0.03/0.18 WORST_CASE(?,O(n^1)) 0.03/0.18 0.03/0.18 Preprocessing Cost Relations 0.03/0.18 ===================================== 0.03/0.18 0.03/0.18 #### Computed strongly connected components 0.03/0.18 0. recursive : [eval_random1d_2/6,eval_random1d_3/6,eval_random1d_bb1_in/6,eval_random1d_bb2_in/6] 0.03/0.18 1. non_recursive : [eval_random1d_stop/4] 0.03/0.18 2. non_recursive : [eval_random1d_bb3_in/4] 0.03/0.18 3. non_recursive : [exit_location/1] 0.03/0.18 4. non_recursive : [eval_random1d_bb1_in_loop_cont/5] 0.03/0.18 5. non_recursive : [eval_random1d_1/4] 0.03/0.18 6. non_recursive : [eval_random1d_0/4] 0.03/0.18 7. non_recursive : [eval_random1d_bb0_in/4] 0.03/0.18 8. non_recursive : [eval_random1d_start/4] 0.03/0.18 0.03/0.18 #### Obtained direct recursion through partial evaluation 0.03/0.18 0. SCC is partially evaluated into eval_random1d_bb1_in/6 0.03/0.18 1. SCC is completely evaluated into other SCCs 0.03/0.18 2. SCC is completely evaluated into other SCCs 0.03/0.18 3. SCC is completely evaluated into other SCCs 0.03/0.18 4. SCC is partially evaluated into eval_random1d_bb1_in_loop_cont/5 0.03/0.18 5. SCC is partially evaluated into eval_random1d_1/4 0.03/0.18 6. SCC is completely evaluated into other SCCs 0.03/0.18 7. SCC is completely evaluated into other SCCs 0.03/0.18 8. SCC is partially evaluated into eval_random1d_start/4 0.03/0.18 0.03/0.18 Control-Flow Refinement of Cost Relations 0.03/0.18 ===================================== 0.03/0.18 0.03/0.18 ### Specialization of cost equations eval_random1d_bb1_in/6 0.03/0.18 * CE 7 is refined into CE [10] 0.03/0.18 * CE 6 is refined into CE [11] 0.03/0.18 * CE 5 is refined into CE [12] 0.03/0.18 * CE 4 is refined into CE [13] 0.03/0.18 0.03/0.18 0.03/0.18 ### Cost equations --> "Loop" of eval_random1d_bb1_in/6 0.03/0.18 * CEs [12] --> Loop 10 0.03/0.18 * CEs [13] --> Loop 11 0.03/0.18 * CEs [10] --> Loop 12 0.03/0.18 * CEs [11] --> Loop 13 0.03/0.18 0.03/0.18 ### Ranking functions of CR eval_random1d_bb1_in(V_2,V_max,V_x_0,B,C,D) 0.03/0.18 * RF of phase [10,11]: [V_max-V_x_0+1] 0.03/0.18 0.03/0.18 #### Partial ranking functions of CR eval_random1d_bb1_in(V_2,V_max,V_x_0,B,C,D) 0.03/0.18 * Partial RF of phase [10,11]: 0.03/0.18 - RF of loop [10:1,11:1]: 0.03/0.18 V_max-V_x_0+1 0.03/0.18 0.03/0.18 0.03/0.18 ### Specialization of cost equations eval_random1d_bb1_in_loop_cont/5 0.03/0.18 * CE 9 is refined into CE [14] 0.03/0.18 * CE 8 is refined into CE [15] 0.03/0.18 0.03/0.18 0.03/0.18 ### Cost equations --> "Loop" of eval_random1d_bb1_in_loop_cont/5 0.03/0.18 * CEs [14] --> Loop 14 0.03/0.18 * CEs [15] --> Loop 15 0.03/0.18 0.03/0.18 ### Ranking functions of CR eval_random1d_bb1_in_loop_cont(A,B,C,D,E) 0.03/0.18 0.03/0.18 #### Partial ranking functions of CR eval_random1d_bb1_in_loop_cont(A,B,C,D,E) 0.03/0.18 0.03/0.18 0.03/0.18 ### Specialization of cost equations eval_random1d_1/4 0.03/0.18 * CE 3 is refined into CE [16,17,18] 0.03/0.18 * CE 2 is refined into CE [19] 0.03/0.18 0.03/0.18 0.03/0.18 ### Cost equations --> "Loop" of eval_random1d_1/4 0.03/0.18 * CEs [16,17,18] --> Loop 16 0.03/0.18 * CEs [19] --> Loop 17 0.03/0.18 0.03/0.18 ### Ranking functions of CR eval_random1d_1(V_2,V_max,V_x_0,B) 0.03/0.18 0.03/0.18 #### Partial ranking functions of CR eval_random1d_1(V_2,V_max,V_x_0,B) 0.03/0.18 0.03/0.18 0.03/0.18 ### Specialization of cost equations eval_random1d_start/4 0.03/0.18 * CE 1 is refined into CE [20,21] 0.03/0.18 0.03/0.18 0.03/0.18 ### Cost equations --> "Loop" of eval_random1d_start/4 0.03/0.18 * CEs [21] --> Loop 18 0.03/0.18 * CEs [20] --> Loop 19 0.03/0.18 0.03/0.18 ### Ranking functions of CR eval_random1d_start(V_2,V_max,V_x_0,B) 0.03/0.18 0.03/0.18 #### Partial ranking functions of CR eval_random1d_start(V_2,V_max,V_x_0,B) 0.03/0.18 0.03/0.18 0.03/0.18 Computing Bounds 0.03/0.18 ===================================== 0.03/0.18 0.03/0.18 #### Cost of chains of eval_random1d_bb1_in(V_2,V_max,V_x_0,B,C,D): 0.03/0.18 * Chain [[10,11],13]: 2*it(10)+0 0.03/0.18 Such that:aux(3) =< V_max-V_x_0+1 0.03/0.18 it(10) =< aux(3) 0.03/0.18 0.03/0.18 with precondition: [B=2,V_max+1=D,V_x_0>=1,V_max>=V_x_0] 0.03/0.18 0.03/0.18 * Chain [[10,11],12]: 2*it(10)+0 0.03/0.18 Such that:aux(4) =< V_max-V_x_0+1 0.03/0.18 it(10) =< aux(4) 0.03/0.18 0.03/0.18 with precondition: [B=3,V_x_0>=1,V_max>=V_x_0] 0.03/0.18 0.03/0.18 * Chain [12]: 0 0.03/0.18 with precondition: [B=3,V_max>=1,V_x_0>=1] 0.03/0.18 0.03/0.18 0.03/0.18 #### Cost of chains of eval_random1d_bb1_in_loop_cont(A,B,C,D,E): 0.03/0.18 * Chain [15]: 0 0.03/0.18 with precondition: [A=2,C>=1] 0.03/0.18 0.03/0.18 * Chain [14]: 0 0.03/0.18 with precondition: [A=3,C>=1] 0.03/0.18 0.03/0.18 0.03/0.18 #### Cost of chains of eval_random1d_1(V_2,V_max,V_x_0,B): 0.03/0.18 * Chain [17]: 0 0.03/0.18 with precondition: [0>=V_max] 0.03/0.18 0.03/0.18 * Chain [16]: 4*s(2)+0 0.03/0.18 Such that:aux(5) =< V_max 0.03/0.18 s(2) =< aux(5) 0.03/0.18 0.03/0.18 with precondition: [V_max>=1] 0.03/0.18 0.03/0.18 0.03/0.18 #### Cost of chains of eval_random1d_start(V_2,V_max,V_x_0,B): 0.03/0.18 * Chain [19]: 0 0.03/0.18 with precondition: [0>=V_max] 0.03/0.18 0.03/0.18 * Chain [18]: 4*s(6)+0 0.03/0.18 Such that:s(5) =< V_max 0.03/0.18 s(6) =< s(5) 0.03/0.18 0.03/0.18 with precondition: [V_max>=1] 0.03/0.18 0.03/0.18 0.03/0.18 Closed-form bounds of eval_random1d_start(V_2,V_max,V_x_0,B): 0.03/0.18 ------------------------------------- 0.03/0.18 * Chain [19] with precondition: [0>=V_max] 0.03/0.18 - Upper bound: 0 0.03/0.18 - Complexity: constant 0.03/0.18 * Chain [18] with precondition: [V_max>=1] 0.03/0.18 - Upper bound: 4*V_max 0.03/0.18 - Complexity: n 0.03/0.18 0.03/0.18 ### Maximum cost of eval_random1d_start(V_2,V_max,V_x_0,B): nat(V_max)*4 0.03/0.18 Asymptotic class: n 0.03/0.18 * Total analysis performed in 120 ms. 0.03/0.18 0.03/0.28 EOF