0.05/0.29 WORST_CASE(?,O(n^1)) 0.05/0.29 0.05/0.29 Preprocessing Cost Relations 0.05/0.29 ===================================== 0.05/0.29 0.05/0.29 #### Computed strongly connected components 0.05/0.29 0. recursive : [eval_wcet1_0/4,eval_wcet1_1/5,eval_wcet1_bb1_in/4,eval_wcet1_bb2_in/5,eval_wcet1_bb3_in/5,eval_wcet1_bb4_in/6] 0.05/0.29 1. non_recursive : [eval_wcet1_stop/1] 0.05/0.29 2. non_recursive : [eval_wcet1_bb5_in/1] 0.05/0.29 3. non_recursive : [eval_wcet1_bb1_in_loop_cont/2] 0.05/0.29 4. non_recursive : [eval_wcet1_bb0_in/2] 0.05/0.29 5. non_recursive : [eval_wcet1_start/2] 0.05/0.29 0.05/0.29 #### Obtained direct recursion through partial evaluation 0.05/0.29 0. SCC is partially evaluated into eval_wcet1_bb1_in/4 0.05/0.29 1. SCC is completely evaluated into other SCCs 0.05/0.29 2. SCC is completely evaluated into other SCCs 0.05/0.29 3. SCC is completely evaluated into other SCCs 0.05/0.29 4. SCC is partially evaluated into eval_wcet1_bb0_in/2 0.05/0.29 5. SCC is partially evaluated into eval_wcet1_start/2 0.05/0.29 0.05/0.29 Control-Flow Refinement of Cost Relations 0.05/0.29 ===================================== 0.05/0.29 0.05/0.29 ### Specialization of cost equations eval_wcet1_bb1_in/4 0.05/0.29 * CE 7 is refined into CE [12] 0.05/0.29 * CE 6 is refined into CE [13] 0.05/0.29 * CE 11 is refined into CE [14] 0.05/0.29 * CE 10 is refined into CE [15] 0.05/0.29 * CE 9 is refined into CE [16] 0.05/0.29 * CE 5 is refined into CE [17] 0.05/0.29 * CE 4 is discarded (unfeasible) 0.05/0.29 * CE 8 is refined into CE [18] 0.05/0.29 0.05/0.29 0.05/0.29 ### Cost equations --> "Loop" of eval_wcet1_bb1_in/4 0.05/0.29 * CEs [16] --> Loop 12 0.05/0.29 * CEs [17] --> Loop 13 0.05/0.29 * CEs [18] --> Loop 14 0.05/0.29 * CEs [14] --> Loop 15 0.05/0.29 * CEs [12] --> Loop 16 0.05/0.29 * CEs [15] --> Loop 17 0.05/0.29 * CEs [13] --> Loop 18 0.05/0.29 0.05/0.29 ### Ranking functions of CR eval_wcet1_bb1_in(V_n,V_j_0,V_i_0,B) 0.05/0.29 * RF of phase [12,13,14]: [V_i_0-1] 0.05/0.29 0.05/0.29 #### Partial ranking functions of CR eval_wcet1_bb1_in(V_n,V_j_0,V_i_0,B) 0.05/0.29 * Partial RF of phase [12,13,14]: 0.05/0.29 - RF of loop [12:1]: 0.05/0.29 V_j_0-1 depends on loops [13:1] 0.05/0.29 - RF of loop [12:1,13:1,14:1]: 0.05/0.29 V_i_0-1 0.05/0.29 - RF of loop [13:1]: 0.05/0.29 V_n-V_j_0-1 depends on loops [12:1,14:1] 0.05/0.29 0.05/0.29 0.05/0.29 ### Specialization of cost equations eval_wcet1_bb0_in/2 0.05/0.29 * CE 3 is refined into CE [19,20,21,22,23,24] 0.05/0.29 * CE 2 is refined into CE [25] 0.05/0.29 0.05/0.29 0.05/0.29 ### Cost equations --> "Loop" of eval_wcet1_bb0_in/2 0.05/0.29 * CEs [23] --> Loop 19 0.05/0.29 * CEs [21,22,24] --> Loop 20 0.05/0.29 * CEs [25] --> Loop 21 0.05/0.29 * CEs [19,20] --> Loop 22 0.05/0.29 0.05/0.29 ### Ranking functions of CR eval_wcet1_bb0_in(V_n,B) 0.05/0.29 0.05/0.29 #### Partial ranking functions of CR eval_wcet1_bb0_in(V_n,B) 0.05/0.29 0.05/0.29 0.05/0.29 ### Specialization of cost equations eval_wcet1_start/2 0.05/0.29 * CE 1 is refined into CE [26,27,28,29] 0.05/0.29 0.05/0.29 0.05/0.29 ### Cost equations --> "Loop" of eval_wcet1_start/2 0.05/0.29 * CEs [29] --> Loop 23 0.05/0.29 * CEs [28] --> Loop 24 0.05/0.29 * CEs [27] --> Loop 25 0.05/0.29 * CEs [26] --> Loop 26 0.05/0.29 0.05/0.29 ### Ranking functions of CR eval_wcet1_start(V_n,B) 0.05/0.29 0.05/0.29 #### Partial ranking functions of CR eval_wcet1_start(V_n,B) 0.05/0.29 0.05/0.29 0.05/0.29 Computing Bounds 0.05/0.29 ===================================== 0.05/0.29 0.05/0.29 #### Cost of chains of eval_wcet1_bb1_in(V_n,V_j_0,V_i_0,B): 0.05/0.29 * Chain [[12,13,14],18]: 3*it(12)+0 0.05/0.29 Such that:aux(7) =< V_i_0 0.05/0.29 it(12) =< aux(7) 0.05/0.29 0.05/0.29 with precondition: [B=2,V_i_0+V_j_0=V_n,V_j_0>=0,V_n>=V_j_0+2] 0.05/0.29 0.05/0.29 * Chain [[12,13,14],17]: 3*it(12)+0 0.05/0.29 Such that:aux(8) =< V_i_0 0.05/0.29 it(12) =< aux(8) 0.05/0.29 0.05/0.29 with precondition: [B=2,V_j_0>=0,V_i_0>=2,V_i_0>=V_j_0,V_n>=V_i_0+V_j_0] 0.05/0.29 0.05/0.29 * Chain [[12,13,14],16]: 3*it(12)+0 0.05/0.29 Such that:aux(9) =< V_i_0 0.05/0.29 it(12) =< aux(9) 0.05/0.29 0.05/0.29 with precondition: [B=2,V_j_0>=0,V_i_0>=2,V_n>=V_i_0+V_j_0] 0.05/0.29 0.05/0.29 * Chain [[12,13,14],15]: 3*it(12)+0 0.05/0.29 Such that:aux(10) =< V_i_0 0.05/0.29 it(12) =< aux(10) 0.05/0.29 0.05/0.29 with precondition: [B=2,V_j_0>=0,V_i_0>=2,V_i_0+V_j_0>=3,V_n>=V_i_0+V_j_0] 0.05/0.29 0.05/0.29 * Chain [18]: 0 0.05/0.29 with precondition: [V_i_0=1,B=2,V_n=V_j_0+1,V_n>=1] 0.05/0.29 0.05/0.29 * Chain [17]: 0 0.05/0.29 with precondition: [V_i_0=1,B=2,1>=V_j_0,V_j_0>=0,V_n>=V_j_0+1] 0.05/0.29 0.05/0.29 0.05/0.29 #### Cost of chains of eval_wcet1_bb0_in(V_n,B): 0.05/0.29 * Chain [22]: 0 0.05/0.29 with precondition: [V_n=1] 0.05/0.29 0.05/0.29 * Chain [21]: 0 0.05/0.29 with precondition: [0>=V_n] 0.05/0.29 0.05/0.29 * Chain [20]: 9*s(2)+0 0.05/0.29 Such that:aux(11) =< V_n 0.05/0.29 s(2) =< aux(11) 0.05/0.29 0.05/0.29 with precondition: [V_n>=2] 0.05/0.29 0.05/0.29 * Chain [19]: 3*s(8)+0 0.05/0.29 Such that:s(7) =< V_n 0.05/0.29 s(8) =< s(7) 0.05/0.29 0.05/0.29 with precondition: [V_n>=3] 0.05/0.29 0.05/0.29 0.05/0.29 #### Cost of chains of eval_wcet1_start(V_n,B): 0.05/0.29 * Chain [26]: 0 0.05/0.29 with precondition: [V_n=1] 0.05/0.29 0.05/0.29 * Chain [25]: 0 0.05/0.29 with precondition: [0>=V_n] 0.05/0.29 0.05/0.29 * Chain [24]: 9*s(10)+0 0.05/0.29 Such that:s(9) =< V_n 0.05/0.29 s(10) =< s(9) 0.05/0.29 0.05/0.29 with precondition: [V_n>=2] 0.05/0.29 0.05/0.29 * Chain [23]: 3*s(12)+0 0.05/0.29 Such that:s(11) =< V_n 0.05/0.29 s(12) =< s(11) 0.05/0.29 0.05/0.29 with precondition: [V_n>=3] 0.05/0.29 0.05/0.29 0.05/0.29 Closed-form bounds of eval_wcet1_start(V_n,B): 0.05/0.29 ------------------------------------- 0.05/0.29 * Chain [26] with precondition: [V_n=1] 0.05/0.29 - Upper bound: 0 0.05/0.29 - Complexity: constant 0.05/0.29 * Chain [25] with precondition: [0>=V_n] 0.05/0.29 - Upper bound: 0 0.05/0.29 - Complexity: constant 0.05/0.29 * Chain [24] with precondition: [V_n>=2] 0.05/0.29 - Upper bound: 9*V_n 0.05/0.29 - Complexity: n 0.05/0.29 * Chain [23] with precondition: [V_n>=3] 0.05/0.29 - Upper bound: 3*V_n 0.05/0.29 - Complexity: n 0.05/0.29 0.05/0.29 ### Maximum cost of eval_wcet1_start(V_n,B): nat(V_n)*9 0.05/0.29 Asymptotic class: n 0.05/0.29 * Total analysis performed in 210 ms. 0.05/0.29 0.05/0.39 EOF