C>=1,B>=A+1] 0.03/0.22 - Upper bound: -2*A+2*B 0.03/0.22 - Complexity: n 0.03/0.22 * Chain [20] with precondition: [A>=1,B>=A+1] 0.03/0.22 - Upper bound: 0 0.03/0.22 - Complexity: constant 0.03/0.22 0.03/0.22 ### Maximum cost of evalfstart(A,B,C,D): max([-2*A+2*B,2*A]) 0.03/0.22 Asymptotic class: n 0.03/0.22 * Total analysis performed in 160 ms. 0.03/0.22 0.03/0.32 EOF