0.03/0.20 WORST_CASE(?,O(n^1)) 0.03/0.20 0.03/0.20 Preprocessing Cost Relations 0.03/0.20 ===================================== 0.03/0.20 0.03/0.20 #### Computed strongly connected components 0.03/0.20 0. recursive : [evalfbb1in/4,evalfbb2in/4] 0.03/0.20 1. recursive : [evalfbb2in_loop_cont/7,evalfbb3in/6,evalfbb4in/6] 0.03/0.20 2. non_recursive : [evalfstop/4] 0.03/0.20 3. non_recursive : [evalfreturnin/4] 0.03/0.20 4. non_recursive : [exit_location/1] 0.03/0.20 5. non_recursive : [evalfbb4in_loop_cont/5] 0.03/0.20 6. non_recursive : [evalfentryin/4] 0.03/0.20 7. non_recursive : [evalfstart/4] 0.03/0.20 0.03/0.20 #### Obtained direct recursion through partial evaluation 0.03/0.20 0. SCC is partially evaluated into evalfbb2in/4 0.03/0.20 1. SCC is partially evaluated into evalfbb4in/6 0.03/0.20 2. SCC is completely evaluated into other SCCs 0.03/0.20 3. SCC is completely evaluated into other SCCs 0.03/0.20 4. SCC is completely evaluated into other SCCs 0.03/0.20 5. SCC is partially evaluated into evalfbb4in_loop_cont/5 0.03/0.20 6. SCC is partially evaluated into evalfentryin/4 0.03/0.20 7. SCC is partially evaluated into evalfstart/4 0.03/0.20 0.03/0.20 Control-Flow Refinement of Cost Relations 0.03/0.20 ===================================== 0.03/0.20 0.03/0.20 ### Specialization of cost equations evalfbb2in/4 0.03/0.20 * CE 11 is refined into CE [12] 0.03/0.20 * CE 10 is refined into CE [13] 0.03/0.20 * CE 9 is refined into CE [14] 0.03/0.20 0.03/0.20 0.03/0.20 ### Cost equations --> "Loop" of evalfbb2in/4 0.03/0.20 * CEs [14] --> Loop 12 0.03/0.20 * CEs [12] --> Loop 13 0.03/0.20 * CEs [13] --> Loop 14 0.03/0.20 0.03/0.20 ### Ranking functions of CR evalfbb2in(A,C,D,E) 0.03/0.20 0.03/0.20 #### Partial ranking functions of CR evalfbb2in(A,C,D,E) 0.03/0.20 0.03/0.20 0.03/0.20 ### Specialization of cost equations evalfbb4in/6 0.03/0.20 * CE 5 is refined into CE [15] 0.03/0.20 * CE 3 is refined into CE [16,17] 0.03/0.20 * CE 6 is refined into CE [18] 0.03/0.20 * CE 4 is refined into CE [19] 0.03/0.20 0.03/0.20 0.03/0.20 ### Cost equations --> "Loop" of evalfbb4in/6 0.03/0.20 * CEs [19] --> Loop 15 0.03/0.20 * CEs [15] --> Loop 16 0.03/0.20 * CEs [16,17] --> Loop 17 0.03/0.20 * CEs [18] --> Loop 18 0.03/0.20 0.03/0.20 ### Ranking functions of CR evalfbb4in(A,B,C,D,E,F) 0.03/0.20 * RF of phase [15]: [B] 0.03/0.20 0.03/0.20 #### Partial ranking functions of CR evalfbb4in(A,B,C,D,E,F) 0.03/0.20 * Partial RF of phase [15]: 0.03/0.20 - RF of loop [15:1]: 0.03/0.20 B 0.03/0.20 0.03/0.20 0.03/0.20 ### Specialization of cost equations evalfbb4in_loop_cont/5 0.03/0.20 * CE 7 is refined into CE [20] 0.03/0.20 * CE 8 is refined into CE [21] 0.03/0.20 0.03/0.20 0.03/0.20 ### Cost equations --> "Loop" of evalfbb4in_loop_cont/5 0.03/0.20 * CEs [20] --> Loop 19 0.03/0.20 * CEs [21] --> Loop 20 0.03/0.20 0.03/0.20 ### Ranking functions of CR evalfbb4in_loop_cont(A,B,C,D,E) 0.03/0.20 0.03/0.20 #### Partial ranking functions of CR evalfbb4in_loop_cont(A,B,C,D,E) 0.03/0.20 0.03/0.20 0.03/0.20 ### Specialization of cost equations evalfentryin/4 0.03/0.20 * CE 2 is refined into CE [22,23,24,25,26] 0.03/0.20 0.03/0.20 0.03/0.20 ### Cost equations --> "Loop" of evalfentryin/4 0.03/0.20 * CEs [24] --> Loop 21 0.03/0.20 * CEs [23,25] --> Loop 22 0.03/0.20 * CEs [26] --> Loop 23 0.03/0.20 * CEs [22] --> Loop 24 0.03/0.20 0.03/0.20 ### Ranking functions of CR evalfentryin(A,B,C,D) 0.03/0.20 0.03/0.20 #### Partial ranking functions of CR evalfentryin(A,B,C,D) 0.03/0.20 0.03/0.20 0.03/0.20 ### Specialization of cost equations evalfstart/4 0.03/0.20 * CE 1 is refined into CE [27,28,29,30] 0.03/0.20 0.03/0.20 0.03/0.20 ### Cost equations --> "Loop" of evalfstart/4 0.03/0.20 * CEs [30] --> Loop 25 0.03/0.20 * CEs [29] --> Loop 26 0.03/0.20 * CEs [28] --> Loop 27 0.03/0.20 * CEs [27] --> Loop 28 0.03/0.20 0.03/0.20 ### Ranking functions of CR evalfstart(A,B,C,D) 0.03/0.20 0.03/0.20 #### Partial ranking functions of CR evalfstart(A,B,C,D) 0.03/0.20 0.03/0.20 0.03/0.20 Computing Bounds 0.03/0.20 ===================================== 0.03/0.20 0.03/0.20 #### Cost of chains of evalfbb2in(A,C,D,E): 0.03/0.20 * Chain [13]: 0 0.03/0.20 with precondition: [D=3,C+1>=A,A>=C] 0.03/0.20 0.03/0.20 * Chain [12,14]: 1 0.03/0.20 with precondition: [D=2,A=C,A=E+1] 0.03/0.20 0.03/0.20 * Chain [12,13]: 1 0.03/0.20 with precondition: [D=3,A=C] 0.03/0.20 0.03/0.20 0.03/0.20 #### Cost of chains of evalfbb4in(A,B,C,D,E,F): 0.03/0.20 * Chain [[15],18]: 2*it(15)+0 0.03/0.20 Such that:it(15) =< B 0.03/0.20 0.03/0.20 with precondition: [D=3,B>=1] 0.03/0.20 0.03/0.20 * Chain [[15],17]: 2*it(15)+1 0.03/0.20 Such that:it(15) =< B 0.03/0.20 0.03/0.20 with precondition: [D=3,B>=2] 0.03/0.20 0.03/0.20 * Chain [[15],16]: 2*it(15)+0 0.03/0.20 Such that:it(15) =< B 0.03/0.20 0.03/0.20 with precondition: [D=4,E=0,A=F+1,B>=1] 0.03/0.20 0.03/0.20 * Chain [18]: 0 0.03/0.20 with precondition: [D=3] 0.03/0.20 0.03/0.20 * Chain [17]: 1 0.03/0.20 with precondition: [D=3,B>=1] 0.03/0.20 0.03/0.20 * Chain [16]: 0 0.03/0.20 with precondition: [D=4,F=C,B=E,0>=B] 0.03/0.20 0.03/0.20 0.03/0.20 #### Cost of chains of evalfbb4in_loop_cont(A,B,C,D,E): 0.03/0.20 * Chain [20]: 0 0.03/0.20 with precondition: [A=3] 0.03/0.20 0.03/0.20 * Chain [19]: 0 0.03/0.20 with precondition: [A=4] 0.03/0.20 0.03/0.20 0.03/0.20 #### Cost of chains of evalfentryin(A,B,C,D): 0.03/0.20 * Chain [24]: 0 0.03/0.20 with precondition: [] 0.03/0.20 0.03/0.20 * Chain [23]: 0 0.03/0.20 with precondition: [0>=A] 0.03/0.20 0.03/0.20 * Chain [22]: 4*s(2)+1 0.03/0.20 Such that:aux(1) =< A 0.03/0.20 s(2) =< aux(1) 0.03/0.20 0.03/0.20 with precondition: [A>=1] 0.03/0.20 0.03/0.20 * Chain [21]: 2*s(4)+1 0.03/0.20 Such that:s(4) =< A 0.03/0.20 0.03/0.20 with precondition: [A>=2] 0.03/0.20 0.03/0.20 0.03/0.20 #### Cost of chains of evalfstart(A,B,C,D): 0.03/0.20 * Chain [28]: 0 0.03/0.20 with precondition: [] 0.03/0.20 0.03/0.20 * Chain [27]: 0 0.03/0.20 with precondition: [0>=A] 0.03/0.20 0.03/0.20 * Chain [26]: 4*s(6)+1 0.03/0.20 Such that:s(5) =< A 0.03/0.20 s(6) =< s(5) 0.03/0.20 0.03/0.20 with precondition: [A>=1] 0.03/0.20 0.03/0.20 * Chain [25]: 2*s(7)+1 0.03/0.20 Such that:s(7) =< A 0.03/0.20 0.03/0.20 with precondition: [A>=2] 0.03/0.20 0.03/0.20 0.03/0.20 Closed-form bounds of evalfstart(A,B,C,D): 0.03/0.20 ------------------------------------- 0.03/0.20 * Chain [28] with precondition: [] 0.03/0.20 - Upper bound: 0 0.03/0.20 - Complexity: constant 0.03/0.20 * Chain [27] with precondition: [0>=A] 0.03/0.20 - Upper bound: 0 0.03/0.20 - Complexity: constant 0.03/0.20 * Chain [26] with precondition: [A>=1] 0.03/0.20 - Upper bound: 4*A+1 0.03/0.20 - Complexity: n 0.03/0.20 * Chain [25] with precondition: [A>=2] 0.03/0.20 - Upper bound: 2*A+1 0.03/0.20 - Complexity: n 0.03/0.20 0.03/0.20 ### Maximum cost of evalfstart(A,B,C,D): nat(A)*4+1 0.03/0.20 Asymptotic class: n 0.03/0.20 * Total analysis performed in 136 ms. 0.03/0.20 0.03/0.30 EOF