0.05/0.45 WORST_CASE(?,O(n^1)) 0.05/0.45 0.05/0.45 Preprocessing Cost Relations 0.05/0.45 ===================================== 0.05/0.45 0.05/0.45 #### Computed strongly connected components 0.05/0.45 0. recursive : [eval_random2d_12/8,eval_random2d_13/8,eval_random2d_LeafBlock1_in/8,eval_random2d_LeafBlock3_in/8,eval_random2d_LeafBlock5_in/8,eval_random2d_LeafBlock_in/8,eval_random2d_NewDefault_in/8,eval_random2d_NodeBlock7_in/8,eval_random2d_NodeBlock9_in/8,eval_random2d_NodeBlock_in/8,eval_random2d_bb1_in/8,eval_random2d_bb2_in/8,eval_random2d_bb3_in/8,eval_random2d_bb4_in/8,eval_random2d_bb5_in/8,eval_random2d_bb6_in/8,eval_random2d_bb7_in/8] 0.05/0.45 1. non_recursive : [eval_random2d_stop/5] 0.05/0.45 2. non_recursive : [eval_random2d_bb8_in/5] 0.05/0.45 3. non_recursive : [exit_location/1] 0.05/0.45 4. non_recursive : [eval_random2d_bb1_in_loop_cont/6] 0.05/0.45 5. non_recursive : [eval_random2d_10/5] 0.05/0.45 6. non_recursive : [eval_random2d_9/5] 0.05/0.45 7. non_recursive : [eval_random2d_8/5] 0.05/0.45 8. non_recursive : [eval_random2d_7/5] 0.05/0.45 9. non_recursive : [eval_random2d_6/5] 0.05/0.45 10. non_recursive : [eval_random2d_5/5] 0.05/0.45 11. non_recursive : [eval_random2d_4/5] 0.05/0.45 12. non_recursive : [eval_random2d_3/5] 0.05/0.45 13. non_recursive : [eval_random2d_2/5] 0.05/0.45 14. non_recursive : [eval_random2d_1/5] 0.05/0.45 15. non_recursive : [eval_random2d_0/5] 0.05/0.45 16. non_recursive : [eval_random2d_bb0_in/5] 0.05/0.45 17. non_recursive : [eval_random2d_start/5] 0.05/0.45 0.05/0.45 #### Obtained direct recursion through partial evaluation 0.05/0.45 0. SCC is partially evaluated into eval_random2d_bb1_in/8 0.05/0.45 1. SCC is completely evaluated into other SCCs 0.05/0.45 2. SCC is completely evaluated into other SCCs 0.05/0.45 3. SCC is completely evaluated into other SCCs 0.05/0.45 4. SCC is partially evaluated into eval_random2d_bb1_in_loop_cont/6 0.05/0.45 5. SCC is partially evaluated into eval_random2d_10/5 0.05/0.45 6. SCC is completely evaluated into other SCCs 0.05/0.45 7. SCC is completely evaluated into other SCCs 0.05/0.45 8. SCC is completely evaluated into other SCCs 0.05/0.45 9. SCC is completely evaluated into other SCCs 0.05/0.45 10. SCC is completely evaluated into other SCCs 0.05/0.45 11. SCC is completely evaluated into other SCCs 0.05/0.45 12. SCC is completely evaluated into other SCCs 0.05/0.45 13. SCC is completely evaluated into other SCCs 0.05/0.45 14. SCC is completely evaluated into other SCCs 0.05/0.45 15. SCC is completely evaluated into other SCCs 0.05/0.45 16. SCC is completely evaluated into other SCCs 0.05/0.45 17. SCC is partially evaluated into eval_random2d_start/5 0.05/0.45 0.05/0.45 Control-Flow Refinement of Cost Relations 0.05/0.45 ===================================== 0.05/0.45 0.05/0.45 ### Specialization of cost equations eval_random2d_bb1_in/8 0.05/0.45 * CE 10 is refined into CE [13] 0.05/0.45 * CE 9 is refined into CE [14] 0.05/0.45 * CE 7 is refined into CE [15] 0.05/0.45 * CE 8 is refined into CE [16] 0.05/0.45 * CE 5 is refined into CE [17] 0.05/0.45 * CE 4 is refined into CE [18] 0.05/0.45 * CE 3 is refined into CE [19] 0.05/0.45 * CE 6 is refined into CE [20] 0.05/0.45 0.05/0.45 0.05/0.45 ### Cost equations --> "Loop" of eval_random2d_bb1_in/8 0.05/0.45 * CEs [15] --> Loop 13 0.05/0.45 * CEs [16] --> Loop 14 0.05/0.45 * CEs [17] --> Loop 15 0.05/0.45 * CEs [18] --> Loop 16 0.05/0.45 * CEs [19] --> Loop 17 0.05/0.45 * CEs [20] --> Loop 18 0.05/0.45 * CEs [13] --> Loop 19 0.05/0.45 * CEs [14] --> Loop 20 0.05/0.45 0.05/0.45 ### Ranking functions of CR eval_random2d_bb1_in(V_1,V_2,V_N,V_i_0,B,C,D,E) 0.05/0.45 * RF of phase [13,14,15,16,17,18]: [V_N-V_i_0] 0.05/0.45 0.05/0.45 #### Partial ranking functions of CR eval_random2d_bb1_in(V_1,V_2,V_N,V_i_0,B,C,D,E) 0.05/0.45 * Partial RF of phase [13,14,15,16,17,18]: 0.05/0.45 - RF of loop [13:1,14:1,15:1,16:1,17:1,18:1]: 0.05/0.45 V_N-V_i_0 0.05/0.45 0.05/0.45 0.05/0.45 ### Specialization of cost equations eval_random2d_bb1_in_loop_cont/6 0.05/0.45 * CE 12 is refined into CE [21] 0.05/0.45 * CE 11 is refined into CE [22] 0.05/0.45 0.05/0.45 0.05/0.45 ### Cost equations --> "Loop" of eval_random2d_bb1_in_loop_cont/6 0.05/0.45 * CEs [21] --> Loop 21 0.05/0.45 * CEs [22] --> Loop 22 0.05/0.45 0.05/0.45 ### Ranking functions of CR eval_random2d_bb1_in_loop_cont(A,B,C,D,E,F) 0.05/0.45 0.05/0.45 #### Partial ranking functions of CR eval_random2d_bb1_in_loop_cont(A,B,C,D,E,F) 0.05/0.45 0.05/0.45 0.05/0.45 ### Specialization of cost equations eval_random2d_10/5 0.05/0.45 * CE 2 is refined into CE [23,24,25,26] 0.05/0.45 0.05/0.45 0.05/0.45 ### Cost equations --> "Loop" of eval_random2d_10/5 0.05/0.45 * CEs [24,26] --> Loop 23 0.05/0.45 * CEs [23] --> Loop 24 0.05/0.45 * CEs [25] --> Loop 25 0.05/0.45 0.05/0.45 ### Ranking functions of CR eval_random2d_10(V_1,V_2,V_N,V_i_0,B) 0.05/0.45 0.05/0.45 #### Partial ranking functions of CR eval_random2d_10(V_1,V_2,V_N,V_i_0,B) 0.05/0.45 0.05/0.45 0.05/0.45 ### Specialization of cost equations eval_random2d_start/5 0.05/0.45 * CE 1 is refined into CE [27,28,29] 0.05/0.45 0.05/0.45 0.05/0.45 ### Cost equations --> "Loop" of eval_random2d_start/5 0.05/0.45 * CEs [29] --> Loop 26 0.05/0.45 * CEs [28] --> Loop 27 0.05/0.45 * CEs [27] --> Loop 28 0.05/0.45 0.05/0.45 ### Ranking functions of CR eval_random2d_start(V_1,V_2,V_N,V_i_0,B) 0.05/0.45 0.05/0.45 #### Partial ranking functions of CR eval_random2d_start(V_1,V_2,V_N,V_i_0,B) 0.05/0.45 0.05/0.45 0.05/0.45 Computing Bounds 0.05/0.45 ===================================== 0.05/0.45 0.05/0.45 #### Cost of chains of eval_random2d_bb1_in(V_1,V_2,V_N,V_i_0,B,C,D,E): 0.05/0.45 * Chain [[13,14,15,16,17,18],20]: 6*it(13)+0 0.05/0.45 Such that:aux(3) =< V_N-V_i_0 0.05/0.45 it(13) =< aux(3) 0.05/0.45 0.05/0.45 with precondition: [B=2,V_N=C,V_N=E,V_i_0>=0,V_N>=V_i_0+1] 0.05/0.45 0.05/0.45 * Chain [[13,14,15,16,17,18],19]: 6*it(13)+0 0.05/0.45 Such that:aux(4) =< V_N-V_i_0 0.05/0.45 it(13) =< aux(4) 0.05/0.45 0.05/0.45 with precondition: [B=3,V_i_0>=0,V_N>=V_i_0+1] 0.05/0.45 0.05/0.45 * Chain [20]: 0 0.05/0.45 with precondition: [B=2,C=V_1,D=V_2,V_i_0=E,V_i_0>=0,V_i_0>=V_N] 0.05/0.45 0.05/0.45 * Chain [19]: 0 0.05/0.45 with precondition: [B=3,V_i_0>=0] 0.05/0.45 0.05/0.45 0.05/0.45 #### Cost of chains of eval_random2d_bb1_in_loop_cont(A,B,C,D,E,F): 0.05/0.45 * Chain [22]: 0 0.05/0.45 with precondition: [A=2] 0.05/0.45 0.05/0.45 * Chain [21]: 0 0.05/0.45 with precondition: [A=3] 0.05/0.45 0.05/0.45 0.05/0.45 #### Cost of chains of eval_random2d_10(V_1,V_2,V_N,V_i_0,B): 0.05/0.45 * Chain [25]: 0 0.05/0.45 with precondition: [] 0.05/0.45 0.05/0.45 * Chain [24]: 0 0.05/0.45 with precondition: [0>=V_N] 0.05/0.45 0.05/0.45 * Chain [23]: 12*s(2)+0 0.05/0.45 Such that:aux(5) =< V_N 0.05/0.45 s(2) =< aux(5) 0.05/0.45 0.05/0.45 with precondition: [V_N>=1] 0.05/0.45 0.05/0.45 0.05/0.45 #### Cost of chains of eval_random2d_start(V_1,V_2,V_N,V_i_0,B): 0.05/0.45 * Chain [28]: 0 0.05/0.45 with precondition: [] 0.05/0.45 0.05/0.45 * Chain [27]: 0 0.05/0.45 with precondition: [0>=V_N] 0.05/0.45 0.05/0.45 * Chain [26]: 12*s(6)+0 0.05/0.45 Such that:s(5) =< V_N 0.05/0.45 s(6) =< s(5) 0.05/0.45 0.05/0.45 with precondition: [V_N>=1] 0.05/0.45 0.05/0.45 0.05/0.45 Closed-form bounds of eval_random2d_start(V_1,V_2,V_N,V_i_0,B): 0.05/0.45 ------------------------------------- 0.05/0.45 * Chain [28] with precondition: [] 0.05/0.45 - Upper bound: 0 0.05/0.45 - Complexity: constant 0.05/0.45 * Chain [27] with precondition: [0>=V_N] 0.05/0.45 - Upper bound: 0 0.05/0.45 - Complexity: constant 0.05/0.45 * Chain [26] with precondition: [V_N>=1] 0.05/0.45 - Upper bound: 12*V_N 0.05/0.45 - Complexity: n 0.05/0.45 0.05/0.45 ### Maximum cost of eval_random2d_start(V_1,V_2,V_N,V_i_0,B): nat(V_N)*12 0.05/0.45 Asymptotic class: n 0.05/0.45 * Total analysis performed in 359 ms. 0.05/0.45 0.46/0.56 EOF