0.03/0.28 WORST_CASE(?,O(n^1)) 0.03/0.28 0.03/0.28 Preprocessing Cost Relations 0.03/0.28 ===================================== 0.03/0.28 0.03/0.28 #### Computed strongly connected components 0.03/0.28 0. recursive : [eval_speedpldi2_bb1_in/6,eval_speedpldi2_bb2_in/6,eval_speedpldi2_bb3_in/6] 0.03/0.28 1. non_recursive : [eval_speedpldi2_stop/5] 0.03/0.28 2. non_recursive : [eval_speedpldi2_bb4_in/5] 0.03/0.28 3. non_recursive : [exit_location/1] 0.03/0.28 4. non_recursive : [eval_speedpldi2_bb1_in_loop_cont/6] 0.03/0.28 5. non_recursive : [eval_speedpldi2_2/5] 0.03/0.28 6. non_recursive : [eval_speedpldi2_1/5] 0.03/0.28 7. non_recursive : [eval_speedpldi2_0/5] 0.03/0.28 8. non_recursive : [eval_speedpldi2_bb0_in/5] 0.03/0.28 9. non_recursive : [eval_speedpldi2_start/5] 0.03/0.28 0.03/0.28 #### Obtained direct recursion through partial evaluation 0.03/0.28 0. SCC is partially evaluated into eval_speedpldi2_bb1_in/6 0.03/0.28 1. SCC is completely evaluated into other SCCs 0.03/0.28 2. SCC is completely evaluated into other SCCs 0.03/0.28 3. SCC is completely evaluated into other SCCs 0.03/0.28 4. SCC is partially evaluated into eval_speedpldi2_bb1_in_loop_cont/6 0.03/0.28 5. SCC is partially evaluated into eval_speedpldi2_2/5 0.03/0.28 6. SCC is completely evaluated into other SCCs 0.03/0.28 7. SCC is completely evaluated into other SCCs 0.03/0.28 8. SCC is completely evaluated into other SCCs 0.03/0.28 9. SCC is partially evaluated into eval_speedpldi2_start/5 0.03/0.28 0.03/0.28 Control-Flow Refinement of Cost Relations 0.03/0.28 ===================================== 0.03/0.28 0.03/0.28 ### Specialization of cost equations eval_speedpldi2_bb1_in/6 0.03/0.28 * CE 8 is refined into CE [11] 0.03/0.28 * CE 7 is refined into CE [12] 0.03/0.28 * CE 6 is refined into CE [13] 0.03/0.28 * CE 5 is refined into CE [14] 0.03/0.28 0.03/0.28 0.03/0.28 ### Cost equations --> "Loop" of eval_speedpldi2_bb1_in/6 0.03/0.28 * CEs [13] --> Loop 11 0.03/0.28 * CEs [14] --> Loop 12 0.03/0.28 * CEs [11] --> Loop 13 0.03/0.28 * CEs [12] --> Loop 14 0.03/0.28 0.03/0.28 ### Ranking functions of CR eval_speedpldi2_bb1_in(V_m,V_v1_0,V_v2_0,B,C,D) 0.03/0.28 * RF of phase [11,12]: [2*V_v1_0+V_v2_0-1] 0.03/0.28 0.03/0.28 #### Partial ranking functions of CR eval_speedpldi2_bb1_in(V_m,V_v1_0,V_v2_0,B,C,D) 0.03/0.28 * Partial RF of phase [11,12]: 0.03/0.28 - RF of loop [11:1]: 0.03/0.28 V_m-V_v2_0 depends on loops [12:1] 0.03/0.28 V_v1_0 0.03/0.28 - RF of loop [12:1]: 0.03/0.28 -V_m+V_v2_0+1 depends on loops [11:1] 0.03/0.28 V_v2_0 depends on loops [11:1] 0.03/0.28 0.03/0.28 0.03/0.28 ### Specialization of cost equations eval_speedpldi2_bb1_in_loop_cont/6 0.03/0.28 * CE 10 is refined into CE [15] 0.03/0.28 * CE 9 is refined into CE [16] 0.03/0.28 0.03/0.28 0.03/0.28 ### Cost equations --> "Loop" of eval_speedpldi2_bb1_in_loop_cont/6 0.03/0.28 * CEs [15] --> Loop 15 0.03/0.28 * CEs [16] --> Loop 16 0.03/0.28 0.03/0.28 ### Ranking functions of CR eval_speedpldi2_bb1_in_loop_cont(A,B,C,D,E,F) 0.03/0.28 0.03/0.28 #### Partial ranking functions of CR eval_speedpldi2_bb1_in_loop_cont(A,B,C,D,E,F) 0.03/0.28 0.03/0.28 0.03/0.28 ### Specialization of cost equations eval_speedpldi2_2/5 0.03/0.28 * CE 4 is refined into CE [17,18,19,20] 0.03/0.28 * CE 2 is refined into CE [21] 0.03/0.28 * CE 3 is refined into CE [22] 0.03/0.28 0.03/0.28 0.03/0.28 ### Cost equations --> "Loop" of eval_speedpldi2_2/5 0.03/0.28 * CEs [18,20] --> Loop 17 0.03/0.28 * CEs [19] --> Loop 18 0.03/0.28 * CEs [21] --> Loop 19 0.03/0.28 * CEs [22] --> Loop 20 0.03/0.28 * CEs [17] --> Loop 21 0.03/0.28 0.03/0.28 ### Ranking functions of CR eval_speedpldi2_2(V_m,V_n,V_v1_0,V_v2_0,B) 0.03/0.28 0.03/0.28 #### Partial ranking functions of CR eval_speedpldi2_2(V_m,V_n,V_v1_0,V_v2_0,B) 0.03/0.28 0.03/0.28 0.03/0.28 ### Specialization of cost equations eval_speedpldi2_start/5 0.03/0.28 * CE 1 is refined into CE [23,24,25,26,27] 0.03/0.28 0.03/0.28 0.03/0.28 ### Cost equations --> "Loop" of eval_speedpldi2_start/5 0.03/0.28 * CEs [27] --> Loop 22 0.03/0.28 * CEs [26] --> Loop 23 0.03/0.28 * CEs [25] --> Loop 24 0.03/0.28 * CEs [24] --> Loop 25 0.03/0.28 * CEs [23] --> Loop 26 0.03/0.28 0.03/0.28 ### Ranking functions of CR eval_speedpldi2_start(V_m,V_n,V_v1_0,V_v2_0,B) 0.03/0.28 0.03/0.28 #### Partial ranking functions of CR eval_speedpldi2_start(V_m,V_n,V_v1_0,V_v2_0,B) 0.03/0.28 0.03/0.28 0.03/0.28 Computing Bounds 0.03/0.28 ===================================== 0.03/0.28 0.03/0.28 #### Cost of chains of eval_speedpldi2_bb1_in(V_m,V_v1_0,V_v2_0,B,C,D): 0.03/0.28 * Chain [[11,12],14]: 1*it(11)+1*it(12)+0 0.03/0.28 Such that:it(11) =< V_v1_0 0.03/0.28 aux(16) =< 2*V_v1_0+V_v2_0 0.03/0.28 aux(17) =< 2*V_v1_0+V_v2_0-D 0.03/0.28 it(11) =< aux(16) 0.03/0.28 it(12) =< aux(16) 0.03/0.28 it(11) =< aux(17) 0.03/0.28 it(12) =< aux(17) 0.03/0.28 0.03/0.28 with precondition: [B=2,C=0,V_m>=1,V_v1_0>=1,V_v2_0>=0,V_m>=D,V_v1_0+V_v2_0>=D] 0.03/0.28 0.03/0.28 * Chain [[11,12],13]: 1*it(11)+1*it(12)+0 0.03/0.28 Such that:it(11) =< V_v1_0 0.03/0.28 aux(20) =< 2*V_v1_0+V_v2_0 0.03/0.28 it(11) =< aux(20) 0.03/0.28 it(12) =< aux(20) 0.03/0.28 0.03/0.28 with precondition: [B=3,V_m>=1,V_v1_0>=1,V_v2_0>=0] 0.03/0.28 0.03/0.28 * Chain [14]: 0 0.03/0.28 with precondition: [V_v1_0=0,B=2,C=0,V_v2_0=D,V_m>=1,V_v2_0>=0] 0.03/0.28 0.03/0.28 * Chain [13]: 0 0.03/0.28 with precondition: [B=3,V_m>=1,V_v1_0>=0,V_v2_0>=0] 0.03/0.28 0.03/0.28 0.03/0.28 #### Cost of chains of eval_speedpldi2_bb1_in_loop_cont(A,B,C,D,E,F): 0.03/0.28 * Chain [16]: 0 0.03/0.28 with precondition: [A=2,B>=1,C>=0] 0.03/0.28 0.03/0.28 * Chain [15]: 0 0.03/0.28 with precondition: [A=3,B>=1,C>=0] 0.03/0.28 0.03/0.28 0.03/0.28 #### Cost of chains of eval_speedpldi2_2(V_m,V_n,V_v1_0,V_v2_0,B): 0.03/0.28 * Chain [21]: 0 0.03/0.28 with precondition: [V_n=0,V_m>=1] 0.03/0.28 0.03/0.28 * Chain [20]: 0 0.03/0.28 with precondition: [0>=V_m] 0.03/0.28 0.03/0.28 * Chain [19]: 0 0.03/0.28 with precondition: [0>=V_n+1] 0.03/0.28 0.03/0.28 * Chain [18]: 0 0.03/0.28 with precondition: [V_m>=1,V_n>=0] 0.03/0.28 0.03/0.28 * Chain [17]: 2*s(1)+2*s(4)+0 0.03/0.28 Such that:aux(21) =< V_n 0.03/0.28 aux(22) =< 2*V_n 0.03/0.28 s(1) =< aux(21) 0.03/0.28 s(1) =< aux(22) 0.03/0.28 s(4) =< aux(22) 0.03/0.28 0.03/0.28 with precondition: [V_m>=1,V_n>=1] 0.03/0.28 0.03/0.28 0.03/0.28 #### Cost of chains of eval_speedpldi2_start(V_m,V_n,V_v1_0,V_v2_0,B): 0.03/0.28 * Chain [26]: 0 0.03/0.28 with precondition: [V_n=0,V_m>=1] 0.03/0.28 0.03/0.28 * Chain [25]: 0 0.03/0.28 with precondition: [0>=V_m] 0.03/0.28 0.03/0.28 * Chain [24]: 0 0.03/0.28 with precondition: [0>=V_n+1] 0.03/0.28 0.03/0.28 * Chain [23]: 0 0.03/0.28 with precondition: [V_m>=1,V_n>=0] 0.03/0.28 0.03/0.28 * Chain [22]: 2*s(10)+2*s(11)+0 0.03/0.28 Such that:s(8) =< V_n 0.03/0.28 s(9) =< 2*V_n 0.03/0.28 s(10) =< s(8) 0.03/0.28 s(10) =< s(9) 0.03/0.28 s(11) =< s(9) 0.03/0.28 0.03/0.28 with precondition: [V_m>=1,V_n>=1] 0.03/0.28 0.03/0.28 0.03/0.28 Closed-form bounds of eval_speedpldi2_start(V_m,V_n,V_v1_0,V_v2_0,B): 0.03/0.28 ------------------------------------- 0.03/0.28 * Chain [26] with precondition: [V_n=0,V_m>=1] 0.03/0.28 - Upper bound: 0 0.03/0.28 - Complexity: constant 0.03/0.28 * Chain [25] with precondition: [0>=V_m] 0.03/0.28 - Upper bound: 0 0.03/0.28 - Complexity: constant 0.03/0.28 * Chain [24] with precondition: [0>=V_n+1] 0.03/0.28 - Upper bound: 0 0.03/0.28 - Complexity: constant 0.03/0.28 * Chain [23] with precondition: [V_m>=1,V_n>=0] 0.03/0.28 - Upper bound: 0 0.03/0.28 - Complexity: constant 0.03/0.28 * Chain [22] with precondition: [V_m>=1,V_n>=1] 0.03/0.28 - Upper bound: 6*V_n 0.03/0.28 - Complexity: n 0.03/0.28 0.03/0.28 ### Maximum cost of eval_speedpldi2_start(V_m,V_n,V_v1_0,V_v2_0,B): nat(2*V_n)*2+nat(V_n)*2 0.03/0.28 Asymptotic class: n 0.03/0.28 * Total analysis performed in 205 ms. 0.03/0.28 0.03/0.38 EOF