0.04/0.22 WORST_CASE(?,O(n^1)) 0.04/0.22 0.04/0.22 Preprocessing Cost Relations 0.04/0.22 ===================================== 0.04/0.22 0.04/0.22 #### Computed strongly connected components 0.04/0.22 0. recursive : [evalfbb1in/6,evalfbb2in/6,evalfbb3in/6,evalfbbin/6] 0.04/0.22 1. non_recursive : [evalfstop/4] 0.04/0.22 2. non_recursive : [evalfreturnin/4] 0.04/0.22 3. non_recursive : [exit_location/1] 0.04/0.22 4. non_recursive : [evalfbb3in_loop_cont/5] 0.04/0.22 5. non_recursive : [evalfentryin/4] 0.04/0.22 6. non_recursive : [evalfstart/4] 0.04/0.22 0.04/0.22 #### Obtained direct recursion through partial evaluation 0.04/0.22 0. SCC is partially evaluated into evalfbb3in/6 0.04/0.22 1. SCC is completely evaluated into other SCCs 0.04/0.22 2. SCC is completely evaluated into other SCCs 0.04/0.22 3. SCC is completely evaluated into other SCCs 0.04/0.22 4. SCC is partially evaluated into evalfbb3in_loop_cont/5 0.04/0.22 5. SCC is partially evaluated into evalfentryin/4 0.04/0.22 6. SCC is partially evaluated into evalfstart/4 0.04/0.22 0.04/0.22 Control-Flow Refinement of Cost Relations 0.04/0.22 ===================================== 0.04/0.22 0.04/0.22 ### Specialization of cost equations evalfbb3in/6 0.04/0.22 * CE 6 is refined into CE [9] 0.04/0.22 * CE 5 is refined into CE [10] 0.04/0.22 * CE 4 is refined into CE [11] 0.04/0.22 * CE 3 is refined into CE [12] 0.04/0.22 0.04/0.22 0.04/0.22 ### Cost equations --> "Loop" of evalfbb3in/6 0.04/0.22 * CEs [11] --> Loop 9 0.04/0.22 * CEs [12] --> Loop 10 0.04/0.22 * CEs [9] --> Loop 11 0.04/0.22 * CEs [10] --> Loop 12 0.04/0.22 0.04/0.22 ### Ranking functions of CR evalfbb3in(A,B,C,D,E,F) 0.04/0.22 * RF of phase [9]: [-B+100] 0.04/0.22 * RF of phase [10]: [-A+C] 0.04/0.22 0.04/0.22 #### Partial ranking functions of CR evalfbb3in(A,B,C,D,E,F) 0.04/0.22 * Partial RF of phase [9]: 0.04/0.22 - RF of loop [9:1]: 0.04/0.22 -B+100 0.04/0.22 * Partial RF of phase [10]: 0.04/0.22 - RF of loop [10:1]: 0.04/0.22 -A+C 0.04/0.22 0.04/0.22 0.04/0.22 ### Specialization of cost equations evalfbb3in_loop_cont/5 0.04/0.22 * CE 8 is refined into CE [13] 0.04/0.22 * CE 7 is refined into CE [14] 0.04/0.22 0.04/0.22 0.04/0.22 ### Cost equations --> "Loop" of evalfbb3in_loop_cont/5 0.04/0.22 * CEs [13] --> Loop 13 0.04/0.22 * CEs [14] --> Loop 14 0.04/0.22 0.04/0.22 ### Ranking functions of CR evalfbb3in_loop_cont(A,B,C,D,E) 0.04/0.22 0.04/0.22 #### Partial ranking functions of CR evalfbb3in_loop_cont(A,B,C,D,E) 0.04/0.22 0.04/0.22 0.04/0.22 ### Specialization of cost equations evalfentryin/4 0.04/0.22 * CE 2 is refined into CE [15,16,17,18,19] 0.04/0.22 0.04/0.22 0.04/0.22 ### Cost equations --> "Loop" of evalfentryin/4 0.04/0.22 * CEs [15,16] --> Loop 15 0.04/0.22 * CEs [17,18] --> Loop 16 0.04/0.22 * CEs [19] --> Loop 17 0.04/0.22 0.04/0.22 ### Ranking functions of CR evalfentryin(A,B,C,D) 0.04/0.22 0.04/0.22 #### Partial ranking functions of CR evalfentryin(A,B,C,D) 0.04/0.22 0.04/0.22 0.04/0.22 ### Specialization of cost equations evalfstart/4 0.04/0.22 * CE 1 is refined into CE [20,21,22] 0.04/0.22 0.04/0.22 0.04/0.22 ### Cost equations --> "Loop" of evalfstart/4 0.04/0.22 * CEs [22] --> Loop 18 0.04/0.22 * CEs [21] --> Loop 19 0.04/0.22 * CEs [20] --> Loop 20 0.04/0.22 0.04/0.22 ### Ranking functions of CR evalfstart(A,B,C,D) 0.04/0.22 0.04/0.22 #### Partial ranking functions of CR evalfstart(A,B,C,D) 0.04/0.22 0.04/0.22 0.04/0.22 Computing Bounds 0.04/0.22 ===================================== 0.04/0.22 0.04/0.22 #### Cost of chains of evalfbb3in(A,B,C,D,E,F): 0.04/0.22 * Chain [[10],[9],12]: 1*it(9)+1*it(10)+0 0.04/0.22 Such that:it(9) =< 100 0.04/0.22 it(10) =< -A+E 0.04/0.22 0.04/0.22 with precondition: [B=0,D=2,F=100,C=E,A>=0,C>=A+1] 0.04/0.22 0.04/0.22 * Chain [[10],[9],11]: 1*it(9)+1*it(10)+0 0.04/0.22 Such that:it(9) =< 100 0.04/0.22 it(10) =< -A+C 0.04/0.22 0.04/0.22 with precondition: [B=0,D=3,A>=0,C>=A+1] 0.04/0.22 0.04/0.22 * Chain [[10],11]: 1*it(10)+0 0.04/0.22 Such that:it(10) =< -A+C 0.04/0.22 0.04/0.22 with precondition: [B=0,D=3,A>=0,C>=A+1] 0.04/0.22 0.04/0.22 * Chain [[9],12]: 1*it(9)+0 0.04/0.22 Such that:it(9) =< -B+100 0.04/0.22 0.04/0.22 with precondition: [D=2,F=100,A=E,99>=B,A>=0,B>=0,A>=C] 0.04/0.22 0.04/0.22 * Chain [[9],11]: 1*it(9)+0 0.04/0.22 Such that:it(9) =< -B+100 0.04/0.22 0.04/0.22 with precondition: [D=3,99>=B,A>=0,B>=0,A>=C] 0.04/0.22 0.04/0.22 * Chain [11]: 0 0.04/0.22 with precondition: [D=3,A>=0,B>=0] 0.04/0.22 0.04/0.22 0.04/0.22 #### Cost of chains of evalfbb3in_loop_cont(A,B,C,D,E): 0.04/0.22 * Chain [14]: 0 0.04/0.22 with precondition: [A=2] 0.04/0.22 0.04/0.22 * Chain [13]: 0 0.04/0.22 with precondition: [A=3] 0.04/0.22 0.04/0.22 0.04/0.22 #### Cost of chains of evalfentryin(A,B,C,D): 0.04/0.22 * Chain [17]: 0 0.04/0.22 with precondition: [] 0.04/0.22 0.04/0.22 * Chain [16]: 200 0.04/0.22 with precondition: [0>=C] 0.04/0.22 0.04/0.22 * Chain [15]: 2*s(6)+3*s(7)+0 0.04/0.22 Such that:aux(3) =< 100 0.04/0.22 aux(4) =< C 0.04/0.22 s(6) =< aux(3) 0.04/0.22 s(7) =< aux(4) 0.04/0.22 0.04/0.22 with precondition: [C>=1] 0.04/0.22 0.04/0.22 0.04/0.22 #### Cost of chains of evalfstart(A,B,C,D): 0.04/0.22 * Chain [20]: 0 0.04/0.22 with precondition: [] 0.04/0.22 0.04/0.22 * Chain [19]: 200 0.04/0.22 with precondition: [0>=C] 0.04/0.22 0.04/0.22 * Chain [18]: 2*s(13)+3*s(14)+0 0.04/0.22 Such that:s(11) =< 100 0.04/0.22 s(12) =< C 0.04/0.22 s(13) =< s(11) 0.04/0.22 s(14) =< s(12) 0.04/0.22 0.04/0.22 with precondition: [C>=1] 0.04/0.22 0.04/0.22 0.04/0.22 Closed-form bounds of evalfstart(A,B,C,D): 0.04/0.22 ------------------------------------- 0.04/0.22 * Chain [20] with precondition: [] 0.04/0.22 - Upper bound: 0 0.04/0.22 - Complexity: constant 0.04/0.22 * Chain [19] with precondition: [0>=C] 0.04/0.22 - Upper bound: 200 0.04/0.22 - Complexity: constant 0.04/0.22 * Chain [18] with precondition: [C>=1] 0.04/0.22 - Upper bound: 3*C+200 0.04/0.22 - Complexity: n 0.04/0.22 0.04/0.22 ### Maximum cost of evalfstart(A,B,C,D): max([200,nat(C)*3+200]) 0.04/0.22 Asymptotic class: n 0.04/0.22 * Total analysis performed in 158 ms. 0.04/0.22 0.04/0.32 EOF