0.05/0.16 WORST_CASE(?,O(n^2)) 0.05/0.16 0.05/0.16 Preprocessing Cost Relations 0.05/0.16 ===================================== 0.05/0.16 0.05/0.16 #### Computed strongly connected components 0.05/0.16 0. recursive : [eval_cousot9_bb1_in/4,eval_cousot9_bb2_in/4] 0.05/0.16 1. non_recursive : [eval_cousot9_stop/1] 0.05/0.16 2. non_recursive : [eval_cousot9_bb3_in/1] 0.05/0.16 3. non_recursive : [eval_cousot9_bb1_in_loop_cont/2] 0.05/0.16 4. non_recursive : [eval_cousot9_bb0_in/3] 0.05/0.16 5. non_recursive : [eval_cousot9_start/3] 0.05/0.16 0.05/0.16 #### Obtained direct recursion through partial evaluation 0.05/0.16 0. SCC is partially evaluated into eval_cousot9_bb1_in/4 0.05/0.16 1. SCC is completely evaluated into other SCCs 0.05/0.16 2. SCC is completely evaluated into other SCCs 0.05/0.16 3. SCC is completely evaluated into other SCCs 0.05/0.16 4. SCC is partially evaluated into eval_cousot9_bb0_in/3 0.05/0.16 5. SCC is partially evaluated into eval_cousot9_start/3 0.05/0.16 0.05/0.16 Control-Flow Refinement of Cost Relations 0.05/0.16 ===================================== 0.05/0.16 0.05/0.16 ### Specialization of cost equations eval_cousot9_bb1_in/4 0.05/0.16 * CE 5 is refined into CE [6] 0.05/0.16 * CE 3 is refined into CE [7] 0.05/0.16 * CE 4 is refined into CE [8] 0.05/0.16 0.05/0.16 0.05/0.16 ### Cost equations --> "Loop" of eval_cousot9_bb1_in/4 0.05/0.16 * CEs [7] --> Loop 6 0.05/0.16 * CEs [8] --> Loop 7 0.05/0.16 * CEs [6] --> Loop 8 0.05/0.16 0.05/0.16 ### Ranking functions of CR eval_cousot9_bb1_in(V_N,V_i_0,V__0,B) 0.05/0.16 0.05/0.16 #### Partial ranking functions of CR eval_cousot9_bb1_in(V_N,V_i_0,V__0,B) 0.05/0.16 * Partial RF of phase [6,7]: 0.05/0.16 - RF of loop [6:1]: 0.05/0.16 -V__0+1 depends on loops [7:1] 0.05/0.16 V_i_0 0.05/0.16 - RF of loop [7:1]: 0.05/0.16 V__0 depends on loops [6:1] 0.05/0.16 0.05/0.16 0.05/0.16 ### Specialization of cost equations eval_cousot9_bb0_in/3 0.05/0.16 * CE 2 is refined into CE [9,10] 0.05/0.16 0.05/0.16 0.05/0.17 ### Cost equations --> "Loop" of eval_cousot9_bb0_in/3 0.05/0.17 * CEs [10] --> Loop 9 0.05/0.17 * CEs [9] --> Loop 10 0.05/0.17 0.05/0.17 ### Ranking functions of CR eval_cousot9_bb0_in(V_j,V_N,B) 0.05/0.17 0.05/0.17 #### Partial ranking functions of CR eval_cousot9_bb0_in(V_j,V_N,B) 0.05/0.17 0.05/0.17 0.05/0.17 ### Specialization of cost equations eval_cousot9_start/3 0.05/0.17 * CE 1 is refined into CE [11,12] 0.05/0.17 0.05/0.17 0.05/0.17 ### Cost equations --> "Loop" of eval_cousot9_start/3 0.05/0.17 * CEs [12] --> Loop 11 0.05/0.17 * CEs [11] --> Loop 12 0.05/0.17 0.05/0.17 ### Ranking functions of CR eval_cousot9_start(V_j,V_N,B) 0.05/0.17 0.05/0.17 #### Partial ranking functions of CR eval_cousot9_start(V_j,V_N,B) 0.05/0.17 0.05/0.17 0.05/0.17 Computing Bounds 0.05/0.17 ===================================== 0.05/0.17 0.05/0.17 #### Cost of chains of eval_cousot9_bb1_in(V_N,V_i_0,V__0,B): 0.05/0.17 * Chain [[6,7],8]: 1*it(6)+1*it(7)+0 0.05/0.17 Such that:aux(7) =< V_N 0.05/0.17 it(6) =< V_i_0 0.05/0.17 aux(4) =< V__0 0.05/0.17 aux(3) =< it(6)*aux(7) 0.05/0.17 it(7) =< aux(3)+aux(4) 0.05/0.17 0.05/0.17 with precondition: [B=2,V_i_0>=1,V_N>=V_i_0] 0.05/0.17 0.05/0.17 * Chain [8]: 0 0.05/0.17 with precondition: [B=2,0>=V_i_0,V_N>=V_i_0] 0.05/0.17 0.05/0.17 0.05/0.17 #### Cost of chains of eval_cousot9_bb0_in(V_j,V_N,B): 0.05/0.17 * Chain [10]: 0 0.05/0.17 with precondition: [0>=V_N] 0.05/0.17 0.05/0.17 * Chain [9]: 1*s(2)+1*s(5)+0 0.05/0.17 Such that:s(3) =< V_j 0.05/0.17 aux(8) =< V_N 0.05/0.17 s(2) =< aux(8) 0.05/0.17 s(4) =< s(2)*aux(8) 0.05/0.17 s(5) =< s(4)+s(3) 0.05/0.17 0.05/0.17 with precondition: [V_N>=1] 0.05/0.17 0.05/0.17 0.05/0.17 #### Cost of chains of eval_cousot9_start(V_j,V_N,B): 0.05/0.17 * Chain [12]: 0 0.05/0.17 with precondition: [0>=V_N] 0.05/0.17 0.05/0.17 * Chain [11]: 1*s(8)+1*s(10)+0 0.05/0.17 Such that:s(6) =< V_j 0.05/0.17 s(7) =< V_N 0.05/0.17 s(8) =< s(7) 0.05/0.17 s(9) =< s(8)*s(7) 0.05/0.17 s(10) =< s(9)+s(6) 0.05/0.17 0.05/0.17 with precondition: [V_N>=1] 0.05/0.17 0.05/0.17 0.05/0.17 Closed-form bounds of eval_cousot9_start(V_j,V_N,B): 0.05/0.17 ------------------------------------- 0.05/0.17 * Chain [12] with precondition: [0>=V_N] 0.05/0.17 - Upper bound: 0 0.05/0.17 - Complexity: constant 0.05/0.17 * Chain [11] with precondition: [V_N>=1] 0.05/0.17 - Upper bound: nat(V_j)+V_N+V_N*V_N 0.05/0.17 - Complexity: n^2 0.05/0.17 0.05/0.17 ### Maximum cost of eval_cousot9_start(V_j,V_N,B): nat(V_N)+nat(V_j)+nat(V_N)*nat(V_N) 0.05/0.17 Asymptotic class: n^2 0.05/0.17 * Total analysis performed in 90 ms. 0.05/0.17 0.05/0.27 EOF