0.05/0.26 WORST_CASE(?,O(n^1)) 0.05/0.26 0.05/0.26 Preprocessing Cost Relations 0.05/0.26 ===================================== 0.05/0.26 0.05/0.26 #### Computed strongly connected components 0.05/0.26 0. recursive : [eval_wcet0_0/4,eval_wcet0_1/5,eval_wcet0_bb1_in/4,eval_wcet0_bb2_in/5,eval_wcet0_bb3_in/5,eval_wcet0_bb4_in/6] 0.05/0.26 1. non_recursive : [eval_wcet0_stop/1] 0.05/0.26 2. non_recursive : [eval_wcet0_bb5_in/1] 0.05/0.26 3. non_recursive : [eval_wcet0_bb1_in_loop_cont/2] 0.05/0.26 4. non_recursive : [eval_wcet0_bb0_in/2] 0.05/0.26 5. non_recursive : [eval_wcet0_start/2] 0.05/0.26 0.05/0.26 #### Obtained direct recursion through partial evaluation 0.05/0.26 0. SCC is partially evaluated into eval_wcet0_bb1_in/4 0.05/0.26 1. SCC is completely evaluated into other SCCs 0.05/0.26 2. SCC is completely evaluated into other SCCs 0.05/0.26 3. SCC is completely evaluated into other SCCs 0.05/0.26 4. SCC is partially evaluated into eval_wcet0_bb0_in/2 0.05/0.26 5. SCC is partially evaluated into eval_wcet0_start/2 0.05/0.26 0.05/0.26 Control-Flow Refinement of Cost Relations 0.05/0.26 ===================================== 0.05/0.26 0.05/0.26 ### Specialization of cost equations eval_wcet0_bb1_in/4 0.05/0.26 * CE 11 is refined into CE [12] 0.05/0.26 * CE 7 is refined into CE [13] 0.05/0.26 * CE 6 is refined into CE [14] 0.05/0.26 * CE 10 is refined into CE [15] 0.05/0.26 * CE 9 is refined into CE [16] 0.05/0.26 * CE 5 is refined into CE [17] 0.05/0.26 * CE 4 is discarded (unfeasible) 0.05/0.26 * CE 8 is discarded (unfeasible) 0.05/0.26 0.05/0.26 0.05/0.26 ### Cost equations --> "Loop" of eval_wcet0_bb1_in/4 0.05/0.26 * CEs [16] --> Loop 12 0.05/0.26 * CEs [17] --> Loop 13 0.05/0.26 * CEs [13] --> Loop 14 0.05/0.26 * CEs [12] --> Loop 15 0.05/0.26 * CEs [15] --> Loop 16 0.05/0.26 * CEs [14] --> Loop 17 0.05/0.26 0.05/0.26 ### Ranking functions of CR eval_wcet0_bb1_in(V_n,V_j_0,V_i_0,B) 0.05/0.26 * RF of phase [12,13]: [V_i_0-1] 0.05/0.26 0.05/0.26 #### Partial ranking functions of CR eval_wcet0_bb1_in(V_n,V_j_0,V_i_0,B) 0.05/0.26 * Partial RF of phase [12,13]: 0.05/0.26 - RF of loop [12:1]: 0.05/0.26 V_n+V_j_0-1 depends on loops [13:1] 0.05/0.26 - RF of loop [12:1,13:1]: 0.05/0.26 V_i_0-1 0.05/0.26 - RF of loop [13:1]: 0.05/0.26 V_n-V_j_0-1 depends on loops [12:1] 0.05/0.26 0.05/0.26 0.05/0.26 ### Specialization of cost equations eval_wcet0_bb0_in/2 0.05/0.26 * CE 3 is refined into CE [18,19,20,21,22] 0.05/0.26 * CE 2 is refined into CE [23] 0.05/0.26 0.05/0.26 0.05/0.26 ### Cost equations --> "Loop" of eval_wcet0_bb0_in/2 0.05/0.26 * CEs [20,21,22] --> Loop 18 0.05/0.26 * CEs [23] --> Loop 19 0.05/0.26 * CEs [18,19] --> Loop 20 0.05/0.26 0.05/0.26 ### Ranking functions of CR eval_wcet0_bb0_in(V_n,B) 0.05/0.26 0.05/0.26 #### Partial ranking functions of CR eval_wcet0_bb0_in(V_n,B) 0.05/0.26 0.05/0.26 0.05/0.26 ### Specialization of cost equations eval_wcet0_start/2 0.05/0.26 * CE 1 is refined into CE [24,25,26] 0.05/0.26 0.05/0.26 0.05/0.26 ### Cost equations --> "Loop" of eval_wcet0_start/2 0.05/0.26 * CEs [26] --> Loop 21 0.05/0.26 * CEs [25] --> Loop 22 0.05/0.26 * CEs [24] --> Loop 23 0.05/0.26 0.05/0.26 ### Ranking functions of CR eval_wcet0_start(V_n,B) 0.05/0.26 0.05/0.26 #### Partial ranking functions of CR eval_wcet0_start(V_n,B) 0.05/0.26 0.05/0.26 0.05/0.26 Computing Bounds 0.05/0.26 ===================================== 0.05/0.26 0.05/0.26 #### Cost of chains of eval_wcet0_bb1_in(V_n,V_j_0,V_i_0,B): 0.05/0.26 * Chain [[12,13],17]: 2*it(12)+0 0.05/0.26 Such that:aux(7) =< V_i_0 0.05/0.26 it(12) =< aux(7) 0.05/0.26 0.05/0.26 with precondition: [B=2,V_n=V_i_0+V_j_0,V_j_0>=0,V_n>=V_j_0+2] 0.05/0.26 0.05/0.26 * Chain [[12,13],16]: 2*it(12)+0 0.05/0.26 Such that:aux(8) =< V_i_0 0.05/0.26 it(12) =< aux(8) 0.05/0.26 0.05/0.26 with precondition: [B=2,V_j_0+V_n=V_i_0,0>=V_j_0,V_j_0+V_n>=2] 0.05/0.26 0.05/0.26 * Chain [[12,13],15]: 2*it(12)+0 0.05/0.26 Such that:aux(9) =< V_i_0 0.05/0.26 it(12) =< aux(9) 0.05/0.26 0.05/0.26 with precondition: [B=2,V_i_0>=2,V_n>=V_i_0+V_j_0,V_j_0+V_n>=V_i_0] 0.05/0.26 0.05/0.26 * Chain [[12,13],14]: 2*it(12)+0 0.05/0.26 Such that:aux(10) =< V_i_0 0.05/0.26 it(12) =< aux(10) 0.05/0.26 0.05/0.26 with precondition: [B=2,V_i_0>=2,V_n>=V_i_0+V_j_0,V_j_0+V_n>=V_i_0] 0.05/0.26 0.05/0.26 * Chain [17]: 0 0.05/0.26 with precondition: [V_i_0=1,B=2,V_n=V_j_0+1,V_n>=1] 0.05/0.26 0.05/0.26 * Chain [16]: 0 0.05/0.26 with precondition: [V_i_0=1,B=2,V_j_0+V_n=1,V_n>=1] 0.05/0.26 0.05/0.26 0.05/0.26 #### Cost of chains of eval_wcet0_bb0_in(V_n,B): 0.05/0.26 * Chain [20]: 0 0.05/0.26 with precondition: [V_n=1] 0.05/0.26 0.05/0.26 * Chain [19]: 0 0.05/0.26 with precondition: [0>=V_n] 0.05/0.26 0.05/0.26 * Chain [18]: 8*s(6)+0 0.05/0.26 Such that:aux(12) =< V_n 0.05/0.26 s(6) =< aux(12) 0.05/0.26 0.05/0.26 with precondition: [V_n>=2] 0.05/0.26 0.05/0.26 0.05/0.26 #### Cost of chains of eval_wcet0_start(V_n,B): 0.05/0.26 * Chain [23]: 0 0.05/0.26 with precondition: [V_n=1] 0.05/0.26 0.05/0.26 * Chain [22]: 0 0.05/0.26 with precondition: [0>=V_n] 0.05/0.26 0.05/0.26 * Chain [21]: 8*s(12)+0 0.05/0.26 Such that:s(11) =< V_n 0.05/0.26 s(12) =< s(11) 0.05/0.26 0.05/0.26 with precondition: [V_n>=2] 0.05/0.26 0.05/0.26 0.05/0.26 Closed-form bounds of eval_wcet0_start(V_n,B): 0.05/0.26 ------------------------------------- 0.05/0.26 * Chain [23] with precondition: [V_n=1] 0.05/0.26 - Upper bound: 0 0.05/0.26 - Complexity: constant 0.05/0.26 * Chain [22] with precondition: [0>=V_n] 0.05/0.26 - Upper bound: 0 0.05/0.26 - Complexity: constant 0.05/0.26 * Chain [21] with precondition: [V_n>=2] 0.05/0.26 - Upper bound: 8*V_n 0.05/0.26 - Complexity: n 0.05/0.26 0.05/0.26 ### Maximum cost of eval_wcet0_start(V_n,B): nat(V_n)*8 0.05/0.26 Asymptotic class: n 0.05/0.26 * Total analysis performed in 188 ms. 0.05/0.26 0.05/0.37 EOF