0.05/0.20 WORST_CASE(?,O(n^2)) 0.05/0.20 0.05/0.20 Preprocessing Cost Relations 0.05/0.20 ===================================== 0.05/0.20 0.05/0.20 #### Computed strongly connected components 0.05/0.20 0. recursive : [eval_speedNestedMultipleDep_bb3_in/4,eval_speedNestedMultipleDep_bb4_in/4] 0.05/0.20 1. recursive : [eval_speedNestedMultipleDep_bb1_in/4,eval_speedNestedMultipleDep_bb2_in/4,eval_speedNestedMultipleDep_bb3_in_loop_cont/5] 0.05/0.20 2. non_recursive : [eval_speedNestedMultipleDep_stop/1] 0.05/0.20 3. non_recursive : [eval_speedNestedMultipleDep_bb5_in/1] 0.05/0.20 4. non_recursive : [eval_speedNestedMultipleDep_bb1_in_loop_cont/2] 0.05/0.20 5. non_recursive : [eval_speedNestedMultipleDep_bb0_in/3] 0.05/0.20 6. non_recursive : [eval_speedNestedMultipleDep_start/3] 0.05/0.20 0.05/0.20 #### Obtained direct recursion through partial evaluation 0.05/0.20 0. SCC is partially evaluated into eval_speedNestedMultipleDep_bb3_in/4 0.05/0.20 1. SCC is partially evaluated into eval_speedNestedMultipleDep_bb1_in/4 0.05/0.20 2. SCC is completely evaluated into other SCCs 0.05/0.20 3. SCC is completely evaluated into other SCCs 0.05/0.20 4. SCC is completely evaluated into other SCCs 0.05/0.20 5. SCC is partially evaluated into eval_speedNestedMultipleDep_bb0_in/3 0.05/0.20 6. SCC is partially evaluated into eval_speedNestedMultipleDep_start/3 0.05/0.20 0.05/0.20 Control-Flow Refinement of Cost Relations 0.05/0.20 ===================================== 0.05/0.20 0.05/0.20 ### Specialization of cost equations eval_speedNestedMultipleDep_bb3_in/4 0.05/0.20 * CE 6 is refined into CE [7] 0.05/0.20 * CE 5 is refined into CE [8] 0.05/0.20 0.05/0.20 0.05/0.20 ### Cost equations --> "Loop" of eval_speedNestedMultipleDep_bb3_in/4 0.05/0.20 * CEs [8] --> Loop 7 0.05/0.20 * CEs [7] --> Loop 8 0.05/0.20 0.05/0.20 ### Ranking functions of CR eval_speedNestedMultipleDep_bb3_in(V_m,V_x_0,V_y_0,B) 0.05/0.20 * RF of phase [7]: [V_m-V_y_0] 0.05/0.20 0.05/0.20 #### Partial ranking functions of CR eval_speedNestedMultipleDep_bb3_in(V_m,V_x_0,V_y_0,B) 0.05/0.20 * Partial RF of phase [7]: 0.05/0.20 - RF of loop [7:1]: 0.05/0.20 V_m-V_y_0 0.05/0.20 0.05/0.20 0.05/0.20 ### Specialization of cost equations eval_speedNestedMultipleDep_bb1_in/4 0.05/0.20 * CE 4 is refined into CE [9] 0.05/0.20 * CE 3 is refined into CE [10,11] 0.05/0.20 0.05/0.20 0.05/0.20 ### Cost equations --> "Loop" of eval_speedNestedMultipleDep_bb1_in/4 0.05/0.20 * CEs [11] --> Loop 9 0.05/0.20 * CEs [10] --> Loop 10 0.05/0.20 * CEs [9] --> Loop 11 0.05/0.20 0.05/0.20 ### Ranking functions of CR eval_speedNestedMultipleDep_bb1_in(V_n,V_m,V_x_0,B) 0.05/0.20 * RF of phase [9]: [V_n-V_x_0] 0.05/0.20 * RF of phase [10]: [V_n-V_x_0] 0.05/0.20 0.05/0.20 #### Partial ranking functions of CR eval_speedNestedMultipleDep_bb1_in(V_n,V_m,V_x_0,B) 0.05/0.20 * Partial RF of phase [9]: 0.05/0.20 - RF of loop [9:1]: 0.05/0.20 V_n-V_x_0 0.05/0.20 * Partial RF of phase [10]: 0.05/0.20 - RF of loop [10:1]: 0.05/0.20 V_n-V_x_0 0.05/0.20 0.05/0.20 0.05/0.20 ### Specialization of cost equations eval_speedNestedMultipleDep_bb0_in/3 0.05/0.20 * CE 2 is refined into CE [12,13,14] 0.05/0.20 0.05/0.20 0.05/0.20 ### Cost equations --> "Loop" of eval_speedNestedMultipleDep_bb0_in/3 0.05/0.20 * CEs [13] --> Loop 12 0.05/0.20 * CEs [12] --> Loop 13 0.05/0.20 * CEs [14] --> Loop 14 0.05/0.20 0.05/0.20 ### Ranking functions of CR eval_speedNestedMultipleDep_bb0_in(V_n,V_m,B) 0.05/0.20 0.05/0.20 #### Partial ranking functions of CR eval_speedNestedMultipleDep_bb0_in(V_n,V_m,B) 0.05/0.20 0.05/0.20 0.05/0.20 ### Specialization of cost equations eval_speedNestedMultipleDep_start/3 0.05/0.20 * CE 1 is refined into CE [15,16,17] 0.05/0.20 0.05/0.20 0.05/0.20 ### Cost equations --> "Loop" of eval_speedNestedMultipleDep_start/3 0.05/0.20 * CEs [17] --> Loop 15 0.05/0.20 * CEs [16] --> Loop 16 0.05/0.20 * CEs [15] --> Loop 17 0.05/0.20 0.05/0.20 ### Ranking functions of CR eval_speedNestedMultipleDep_start(V_n,V_m,B) 0.05/0.20 0.05/0.20 #### Partial ranking functions of CR eval_speedNestedMultipleDep_start(V_n,V_m,B) 0.05/0.20 0.05/0.20 0.05/0.20 Computing Bounds 0.05/0.20 ===================================== 0.05/0.20 0.05/0.20 #### Cost of chains of eval_speedNestedMultipleDep_bb3_in(V_m,V_x_0,V_y_0,B): 0.05/0.20 * Chain [[7],8]: 1*it(7)+0 0.05/0.20 Such that:it(7) =< V_m-V_y_0 0.05/0.20 0.05/0.20 with precondition: [B=2,V_x_0>=0,V_y_0>=0,V_m>=V_y_0+1] 0.05/0.20 0.05/0.20 * Chain [8]: 0 0.05/0.20 with precondition: [B=2,V_x_0>=0,V_y_0>=0,V_y_0>=V_m] 0.05/0.20 0.05/0.20 0.05/0.20 #### Cost of chains of eval_speedNestedMultipleDep_bb1_in(V_n,V_m,V_x_0,B): 0.05/0.20 * Chain [[10],11]: 1*it(10)+0 0.05/0.20 Such that:it(10) =< V_n-V_x_0 0.05/0.20 0.05/0.20 with precondition: [B=3,0>=V_m,V_x_0>=0,V_n>=V_x_0+1] 0.05/0.20 0.05/0.20 * Chain [[9],11]: 1*it(9)+1*s(3)+0 0.05/0.20 Such that:it(9) =< V_n-V_x_0 0.05/0.20 aux(1) =< V_m 0.05/0.20 s(3) =< it(9)*aux(1) 0.05/0.20 0.05/0.20 with precondition: [B=3,V_m>=1,V_x_0>=0,V_n>=V_x_0+1] 0.05/0.20 0.05/0.20 * Chain [11]: 0 0.05/0.20 with precondition: [B=3,V_x_0>=0,V_x_0>=V_n] 0.05/0.20 0.05/0.20 0.05/0.20 #### Cost of chains of eval_speedNestedMultipleDep_bb0_in(V_n,V_m,B): 0.05/0.20 * Chain [14]: 0 0.05/0.20 with precondition: [0>=V_n] 0.05/0.20 0.05/0.20 * Chain [13]: 1*s(4)+0 0.05/0.20 Such that:s(4) =< V_n 0.05/0.20 0.05/0.20 with precondition: [0>=V_m,V_n>=1] 0.05/0.20 0.05/0.20 * Chain [12]: 1*s(5)+1*s(7)+0 0.05/0.20 Such that:s(5) =< V_n 0.05/0.20 s(6) =< V_m 0.05/0.20 s(7) =< s(5)*s(6) 0.05/0.20 0.05/0.20 with precondition: [V_n>=1,V_m>=1] 0.05/0.20 0.05/0.20 0.05/0.20 #### Cost of chains of eval_speedNestedMultipleDep_start(V_n,V_m,B): 0.05/0.20 * Chain [17]: 0 0.05/0.20 with precondition: [0>=V_n] 0.05/0.20 0.05/0.20 * Chain [16]: 1*s(8)+0 0.05/0.20 Such that:s(8) =< V_n 0.05/0.20 0.05/0.20 with precondition: [0>=V_m,V_n>=1] 0.05/0.20 0.05/0.20 * Chain [15]: 1*s(9)+1*s(11)+0 0.05/0.20 Such that:s(9) =< V_n 0.05/0.20 s(10) =< V_m 0.05/0.20 s(11) =< s(9)*s(10) 0.05/0.20 0.05/0.20 with precondition: [V_n>=1,V_m>=1] 0.05/0.20 0.05/0.20 0.05/0.20 Closed-form bounds of eval_speedNestedMultipleDep_start(V_n,V_m,B): 0.05/0.20 ------------------------------------- 0.05/0.20 * Chain [17] with precondition: [0>=V_n] 0.05/0.20 - Upper bound: 0 0.05/0.20 - Complexity: constant 0.05/0.20 * Chain [16] with precondition: [0>=V_m,V_n>=1] 0.05/0.20 - Upper bound: V_n 0.05/0.20 - Complexity: n 0.05/0.20 * Chain [15] with precondition: [V_n>=1,V_m>=1] 0.05/0.20 - Upper bound: V_m*V_n+V_n 0.05/0.20 - Complexity: n^2 0.05/0.20 0.05/0.20 ### Maximum cost of eval_speedNestedMultipleDep_start(V_n,V_m,B): nat(V_m)*nat(V_n)+nat(V_n) 0.05/0.20 Asymptotic class: n^2 0.05/0.20 * Total analysis performed in 128 ms. 0.05/0.20 0.05/0.30 EOF