0.03/0.22 WORST_CASE(?,O(n^1)) 0.03/0.22 0.03/0.22 Preprocessing Cost Relations 0.03/0.22 ===================================== 0.03/0.22 0.03/0.22 #### Computed strongly connected components 0.03/0.22 0. recursive : [eval_speedpldi4_bb1_in/4,eval_speedpldi4_bb2_in/4] 0.03/0.22 1. non_recursive : [eval_speedpldi4_stop/4] 0.03/0.22 2. non_recursive : [eval_speedpldi4_bb3_in/4] 0.03/0.22 3. non_recursive : [exit_location/1] 0.03/0.22 4. non_recursive : [eval_speedpldi4_bb1_in_loop_cont/5] 0.03/0.22 5. non_recursive : [eval_speedpldi4_2/4] 0.03/0.22 6. non_recursive : [eval_speedpldi4_1/4] 0.03/0.22 7. non_recursive : [eval_speedpldi4_0/4] 0.03/0.22 8. non_recursive : [eval_speedpldi4_bb0_in/4] 0.03/0.22 9. non_recursive : [eval_speedpldi4_start/4] 0.03/0.22 0.03/0.22 #### Obtained direct recursion through partial evaluation 0.03/0.22 0. SCC is partially evaluated into eval_speedpldi4_bb1_in/4 0.03/0.22 1. SCC is completely evaluated into other SCCs 0.03/0.22 2. SCC is completely evaluated into other SCCs 0.03/0.22 3. SCC is completely evaluated into other SCCs 0.03/0.22 4. SCC is partially evaluated into eval_speedpldi4_bb1_in_loop_cont/5 0.03/0.22 5. SCC is partially evaluated into eval_speedpldi4_2/4 0.03/0.22 6. SCC is completely evaluated into other SCCs 0.03/0.22 7. SCC is completely evaluated into other SCCs 0.03/0.22 8. SCC is completely evaluated into other SCCs 0.03/0.22 9. SCC is partially evaluated into eval_speedpldi4_start/4 0.03/0.22 0.03/0.22 Control-Flow Refinement of Cost Relations 0.03/0.22 ===================================== 0.03/0.22 0.03/0.22 ### Specialization of cost equations eval_speedpldi4_bb1_in/4 0.03/0.22 * CE 8 is refined into CE [11] 0.03/0.22 * CE 7 is refined into CE [12] 0.03/0.22 * CE 5 is refined into CE [13] 0.03/0.22 * CE 6 is refined into CE [14] 0.03/0.22 0.03/0.22 0.03/0.22 ### Cost equations --> "Loop" of eval_speedpldi4_bb1_in/4 0.03/0.22 * CEs [13] --> Loop 11 0.03/0.22 * CEs [14] --> Loop 12 0.03/0.22 * CEs [11] --> Loop 13 0.03/0.22 * CEs [12] --> Loop 14 0.03/0.22 0.03/0.22 ### Ranking functions of CR eval_speedpldi4_bb1_in(V_i_0,V_m,B,C) 0.03/0.22 * RF of phase [11]: [V_i_0,V_i_0-V_m+1] 0.03/0.22 * RF of phase [12]: [V_i_0] 0.03/0.22 0.03/0.22 #### Partial ranking functions of CR eval_speedpldi4_bb1_in(V_i_0,V_m,B,C) 0.03/0.22 * Partial RF of phase [11]: 0.03/0.22 - RF of loop [11:1]: 0.03/0.22 V_i_0 0.03/0.22 V_i_0-V_m+1 0.03/0.22 * Partial RF of phase [12]: 0.03/0.22 - RF of loop [12:1]: 0.03/0.22 V_i_0 0.03/0.22 0.03/0.22 0.03/0.22 ### Specialization of cost equations eval_speedpldi4_bb1_in_loop_cont/5 0.03/0.22 * CE 10 is refined into CE [15] 0.03/0.22 * CE 9 is refined into CE [16] 0.03/0.22 0.03/0.22 0.03/0.22 ### Cost equations --> "Loop" of eval_speedpldi4_bb1_in_loop_cont/5 0.03/0.22 * CEs [15] --> Loop 15 0.03/0.22 * CEs [16] --> Loop 16 0.03/0.22 0.03/0.22 ### Ranking functions of CR eval_speedpldi4_bb1_in_loop_cont(A,B,C,D,E) 0.03/0.22 0.03/0.22 #### Partial ranking functions of CR eval_speedpldi4_bb1_in_loop_cont(A,B,C,D,E) 0.03/0.22 0.03/0.22 0.03/0.22 ### Specialization of cost equations eval_speedpldi4_2/4 0.03/0.22 * CE 3 is refined into CE [17] 0.03/0.22 * CE 4 is refined into CE [18,19,20,21,22] 0.03/0.22 * CE 2 is refined into CE [23] 0.03/0.22 0.03/0.22 0.03/0.22 ### Cost equations --> "Loop" of eval_speedpldi4_2/4 0.03/0.22 * CEs [17] --> Loop 17 0.03/0.22 * CEs [19,22] --> Loop 18 0.03/0.22 * CEs [18,20,21] --> Loop 19 0.03/0.22 * CEs [23] --> Loop 20 0.03/0.22 0.03/0.22 ### Ranking functions of CR eval_speedpldi4_2(V_i_0,V_m,V_n,B) 0.03/0.22 0.03/0.22 #### Partial ranking functions of CR eval_speedpldi4_2(V_i_0,V_m,V_n,B) 0.03/0.22 0.03/0.22 0.03/0.22 ### Specialization of cost equations eval_speedpldi4_start/4 0.03/0.22 * CE 1 is refined into CE [24,25,26,27] 0.03/0.22 0.03/0.22 0.03/0.22 ### Cost equations --> "Loop" of eval_speedpldi4_start/4 0.03/0.22 * CEs [27] --> Loop 21 0.03/0.22 * CEs [26] --> Loop 22 0.03/0.22 * CEs [25] --> Loop 23 0.03/0.22 * CEs [24] --> Loop 24 0.03/0.22 0.03/0.22 ### Ranking functions of CR eval_speedpldi4_start(V_i_0,V_m,V_n,B) 0.03/0.22 0.03/0.22 #### Partial ranking functions of CR eval_speedpldi4_start(V_i_0,V_m,V_n,B) 0.03/0.22 0.03/0.22 0.03/0.22 Computing Bounds 0.03/0.22 ===================================== 0.03/0.22 0.03/0.22 #### Cost of chains of eval_speedpldi4_bb1_in(V_i_0,V_m,B,C): 0.03/0.22 * Chain [[11],[12],14]: 1*it(11)+1*it(12)+0 0.03/0.22 Such that:it(12) =< V_i_0-V_m 0.03/0.22 it(11) =< V_i_0-V_m+1 0.03/0.22 it(12) =< V_m 0.03/0.22 0.03/0.22 with precondition: [B=2,C=0,V_m>=2,V_i_0>=V_m+1] 0.03/0.22 0.03/0.22 * Chain [[11],[12],13]: 1*it(11)+1*it(12)+0 0.03/0.22 Such that:it(12) =< V_i_0-V_m 0.03/0.22 it(11) =< V_i_0-V_m+1 0.03/0.22 it(12) =< V_m 0.03/0.22 0.03/0.22 with precondition: [B=3,V_m>=2,V_i_0>=V_m+1] 0.03/0.22 0.03/0.22 * Chain [[11],14]: 1*it(11)+0 0.03/0.22 Such that:it(11) =< V_i_0-V_m+1 0.03/0.22 0.03/0.22 with precondition: [B=2,C=0,V_m>=1,V_i_0>=V_m] 0.03/0.22 0.03/0.22 * Chain [[11],13]: 1*it(11)+0 0.03/0.22 Such that:it(11) =< V_i_0-V_m+1 0.03/0.22 0.03/0.22 with precondition: [B=3,V_m>=1,V_i_0>=V_m] 0.03/0.22 0.03/0.22 * Chain [13]: 0 0.03/0.22 with precondition: [B=3,V_m>=1] 0.03/0.22 0.03/0.22 0.03/0.22 #### Cost of chains of eval_speedpldi4_bb1_in_loop_cont(A,B,C,D,E): 0.03/0.22 * Chain [16]: 0 0.03/0.22 with precondition: [A=2,C>=1,D>=C+1] 0.03/0.22 0.03/0.22 * Chain [15]: 0 0.03/0.22 with precondition: [A=3,C>=1,D>=C+1] 0.03/0.22 0.03/0.22 0.03/0.22 #### Cost of chains of eval_speedpldi4_2(V_i_0,V_m,V_n,B): 0.03/0.22 * Chain [20]: 0 0.03/0.22 with precondition: [0>=V_m] 0.03/0.22 0.03/0.22 * Chain [19]: 2*s(1)+0 0.03/0.22 Such that:aux(1) =< -V_m+V_n+1 0.03/0.22 s(1) =< aux(1) 0.03/0.22 0.03/0.22 with precondition: [V_m>=1,V_n>=V_m+1] 0.03/0.22 0.03/0.22 * Chain [18]: 2*s(3)+2*s(4)+0 0.03/0.22 Such that:aux(2) =< -V_m+V_n 0.03/0.22 aux(3) =< -V_m+V_n+1 0.03/0.22 aux(4) =< V_m 0.03/0.22 s(3) =< aux(2) 0.03/0.22 s(4) =< aux(3) 0.03/0.22 s(3) =< aux(4) 0.03/0.22 0.03/0.22 with precondition: [V_m>=2,V_n>=V_m+1] 0.03/0.22 0.03/0.22 * Chain [17]: 0 0.03/0.22 with precondition: [V_m>=V_n] 0.03/0.22 0.03/0.22 0.03/0.22 #### Cost of chains of eval_speedpldi4_start(V_i_0,V_m,V_n,B): 0.03/0.22 * Chain [24]: 0 0.03/0.22 with precondition: [0>=V_m] 0.03/0.22 0.03/0.22 * Chain [23]: 2*s(8)+0 0.03/0.22 Such that:s(7) =< -V_m+V_n+1 0.03/0.22 s(8) =< s(7) 0.03/0.22 0.03/0.22 with precondition: [V_m>=1,V_n>=V_m+1] 0.03/0.22 0.03/0.22 * Chain [22]: 2*s(12)+2*s(13)+0 0.03/0.22 Such that:s(9) =< -V_m+V_n 0.03/0.22 s(10) =< -V_m+V_n+1 0.03/0.22 s(11) =< V_m 0.03/0.22 s(12) =< s(9) 0.03/0.22 s(13) =< s(10) 0.03/0.22 s(12) =< s(11) 0.03/0.22 0.03/0.22 with precondition: [V_m>=2,V_n>=V_m+1] 0.03/0.22 0.03/0.22 * Chain [21]: 0 0.03/0.22 with precondition: [V_m>=V_n] 0.03/0.22 0.03/0.22 0.03/0.22 Closed-form bounds of eval_speedpldi4_start(V_i_0,V_m,V_n,B): 0.03/0.22 ------------------------------------- 0.03/0.22 * Chain [24] with precondition: [0>=V_m] 0.03/0.22 - Upper bound: 0 0.03/0.22 - Complexity: constant 0.03/0.22 * Chain [23] with precondition: [V_m>=1,V_n>=V_m+1] 0.03/0.22 - Upper bound: -2*V_m+2*V_n+2 0.03/0.22 - Complexity: n 0.03/0.22 * Chain [22] with precondition: [V_m>=2,V_n>=V_m+1] 0.03/0.22 - Upper bound: -4*V_m+4*V_n+2 0.03/0.22 - Complexity: n 0.03/0.22 * Chain [21] with precondition: [V_m>=V_n] 0.03/0.22 - Upper bound: 0 0.03/0.22 - Complexity: constant 0.03/0.22 0.03/0.22 ### Maximum cost of eval_speedpldi4_start(V_i_0,V_m,V_n,B): nat(-V_m+V_n+1)*2+nat(-V_m+V_n)*2 0.03/0.22 Asymptotic class: n 0.03/0.22 * Total analysis performed in 161 ms. 0.03/0.22 0.03/0.33 EOF