0.03/0.33 WORST_CASE(?,O(n^2)) 0.03/0.33 0.03/0.33 Preprocessing Cost Relations 0.03/0.33 ===================================== 0.03/0.33 0.03/0.33 #### Computed strongly connected components 0.03/0.33 0. recursive : [eval_speedpldi3_bb1_in/7,eval_speedpldi3_bb2_in/7] 0.03/0.33 1. non_recursive : [eval_speedpldi3_stop/5] 0.03/0.33 2. non_recursive : [eval_speedpldi3_bb3_in/5] 0.03/0.33 3. non_recursive : [exit_location/1] 0.03/0.33 4. non_recursive : [eval_speedpldi3_bb1_in_loop_cont/6] 0.03/0.33 5. non_recursive : [eval_speedpldi3_2/5] 0.03/0.33 6. non_recursive : [eval_speedpldi3_1/5] 0.03/0.33 7. non_recursive : [eval_speedpldi3_0/5] 0.03/0.33 8. non_recursive : [eval_speedpldi3_bb0_in/5] 0.03/0.33 9. non_recursive : [eval_speedpldi3_start/5] 0.03/0.33 0.03/0.33 #### Obtained direct recursion through partial evaluation 0.03/0.33 0. SCC is partially evaluated into eval_speedpldi3_bb1_in/7 0.03/0.33 1. SCC is completely evaluated into other SCCs 0.03/0.33 2. SCC is completely evaluated into other SCCs 0.03/0.33 3. SCC is completely evaluated into other SCCs 0.03/0.33 4. SCC is partially evaluated into eval_speedpldi3_bb1_in_loop_cont/6 0.03/0.33 5. SCC is partially evaluated into eval_speedpldi3_2/5 0.03/0.33 6. SCC is completely evaluated into other SCCs 0.03/0.33 7. SCC is completely evaluated into other SCCs 0.03/0.33 8. SCC is completely evaluated into other SCCs 0.03/0.33 9. SCC is partially evaluated into eval_speedpldi3_start/5 0.03/0.33 0.03/0.33 Control-Flow Refinement of Cost Relations 0.03/0.33 ===================================== 0.03/0.33 0.03/0.33 ### Specialization of cost equations eval_speedpldi3_bb1_in/7 0.03/0.33 * CE 8 is refined into CE [11] 0.03/0.33 * CE 7 is refined into CE [12] 0.03/0.33 * CE 6 is refined into CE [13] 0.03/0.33 * CE 5 is refined into CE [14] 0.03/0.33 0.03/0.33 0.03/0.33 ### Cost equations --> "Loop" of eval_speedpldi3_bb1_in/7 0.03/0.33 * CEs [13] --> Loop 11 0.03/0.33 * CEs [14] --> Loop 12 0.03/0.33 * CEs [11] --> Loop 13 0.03/0.33 * CEs [12] --> Loop 14 0.03/0.33 0.03/0.33 ### Ranking functions of CR eval_speedpldi3_bb1_in(V_i_0,V_j_0,V_m,V_n,B,C,D) 0.03/0.33 0.03/0.33 #### Partial ranking functions of CR eval_speedpldi3_bb1_in(V_i_0,V_j_0,V_m,V_n,B,C,D) 0.03/0.33 * Partial RF of phase [11,12]: 0.03/0.33 - RF of loop [11:1]: 0.03/0.33 -V_j_0+V_m depends on loops [12:1] 0.03/0.33 -V_j_0+V_n-1 depends on loops [12:1] 0.03/0.33 - RF of loop [12:1]: 0.03/0.33 -V_i_0+V_n 0.03/0.33 V_j_0 depends on loops [11:1] 0.03/0.33 V_j_0-V_m+1 depends on loops [11:1] 0.03/0.33 0.03/0.33 0.03/0.33 ### Specialization of cost equations eval_speedpldi3_bb1_in_loop_cont/6 0.03/0.33 * CE 10 is refined into CE [15] 0.03/0.33 * CE 9 is refined into CE [16] 0.03/0.33 0.03/0.33 0.03/0.33 ### Cost equations --> "Loop" of eval_speedpldi3_bb1_in_loop_cont/6 0.03/0.33 * CEs [15] --> Loop 15 0.03/0.33 * CEs [16] --> Loop 16 0.03/0.33 0.03/0.33 ### Ranking functions of CR eval_speedpldi3_bb1_in_loop_cont(A,B,C,D,E,F) 0.03/0.33 0.03/0.33 #### Partial ranking functions of CR eval_speedpldi3_bb1_in_loop_cont(A,B,C,D,E,F) 0.03/0.33 0.03/0.33 0.03/0.33 ### Specialization of cost equations eval_speedpldi3_2/5 0.03/0.33 * CE 3 is refined into CE [17] 0.03/0.33 * CE 4 is refined into CE [18,19,20] 0.03/0.33 * CE 2 is refined into CE [21] 0.03/0.33 0.03/0.33 0.03/0.33 ### Cost equations --> "Loop" of eval_speedpldi3_2/5 0.03/0.33 * CEs [17] --> Loop 17 0.03/0.33 * CEs [18,19,20] --> Loop 18 0.03/0.33 * CEs [21] --> Loop 19 0.03/0.33 0.03/0.33 ### Ranking functions of CR eval_speedpldi3_2(V_i_0,V_j_0,V_m,V_n,B) 0.03/0.33 0.03/0.33 #### Partial ranking functions of CR eval_speedpldi3_2(V_i_0,V_j_0,V_m,V_n,B) 0.03/0.33 0.03/0.33 0.03/0.33 ### Specialization of cost equations eval_speedpldi3_start/5 0.03/0.33 * CE 1 is refined into CE [22,23,24] 0.03/0.33 0.03/0.33 0.03/0.33 ### Cost equations --> "Loop" of eval_speedpldi3_start/5 0.03/0.33 * CEs [24] --> Loop 20 0.03/0.33 * CEs [23] --> Loop 21 0.03/0.33 * CEs [22] --> Loop 22 0.03/0.33 0.03/0.33 ### Ranking functions of CR eval_speedpldi3_start(V_i_0,V_j_0,V_m,V_n,B) 0.03/0.33 0.03/0.33 #### Partial ranking functions of CR eval_speedpldi3_start(V_i_0,V_j_0,V_m,V_n,B) 0.03/0.33 0.03/0.33 0.03/0.33 Computing Bounds 0.03/0.33 ===================================== 0.03/0.33 0.03/0.33 #### Cost of chains of eval_speedpldi3_bb1_in(V_i_0,V_j_0,V_m,V_n,B,C,D): 0.03/0.33 * Chain [[11,12],14]: 1*it(11)+1*it(12)+0 0.03/0.33 Such that:it(12) =< -V_i_0+V_n 0.03/0.33 aux(4) =< -V_j_0+V_n 0.03/0.33 aux(21) =< V_n 0.03/0.33 aux(3) =< it(12)*aux(21) 0.03/0.33 it(11) =< aux(3)+aux(4) 0.03/0.33 0.03/0.33 with precondition: [B=2,D=0,V_n=C,V_i_0>=0,V_j_0>=0,V_m>=1,V_n>=V_i_0+1,V_n>=V_m+1] 0.03/0.33 0.03/0.33 * Chain [[11,12],13]: 1*it(11)+1*it(12)+0 0.03/0.33 Such that:it(12) =< -V_i_0+V_n 0.03/0.33 aux(4) =< -V_j_0+V_n 0.03/0.33 aux(21) =< V_n 0.03/0.33 aux(3) =< it(12)*aux(21) 0.03/0.33 it(11) =< aux(3)+aux(4) 0.03/0.33 0.03/0.33 with precondition: [B=3,V_i_0>=0,V_j_0>=0,V_m>=1,V_n>=V_i_0+1,V_n>=V_m+1] 0.03/0.33 0.03/0.33 * Chain [13]: 0 0.03/0.33 with precondition: [B=3,V_i_0>=0,V_j_0>=0,V_m>=1,V_n>=V_m+1] 0.03/0.33 0.03/0.33 0.03/0.33 #### Cost of chains of eval_speedpldi3_bb1_in_loop_cont(A,B,C,D,E,F): 0.03/0.33 * Chain [16]: 0 0.03/0.33 with precondition: [A=2,D>=1,E>=D+1] 0.03/0.33 0.03/0.33 * Chain [15]: 0 0.03/0.33 with precondition: [A=3,D>=1,E>=D+1] 0.03/0.33 0.03/0.33 0.03/0.33 #### Cost of chains of eval_speedpldi3_2(V_i_0,V_j_0,V_m,V_n,B): 0.03/0.33 * Chain [19]: 0 0.03/0.33 with precondition: [0>=V_m] 0.03/0.33 0.03/0.33 * Chain [18]: 2*s(1)+2*s(5)+0 0.03/0.33 Such that:aux(24) =< V_n 0.03/0.33 s(1) =< aux(24) 0.03/0.33 s(4) =< s(1)*aux(24) 0.03/0.33 s(5) =< s(4)+aux(24) 0.03/0.33 0.03/0.33 with precondition: [V_m>=1,V_n>=V_m+1] 0.03/0.33 0.03/0.33 * Chain [17]: 0 0.03/0.33 with precondition: [V_m>=V_n] 0.03/0.33 0.03/0.33 0.03/0.33 #### Cost of chains of eval_speedpldi3_start(V_i_0,V_j_0,V_m,V_n,B): 0.03/0.33 * Chain [22]: 0 0.03/0.33 with precondition: [0>=V_m] 0.03/0.33 0.03/0.33 * Chain [21]: 2*s(12)+2*s(14)+0 0.03/0.33 Such that:s(11) =< V_n 0.03/0.33 s(12) =< s(11) 0.03/0.33 s(13) =< s(12)*s(11) 0.03/0.33 s(14) =< s(13)+s(11) 0.03/0.33 0.03/0.33 with precondition: [V_m>=1,V_n>=V_m+1] 0.03/0.33 0.03/0.33 * Chain [20]: 0 0.03/0.33 with precondition: [V_m>=V_n] 0.03/0.33 0.03/0.33 0.03/0.33 Closed-form bounds of eval_speedpldi3_start(V_i_0,V_j_0,V_m,V_n,B): 0.03/0.33 ------------------------------------- 0.03/0.33 * Chain [22] with precondition: [0>=V_m] 0.03/0.33 - Upper bound: 0 0.03/0.33 - Complexity: constant 0.03/0.33 * Chain [21] with precondition: [V_m>=1,V_n>=V_m+1] 0.03/0.33 - Upper bound: 2*V_n*V_n+4*V_n 0.03/0.33 - Complexity: n^2 0.03/0.33 * Chain [20] with precondition: [V_m>=V_n] 0.03/0.33 - Upper bound: 0 0.03/0.33 - Complexity: constant 0.03/0.33 0.03/0.33 ### Maximum cost of eval_speedpldi3_start(V_i_0,V_j_0,V_m,V_n,B): nat(V_n)*2*nat(V_n)+nat(V_n)*4 0.03/0.33 Asymptotic class: n^2 0.03/0.33 * Total analysis performed in 254 ms. 0.03/0.33 0.03/0.43 EOF