0.04/0.52 WORST_CASE(?,O(n^1)) 0.04/0.52 0.04/0.52 Preprocessing Cost Relations 0.04/0.52 ===================================== 0.04/0.52 0.04/0.52 #### Computed strongly connected components 0.04/0.52 0. recursive : [eval_wcet1_4/10,eval_wcet1_5/10,eval_wcet1_bb1_in/10,eval_wcet1_bb2_in/10,eval_wcet1_bb3_in/10,eval_wcet1_bb4_in/10] 0.04/0.52 1. non_recursive : [eval_wcet1_stop/6] 0.04/0.52 2. non_recursive : [eval_wcet1_bb5_in/6] 0.04/0.52 3. non_recursive : [exit_location/1] 0.04/0.52 4. non_recursive : [eval_wcet1_bb1_in_loop_cont/7] 0.04/0.52 5. non_recursive : [eval_wcet1_3/6] 0.04/0.52 6. non_recursive : [eval_wcet1_2/6] 0.04/0.52 7. non_recursive : [eval_wcet1_1/6] 0.04/0.52 8. non_recursive : [eval_wcet1_0/6] 0.04/0.52 9. non_recursive : [eval_wcet1_bb0_in/6] 0.04/0.52 10. non_recursive : [eval_wcet1_start/6] 0.04/0.52 0.04/0.52 #### Obtained direct recursion through partial evaluation 0.04/0.52 0. SCC is partially evaluated into eval_wcet1_bb1_in/10 0.04/0.52 1. SCC is completely evaluated into other SCCs 0.04/0.52 2. SCC is completely evaluated into other SCCs 0.04/0.52 3. SCC is completely evaluated into other SCCs 0.04/0.52 4. SCC is partially evaluated into eval_wcet1_bb1_in_loop_cont/7 0.04/0.52 5. SCC is partially evaluated into eval_wcet1_3/6 0.04/0.52 6. SCC is completely evaluated into other SCCs 0.04/0.52 7. SCC is completely evaluated into other SCCs 0.04/0.52 8. SCC is completely evaluated into other SCCs 0.04/0.52 9. SCC is completely evaluated into other SCCs 0.04/0.52 10. SCC is partially evaluated into eval_wcet1_start/6 0.04/0.52 0.04/0.52 Control-Flow Refinement of Cost Relations 0.04/0.52 ===================================== 0.04/0.52 0.04/0.52 ### Specialization of cost equations eval_wcet1_bb1_in/10 0.04/0.52 * CE 11 is refined into CE [15] 0.04/0.52 * CE 7 is refined into CE [16] 0.04/0.52 * CE 6 is refined into CE [17] 0.04/0.52 * CE 10 is refined into CE [18] 0.04/0.52 * CE 12 is refined into CE [19] 0.04/0.52 * CE 5 is refined into CE [20] 0.04/0.52 * CE 9 is refined into CE [21] 0.04/0.52 * CE 4 is discarded (unfeasible) 0.04/0.52 * CE 8 is refined into CE [22] 0.04/0.52 0.04/0.52 0.04/0.52 ### Cost equations --> "Loop" of eval_wcet1_bb1_in/10 0.04/0.52 * CEs [20] --> Loop 15 0.04/0.52 * CEs [21] --> Loop 16 0.04/0.52 * CEs [22] --> Loop 17 0.04/0.52 * CEs [19] --> Loop 18 0.04/0.52 * CEs [15] --> Loop 19 0.04/0.52 * CEs [16] --> Loop 20 0.04/0.52 * CEs [18] --> Loop 21 0.04/0.52 * CEs [17] --> Loop 22 0.04/0.52 0.04/0.52 ### Ranking functions of CR eval_wcet1_bb1_in(V_1,V_i_0,V_j_0,V_j_3,V_n,B,C,D,E,F) 0.04/0.52 * RF of phase [15,16,17]: [V_i_0-1] 0.04/0.52 0.04/0.52 #### Partial ranking functions of CR eval_wcet1_bb1_in(V_1,V_i_0,V_j_0,V_j_3,V_n,B,C,D,E,F) 0.04/0.52 * Partial RF of phase [15,16,17]: 0.04/0.52 - RF of loop [15:1]: 0.04/0.52 -V_j_0+V_n-1 depends on loops [16:1,17:1] 0.04/0.52 - RF of loop [15:1,16:1,17:1]: 0.04/0.52 V_i_0-1 0.04/0.52 - RF of loop [16:1]: 0.04/0.52 V_j_0-1 depends on loops [15:1] 0.04/0.52 0.04/0.52 0.04/0.52 ### Specialization of cost equations eval_wcet1_bb1_in_loop_cont/7 0.04/0.52 * CE 14 is refined into CE [23] 0.04/0.52 * CE 13 is refined into CE [24] 0.04/0.52 0.04/0.52 0.04/0.52 ### Cost equations --> "Loop" of eval_wcet1_bb1_in_loop_cont/7 0.04/0.52 * CEs [23] --> Loop 23 0.04/0.52 * CEs [24] --> Loop 24 0.04/0.52 0.04/0.52 ### Ranking functions of CR eval_wcet1_bb1_in_loop_cont(A,B,C,D,E,F,G) 0.04/0.52 0.04/0.52 #### Partial ranking functions of CR eval_wcet1_bb1_in_loop_cont(A,B,C,D,E,F,G) 0.04/0.52 0.04/0.52 0.04/0.52 ### Specialization of cost equations eval_wcet1_3/6 0.04/0.52 * CE 3 is refined into CE [25,26,27,28,29,30,31,32] 0.04/0.52 * CE 2 is refined into CE [33] 0.04/0.52 0.04/0.52 0.04/0.52 ### Cost equations --> "Loop" of eval_wcet1_3/6 0.04/0.52 * CEs [32] --> Loop 25 0.04/0.52 * CEs [28,29,30,31] --> Loop 26 0.04/0.52 * CEs [27] --> Loop 27 0.04/0.52 * CEs [33] --> Loop 28 0.04/0.52 * CEs [25,26] --> Loop 29 0.04/0.52 0.04/0.52 ### Ranking functions of CR eval_wcet1_3(V_1,V_i_0,V_j_0,V_j_3,V_n,B) 0.04/0.52 0.04/0.52 #### Partial ranking functions of CR eval_wcet1_3(V_1,V_i_0,V_j_0,V_j_3,V_n,B) 0.04/0.52 0.04/0.52 0.04/0.52 ### Specialization of cost equations eval_wcet1_start/6 0.04/0.52 * CE 1 is refined into CE [34,35,36,37,38] 0.04/0.52 0.04/0.52 0.04/0.52 ### Cost equations --> "Loop" of eval_wcet1_start/6 0.04/0.52 * CEs [38] --> Loop 30 0.04/0.52 * CEs [37] --> Loop 31 0.04/0.52 * CEs [36] --> Loop 32 0.04/0.52 * CEs [35] --> Loop 33 0.04/0.52 * CEs [34] --> Loop 34 0.04/0.52 0.04/0.52 ### Ranking functions of CR eval_wcet1_start(V_1,V_i_0,V_j_0,V_j_3,V_n,B) 0.04/0.52 0.04/0.52 #### Partial ranking functions of CR eval_wcet1_start(V_1,V_i_0,V_j_0,V_j_3,V_n,B) 0.04/0.52 0.04/0.52 0.04/0.52 Computing Bounds 0.04/0.52 ===================================== 0.04/0.52 0.04/0.52 #### Cost of chains of eval_wcet1_bb1_in(V_1,V_i_0,V_j_0,V_j_3,V_n,B,C,D,E,F): 0.04/0.52 * Chain [[15,16,17],22]: 3*it(15)+0 0.04/0.52 Such that:aux(7) =< V_i_0 0.04/0.52 it(15) =< aux(7) 0.04/0.52 0.04/0.52 with precondition: [B=3,D=1,F=0,V_i_0+V_j_0=V_n,V_i_0+V_j_0=E+1,V_i_0>=2,V_j_0>=0,C>=1] 0.04/0.52 0.04/0.52 * Chain [[15,16,17],21]: 3*it(15)+0 0.04/0.52 Such that:aux(8) =< V_i_0 0.04/0.52 it(15) =< aux(8) 0.04/0.52 0.04/0.52 with precondition: [B=3,D=1,F=0,0>=C,1>=E,V_i_0>=2,V_j_0>=0,E>=0,V_n>=V_i_0+V_j_0,V_i_0+E>=V_j_0+1] 0.04/0.52 0.04/0.52 * Chain [[15,16,17],20]: 3*it(15)+0 0.04/0.52 Such that:aux(9) =< V_i_0 0.04/0.52 it(15) =< aux(9) 0.04/0.52 0.04/0.52 with precondition: [B=3,D=1,E+1=F,V_i_0>=2,V_j_0>=0,C>=1,E>=0,V_n>=E+2,V_n>=V_i_0+V_j_0,V_i_0+E>=V_j_0+1,V_i_0+V_j_0>=E+1] 0.04/0.52 0.04/0.52 * Chain [[15,16,17],19]: 3*it(15)+0 0.04/0.52 Such that:aux(10) =< V_i_0 0.04/0.52 it(15) =< aux(10) 0.04/0.52 0.04/0.52 with precondition: [B=3,D=1,E=F+1,0>=C,V_i_0>=2,V_j_0>=0,E>=2,V_n>=V_i_0+V_j_0,V_i_0+E>=V_j_0+1,V_i_0+V_j_0>=E+1] 0.04/0.52 0.04/0.52 * Chain [[15,16,17],18]: 3*it(15)+0 0.04/0.52 Such that:aux(11) =< V_i_0 0.04/0.52 it(15) =< aux(11) 0.04/0.52 0.04/0.52 with precondition: [B=2,V_i_0>=2,V_j_0>=0,V_n>=V_i_0+V_j_0] 0.04/0.52 0.04/0.52 * Chain [22]: 0 0.04/0.52 with precondition: [V_i_0=1,B=3,D=1,F=0,V_n=V_j_0+1,V_n=E+1,V_n>=1,C>=1] 0.04/0.52 0.04/0.52 * Chain [21]: 0 0.04/0.52 with precondition: [V_i_0=1,B=3,D=1,F=0,V_j_0=E,1>=V_j_0,0>=C,V_j_0>=0,V_n>=V_j_0+1] 0.04/0.52 0.04/0.52 * Chain [18]: 0 0.04/0.52 with precondition: [B=2,V_i_0>=1,V_j_0>=0,V_n>=V_i_0+V_j_0] 0.04/0.52 0.04/0.52 0.04/0.52 #### Cost of chains of eval_wcet1_bb1_in_loop_cont(A,B,C,D,E,F,G): 0.04/0.52 * Chain [24]: 0 0.04/0.52 with precondition: [A=2,F>=1] 0.04/0.52 0.04/0.52 * Chain [23]: 0 0.04/0.52 with precondition: [A=3,F>=1] 0.04/0.52 0.04/0.52 0.04/0.52 #### Cost of chains of eval_wcet1_3(V_1,V_i_0,V_j_0,V_j_3,V_n,B): 0.04/0.52 * Chain [29]: 0 0.04/0.52 with precondition: [V_n=1] 0.04/0.52 0.04/0.52 * Chain [28]: 0 0.04/0.52 with precondition: [0>=V_n] 0.04/0.52 0.04/0.52 * Chain [27]: 0 0.04/0.52 with precondition: [V_n>=1] 0.04/0.52 0.04/0.52 * Chain [26]: 12*s(2)+0 0.04/0.52 Such that:aux(12) =< V_n 0.04/0.52 s(2) =< aux(12) 0.04/0.52 0.04/0.52 with precondition: [V_n>=2] 0.04/0.52 0.04/0.52 * Chain [25]: 3*s(10)+0 0.04/0.52 Such that:s(9) =< V_n 0.04/0.52 s(10) =< s(9) 0.04/0.52 0.04/0.52 with precondition: [V_n>=3] 0.04/0.52 0.04/0.52 0.04/0.52 #### Cost of chains of eval_wcet1_start(V_1,V_i_0,V_j_0,V_j_3,V_n,B): 0.04/0.52 * Chain [34]: 0 0.04/0.52 with precondition: [V_n=1] 0.04/0.52 0.04/0.52 * Chain [33]: 0 0.04/0.52 with precondition: [0>=V_n] 0.04/0.52 0.04/0.52 * Chain [32]: 0 0.04/0.52 with precondition: [V_n>=1] 0.04/0.52 0.04/0.52 * Chain [31]: 12*s(12)+0 0.04/0.52 Such that:s(11) =< V_n 0.04/0.52 s(12) =< s(11) 0.04/0.52 0.04/0.52 with precondition: [V_n>=2] 0.04/0.52 0.04/0.52 * Chain [30]: 3*s(14)+0 0.04/0.52 Such that:s(13) =< V_n 0.04/0.52 s(14) =< s(13) 0.04/0.52 0.04/0.52 with precondition: [V_n>=3] 0.04/0.52 0.04/0.52 0.04/0.52 Closed-form bounds of eval_wcet1_start(V_1,V_i_0,V_j_0,V_j_3,V_n,B): 0.04/0.52 ------------------------------------- 0.04/0.52 * Chain [34] with precondition: [V_n=1] 0.04/0.52 - Upper bound: 0 0.04/0.52 - Complexity: constant 0.04/0.52 * Chain [33] with precondition: [0>=V_n] 0.04/0.52 - Upper bound: 0 0.04/0.52 - Complexity: constant 0.04/0.52 * Chain [32] with precondition: [V_n>=1] 0.04/0.52 - Upper bound: 0 0.04/0.52 - Complexity: constant 0.04/0.52 * Chain [31] with precondition: [V_n>=2] 0.04/0.52 - Upper bound: 12*V_n 0.04/0.52 - Complexity: n 0.04/0.52 * Chain [30] with precondition: [V_n>=3] 0.04/0.52 - Upper bound: 3*V_n 0.04/0.52 - Complexity: n 0.04/0.52 0.04/0.52 ### Maximum cost of eval_wcet1_start(V_1,V_i_0,V_j_0,V_j_3,V_n,B): nat(V_n)*12 0.04/0.52 Asymptotic class: n 0.04/0.52 * Total analysis performed in 434 ms. 0.04/0.52 0.52/0.62 EOF