0.06/0.25 WORST_CASE(?,O(n^1)) 0.06/0.25 0.06/0.25 Preprocessing Cost Relations 0.06/0.25 ===================================== 0.06/0.25 0.06/0.25 #### Computed strongly connected components 0.06/0.25 0. recursive : [eval_speedSingleSingle2_0/5,eval_speedSingleSingle2_1/6,eval_speedSingleSingle2_bb1_in/5,eval_speedSingleSingle2_bb2_in/6,eval_speedSingleSingle2_bb3_in/6,eval_speedSingleSingle2_bb4_in/6,eval_speedSingleSingle2_bb5_in/6] 0.06/0.25 1. non_recursive : [eval_speedSingleSingle2_stop/1] 0.06/0.25 2. non_recursive : [eval_speedSingleSingle2_bb6_in/1] 0.06/0.25 3. non_recursive : [eval_speedSingleSingle2_bb1_in_loop_cont/2] 0.06/0.25 4. non_recursive : [eval_speedSingleSingle2_bb0_in/3] 0.06/0.25 5. non_recursive : [eval_speedSingleSingle2_start/3] 0.06/0.25 0.06/0.25 #### Obtained direct recursion through partial evaluation 0.06/0.25 0. SCC is partially evaluated into eval_speedSingleSingle2_bb1_in/5 0.06/0.25 1. SCC is completely evaluated into other SCCs 0.06/0.25 2. SCC is completely evaluated into other SCCs 0.06/0.25 3. SCC is completely evaluated into other SCCs 0.06/0.25 4. SCC is partially evaluated into eval_speedSingleSingle2_bb0_in/3 0.06/0.25 5. SCC is partially evaluated into eval_speedSingleSingle2_start/3 0.06/0.25 0.06/0.25 Control-Flow Refinement of Cost Relations 0.06/0.25 ===================================== 0.06/0.25 0.06/0.25 ### Specialization of cost equations eval_speedSingleSingle2_bb1_in/5 0.06/0.25 * CE 7 is refined into CE [8] 0.06/0.25 * CE 5 is refined into CE [9] 0.06/0.25 * CE 6 is refined into CE [10] 0.06/0.25 0.06/0.25 0.06/0.25 ### Cost equations --> "Loop" of eval_speedSingleSingle2_bb1_in/5 0.06/0.25 * CEs [9] --> Loop 8 0.06/0.25 * CEs [10] --> Loop 9 0.06/0.25 * CEs [8] --> Loop 10 0.06/0.25 0.06/0.25 ### Ranking functions of CR eval_speedSingleSingle2_bb1_in(V_n,V_m,V_y_0,V_x_0,B) 0.06/0.25 * RF of phase [8]: [V_n-V_x_0,V_n-V_y_0] 0.06/0.25 * RF of phase [9]: [V_m-V_x_0,V_m-V_y_0] 0.06/0.25 0.06/0.25 #### Partial ranking functions of CR eval_speedSingleSingle2_bb1_in(V_n,V_m,V_y_0,V_x_0,B) 0.06/0.25 * Partial RF of phase [8]: 0.06/0.25 - RF of loop [8:1]: 0.06/0.25 V_n-V_x_0 0.06/0.25 V_n-V_y_0 0.06/0.25 * Partial RF of phase [9]: 0.06/0.25 - RF of loop [9:1]: 0.06/0.25 V_m-V_x_0 0.06/0.25 V_m-V_y_0 0.06/0.25 0.06/0.25 0.06/0.25 ### Specialization of cost equations eval_speedSingleSingle2_bb0_in/3 0.06/0.25 * CE 4 is refined into CE [11,12,13,14] 0.06/0.25 * CE 3 is refined into CE [15] 0.06/0.25 * CE 2 is refined into CE [16] 0.06/0.25 0.06/0.25 0.06/0.25 ### Cost equations --> "Loop" of eval_speedSingleSingle2_bb0_in/3 0.06/0.25 * CEs [14] --> Loop 11 0.06/0.25 * CEs [13] --> Loop 12 0.06/0.25 * CEs [11] --> Loop 13 0.06/0.25 * CEs [15] --> Loop 14 0.06/0.25 * CEs [16] --> Loop 15 0.06/0.25 * CEs [12] --> Loop 16 0.06/0.25 0.06/0.25 ### Ranking functions of CR eval_speedSingleSingle2_bb0_in(V_n,V_m,B) 0.06/0.25 0.06/0.25 #### Partial ranking functions of CR eval_speedSingleSingle2_bb0_in(V_n,V_m,B) 0.06/0.25 0.06/0.25 0.06/0.25 ### Specialization of cost equations eval_speedSingleSingle2_start/3 0.06/0.25 * CE 1 is refined into CE [17,18,19,20,21,22] 0.06/0.25 0.06/0.25 0.06/0.25 ### Cost equations --> "Loop" of eval_speedSingleSingle2_start/3 0.06/0.25 * CEs [22] --> Loop 17 0.06/0.25 * CEs [21] --> Loop 18 0.06/0.25 * CEs [20] --> Loop 19 0.06/0.25 * CEs [19] --> Loop 20 0.06/0.25 * CEs [18] --> Loop 21 0.06/0.25 * CEs [17] --> Loop 22 0.06/0.25 0.06/0.25 ### Ranking functions of CR eval_speedSingleSingle2_start(V_n,V_m,B) 0.06/0.25 0.06/0.25 #### Partial ranking functions of CR eval_speedSingleSingle2_start(V_n,V_m,B) 0.06/0.25 0.06/0.25 0.06/0.25 Computing Bounds 0.06/0.25 ===================================== 0.06/0.25 0.06/0.25 #### Cost of chains of eval_speedSingleSingle2_bb1_in(V_n,V_m,V_y_0,V_x_0,B): 0.06/0.25 * Chain [[9],10]: 1*it(9)+0 0.06/0.25 Such that:it(9) =< V_m-V_x_0 0.06/0.25 0.06/0.25 with precondition: [B=2,V_y_0=V_x_0,V_n>=0,V_y_0>=V_n,V_m>=V_y_0+1] 0.06/0.25 0.06/0.25 * Chain [[8],[9],10]: 1*it(8)+1*it(9)+0 0.06/0.25 Such that:it(9) =< -V_n+V_m 0.06/0.25 it(8) =< V_n-V_x_0 0.06/0.25 0.06/0.25 with precondition: [B=2,V_y_0=V_x_0,V_y_0>=0,V_m>=V_n+1,V_n>=V_y_0+1] 0.06/0.25 0.06/0.25 * Chain [[8],10]: 1*it(8)+0 0.06/0.25 Such that:it(8) =< V_n-V_y_0 0.06/0.25 0.06/0.25 with precondition: [B=2,V_y_0=V_x_0,V_m>=0,V_y_0>=0,V_n>=V_y_0+1] 0.06/0.25 0.06/0.25 * Chain [10]: 0 0.06/0.25 with precondition: [B=2,V_x_0=V_y_0,V_n>=0,V_m>=0,V_x_0>=0,V_m+V_n>=V_x_0] 0.06/0.25 0.06/0.25 0.06/0.25 #### Cost of chains of eval_speedSingleSingle2_bb0_in(V_n,V_m,B): 0.06/0.25 * Chain [16]: 1*s(1)+0 0.06/0.25 Such that:s(1) =< V_m 0.06/0.25 0.06/0.25 with precondition: [V_n=0,V_m>=1] 0.06/0.25 0.06/0.25 * Chain [15]: 0 0.06/0.25 with precondition: [0>=V_n+1] 0.06/0.25 0.06/0.25 * Chain [14]: 0 0.06/0.25 with precondition: [0>=V_m+1] 0.06/0.25 0.06/0.25 * Chain [13]: 0 0.06/0.25 with precondition: [V_n>=0,V_m>=0] 0.06/0.25 0.06/0.25 * Chain [12]: 1*s(2)+0 0.06/0.25 Such that:s(2) =< V_n 0.06/0.25 0.06/0.25 with precondition: [V_n>=1,V_m>=0] 0.06/0.25 0.06/0.25 * Chain [11]: 1*s(3)+1*s(4)+0 0.06/0.25 Such that:s(3) =< -V_n+V_m 0.06/0.25 s(4) =< V_n 0.06/0.25 0.06/0.25 with precondition: [V_n>=1,V_m>=V_n+1] 0.06/0.25 0.06/0.25 0.06/0.25 #### Cost of chains of eval_speedSingleSingle2_start(V_n,V_m,B): 0.06/0.25 * Chain [22]: 1*s(5)+0 0.06/0.25 Such that:s(5) =< V_m 0.06/0.25 0.06/0.25 with precondition: [V_n=0,V_m>=1] 0.06/0.25 0.06/0.25 * Chain [21]: 0 0.06/0.25 with precondition: [0>=V_n+1] 0.06/0.25 0.06/0.25 * Chain [20]: 0 0.06/0.25 with precondition: [0>=V_m+1] 0.06/0.25 0.06/0.25 * Chain [19]: 0 0.06/0.25 with precondition: [V_n>=0,V_m>=0] 0.06/0.25 0.06/0.25 * Chain [18]: 1*s(6)+0 0.06/0.25 Such that:s(6) =< V_n 0.06/0.25 0.06/0.25 with precondition: [V_n>=1,V_m>=0] 0.06/0.25 0.06/0.25 * Chain [17]: 1*s(7)+1*s(8)+0 0.06/0.25 Such that:s(7) =< -V_n+V_m 0.06/0.25 s(8) =< V_n 0.06/0.25 0.06/0.25 with precondition: [V_n>=1,V_m>=V_n+1] 0.06/0.25 0.06/0.25 0.06/0.25 Closed-form bounds of eval_speedSingleSingle2_start(V_n,V_m,B): 0.06/0.25 ------------------------------------- 0.06/0.25 * Chain [22] with precondition: [V_n=0,V_m>=1] 0.06/0.25 - Upper bound: V_m 0.06/0.25 - Complexity: n 0.06/0.25 * Chain [21] with precondition: [0>=V_n+1] 0.06/0.25 - Upper bound: 0 0.06/0.25 - Complexity: constant 0.06/0.25 * Chain [20] with precondition: [0>=V_m+1] 0.06/0.25 - Upper bound: 0 0.06/0.25 - Complexity: constant 0.06/0.25 * Chain [19] with precondition: [V_n>=0,V_m>=0] 0.06/0.25 - Upper bound: 0 0.06/0.25 - Complexity: constant 0.06/0.25 * Chain [18] with precondition: [V_n>=1,V_m>=0] 0.06/0.25 - Upper bound: V_n 0.06/0.25 - Complexity: n 0.06/0.25 * Chain [17] with precondition: [V_n>=1,V_m>=V_n+1] 0.06/0.25 - Upper bound: V_m 0.06/0.25 - Complexity: n 0.06/0.25 0.06/0.25 ### Maximum cost of eval_speedSingleSingle2_start(V_n,V_m,B): max([nat(V_m),nat(-V_n+V_m)+nat(V_n)]) 0.06/0.25 Asymptotic class: n 0.06/0.25 * Total analysis performed in 171 ms. 0.06/0.25 0.06/0.35 EOF