0.04/0.23 WORST_CASE(?,O(n^2)) 0.04/0.23 0.04/0.23 Preprocessing Cost Relations 0.04/0.23 ===================================== 0.04/0.23 0.04/0.23 #### Computed strongly connected components 0.04/0.23 0. recursive : [eval_cousot9_bb1_in/6,eval_cousot9_bb2_in/6] 0.04/0.23 1. non_recursive : [eval_cousot9_stop/5] 0.04/0.23 2. non_recursive : [eval_cousot9_bb3_in/5] 0.04/0.23 3. non_recursive : [exit_location/1] 0.04/0.23 4. non_recursive : [eval_cousot9_bb1_in_loop_cont/6] 0.04/0.23 5. non_recursive : [eval_cousot9_6/5] 0.04/0.23 6. non_recursive : [eval_cousot9_5/5] 0.04/0.23 7. non_recursive : [eval_cousot9_4/5] 0.04/0.23 8. non_recursive : [eval_cousot9_3/5] 0.04/0.23 9. non_recursive : [eval_cousot9_2/5] 0.04/0.23 10. non_recursive : [eval_cousot9_1/5] 0.04/0.23 11. non_recursive : [eval_cousot9_0/5] 0.04/0.23 12. non_recursive : [eval_cousot9_bb0_in/5] 0.04/0.23 13. non_recursive : [eval_cousot9_start/5] 0.04/0.23 0.04/0.23 #### Obtained direct recursion through partial evaluation 0.04/0.23 0. SCC is partially evaluated into eval_cousot9_bb1_in/6 0.04/0.23 1. SCC is completely evaluated into other SCCs 0.04/0.23 2. SCC is completely evaluated into other SCCs 0.04/0.23 3. SCC is completely evaluated into other SCCs 0.04/0.23 4. SCC is partially evaluated into eval_cousot9_bb1_in_loop_cont/6 0.04/0.23 5. SCC is partially evaluated into eval_cousot9_6/5 0.04/0.23 6. SCC is completely evaluated into other SCCs 0.04/0.23 7. SCC is completely evaluated into other SCCs 0.04/0.23 8. SCC is completely evaluated into other SCCs 0.04/0.23 9. SCC is completely evaluated into other SCCs 0.04/0.23 10. SCC is completely evaluated into other SCCs 0.04/0.23 11. SCC is completely evaluated into other SCCs 0.04/0.23 12. SCC is completely evaluated into other SCCs 0.04/0.23 13. SCC is partially evaluated into eval_cousot9_start/5 0.04/0.23 0.04/0.23 Control-Flow Refinement of Cost Relations 0.04/0.23 ===================================== 0.04/0.23 0.04/0.23 ### Specialization of cost equations eval_cousot9_bb1_in/6 0.04/0.23 * CE 6 is refined into CE [9] 0.04/0.23 * CE 5 is refined into CE [10] 0.04/0.23 * CE 3 is refined into CE [11] 0.04/0.23 * CE 4 is refined into CE [12] 0.04/0.23 0.04/0.23 0.04/0.23 ### Cost equations --> "Loop" of eval_cousot9_bb1_in/6 0.04/0.23 * CEs [11] --> Loop 9 0.04/0.23 * CEs [12] --> Loop 10 0.04/0.23 * CEs [9] --> Loop 11 0.04/0.23 * CEs [10] --> Loop 12 0.04/0.23 0.04/0.23 ### Ranking functions of CR eval_cousot9_bb1_in(V__0,V_N,V_i_0,B,C,D) 0.04/0.23 0.04/0.23 #### Partial ranking functions of CR eval_cousot9_bb1_in(V__0,V_N,V_i_0,B,C,D) 0.04/0.23 * Partial RF of phase [9,10]: 0.04/0.23 - RF of loop [9:1]: 0.04/0.23 -V__0+1 depends on loops [10:1] 0.04/0.23 V_i_0 0.04/0.23 - RF of loop [10:1]: 0.04/0.23 V__0 depends on loops [9:1] 0.04/0.23 0.04/0.23 0.04/0.23 ### Specialization of cost equations eval_cousot9_bb1_in_loop_cont/6 0.04/0.23 * CE 8 is refined into CE [13] 0.04/0.23 * CE 7 is refined into CE [14] 0.04/0.23 0.04/0.23 0.04/0.23 ### Cost equations --> "Loop" of eval_cousot9_bb1_in_loop_cont/6 0.04/0.23 * CEs [13] --> Loop 13 0.04/0.23 * CEs [14] --> Loop 14 0.04/0.23 0.04/0.23 ### Ranking functions of CR eval_cousot9_bb1_in_loop_cont(A,B,C,D,E,F) 0.04/0.23 0.04/0.23 #### Partial ranking functions of CR eval_cousot9_bb1_in_loop_cont(A,B,C,D,E,F) 0.04/0.23 0.04/0.23 0.04/0.23 ### Specialization of cost equations eval_cousot9_6/5 0.04/0.23 * CE 2 is refined into CE [15,16,17,18] 0.04/0.23 0.04/0.23 0.04/0.23 ### Cost equations --> "Loop" of eval_cousot9_6/5 0.04/0.23 * CEs [15,17] --> Loop 15 0.04/0.23 * CEs [16] --> Loop 16 0.04/0.23 * CEs [18] --> Loop 17 0.04/0.23 0.04/0.23 ### Ranking functions of CR eval_cousot9_6(V__0,V_N,V_i_0,V_j,B) 0.04/0.23 0.04/0.23 #### Partial ranking functions of CR eval_cousot9_6(V__0,V_N,V_i_0,V_j,B) 0.04/0.23 0.04/0.23 0.04/0.23 ### Specialization of cost equations eval_cousot9_start/5 0.04/0.23 * CE 1 is refined into CE [19,20,21] 0.04/0.23 0.04/0.23 0.04/0.23 ### Cost equations --> "Loop" of eval_cousot9_start/5 0.04/0.23 * CEs [21] --> Loop 18 0.04/0.23 * CEs [20] --> Loop 19 0.04/0.23 * CEs [19] --> Loop 20 0.04/0.23 0.04/0.23 ### Ranking functions of CR eval_cousot9_start(V__0,V_N,V_i_0,V_j,B) 0.04/0.23 0.04/0.23 #### Partial ranking functions of CR eval_cousot9_start(V__0,V_N,V_i_0,V_j,B) 0.04/0.23 0.04/0.23 0.04/0.23 Computing Bounds 0.04/0.23 ===================================== 0.04/0.23 0.04/0.23 #### Cost of chains of eval_cousot9_bb1_in(V__0,V_N,V_i_0,B,C,D): 0.04/0.23 * Chain [[9,10],12]: 1*it(9)+1*it(10)+0 0.04/0.23 Such that:aux(4) =< V__0 0.04/0.23 aux(7) =< V_N 0.04/0.23 it(9) =< V_i_0 0.04/0.23 aux(3) =< it(9)*aux(7) 0.04/0.23 it(10) =< aux(3)+aux(4) 0.04/0.23 0.04/0.23 with precondition: [B=2,D=0,V_N=C,V_i_0>=1,V_N>=V_i_0] 0.04/0.23 0.04/0.23 * Chain [[9,10],11]: 1*it(9)+1*it(10)+0 0.04/0.23 Such that:aux(4) =< V__0 0.04/0.23 aux(7) =< V_N 0.04/0.23 it(9) =< V_i_0 0.04/0.23 aux(3) =< it(9)*aux(7) 0.04/0.23 it(10) =< aux(3)+aux(4) 0.04/0.23 0.04/0.23 with precondition: [B=3,V_i_0>=1,V_N>=V_i_0] 0.04/0.23 0.04/0.23 * Chain [12]: 0 0.04/0.23 with precondition: [B=2,C=V__0,V_i_0=D,0>=V_i_0,V_N>=V_i_0] 0.04/0.23 0.04/0.23 * Chain [11]: 0 0.04/0.23 with precondition: [B=3,V_N>=V_i_0] 0.04/0.23 0.04/0.23 0.04/0.23 #### Cost of chains of eval_cousot9_bb1_in_loop_cont(A,B,C,D,E,F): 0.04/0.23 * Chain [14]: 0 0.04/0.23 with precondition: [A=2] 0.04/0.23 0.04/0.23 * Chain [13]: 0 0.04/0.23 with precondition: [A=3] 0.04/0.23 0.04/0.23 0.04/0.23 #### Cost of chains of eval_cousot9_6(V__0,V_N,V_i_0,V_j,B): 0.04/0.23 * Chain [17]: 0 0.04/0.23 with precondition: [] 0.04/0.23 0.04/0.23 * Chain [16]: 0 0.04/0.23 with precondition: [0>=V_N] 0.04/0.23 0.04/0.23 * Chain [15]: 2*s(3)+2*s(5)+0 0.04/0.23 Such that:aux(10) =< V_N 0.04/0.23 aux(11) =< V_j 0.04/0.23 s(3) =< aux(10) 0.04/0.23 s(4) =< s(3)*aux(10) 0.04/0.23 s(5) =< s(4)+aux(11) 0.04/0.23 0.04/0.23 with precondition: [V_N>=1] 0.04/0.23 0.04/0.23 0.04/0.23 #### Cost of chains of eval_cousot9_start(V__0,V_N,V_i_0,V_j,B): 0.04/0.23 * Chain [20]: 0 0.04/0.23 with precondition: [] 0.04/0.23 0.04/0.23 * Chain [19]: 0 0.04/0.23 with precondition: [0>=V_N] 0.04/0.23 0.04/0.23 * Chain [18]: 2*s(13)+2*s(15)+0 0.04/0.23 Such that:s(11) =< V_N 0.04/0.23 s(12) =< V_j 0.04/0.23 s(13) =< s(11) 0.04/0.23 s(14) =< s(13)*s(11) 0.04/0.23 s(15) =< s(14)+s(12) 0.04/0.23 0.04/0.23 with precondition: [V_N>=1] 0.04/0.23 0.04/0.23 0.04/0.23 Closed-form bounds of eval_cousot9_start(V__0,V_N,V_i_0,V_j,B): 0.04/0.23 ------------------------------------- 0.04/0.23 * Chain [20] with precondition: [] 0.04/0.23 - Upper bound: 0 0.04/0.23 - Complexity: constant 0.04/0.23 * Chain [19] with precondition: [0>=V_N] 0.04/0.23 - Upper bound: 0 0.04/0.23 - Complexity: constant 0.04/0.23 * Chain [18] with precondition: [V_N>=1] 0.04/0.23 - Upper bound: 2*V_N*V_N+2*V_N+nat(V_j)*2 0.04/0.23 - Complexity: n^2 0.04/0.23 0.04/0.23 ### Maximum cost of eval_cousot9_start(V__0,V_N,V_i_0,V_j,B): nat(V_N)*2*nat(V_N)+nat(V_N)*2+nat(V_j)*2 0.04/0.23 Asymptotic class: n^2 0.04/0.23 * Total analysis performed in 160 ms. 0.04/0.23 0.04/0.33 EOF