0.04/0.17 WORST_CASE(?,O(n^1)) 0.04/0.17 0.04/0.17 Preprocessing Cost Relations 0.04/0.17 ===================================== 0.04/0.17 0.04/0.17 #### Computed strongly connected components 0.04/0.17 0. recursive : [eval_t16_bb3_in/3,eval_t16_bb4_in/3] 0.04/0.17 1. recursive : [eval_t16_bb1_in/3,eval_t16_bb2_in/3,eval_t16_bb3_in_loop_cont/4] 0.04/0.17 2. non_recursive : [eval_t16_stop/1] 0.04/0.17 3. non_recursive : [eval_t16_bb5_in/1] 0.04/0.17 4. non_recursive : [eval_t16_bb1_in_loop_cont/2] 0.04/0.17 5. non_recursive : [eval_t16_bb0_in/3] 0.04/0.17 6. non_recursive : [eval_t16_start/3] 0.04/0.17 0.04/0.17 #### Obtained direct recursion through partial evaluation 0.04/0.17 0. SCC is partially evaluated into eval_t16_bb3_in/3 0.04/0.17 1. SCC is partially evaluated into eval_t16_bb1_in/3 0.04/0.17 2. SCC is completely evaluated into other SCCs 0.04/0.17 3. SCC is completely evaluated into other SCCs 0.04/0.17 4. SCC is completely evaluated into other SCCs 0.04/0.17 5. SCC is partially evaluated into eval_t16_bb0_in/3 0.04/0.17 6. SCC is partially evaluated into eval_t16_start/3 0.04/0.17 0.04/0.17 Control-Flow Refinement of Cost Relations 0.04/0.17 ===================================== 0.04/0.17 0.04/0.17 ### Specialization of cost equations eval_t16_bb3_in/3 0.04/0.17 * CE 7 is refined into CE [8] 0.04/0.17 * CE 6 is refined into CE [9] 0.04/0.17 0.04/0.17 0.04/0.17 ### Cost equations --> "Loop" of eval_t16_bb3_in/3 0.04/0.17 * CEs [9] --> Loop 8 0.04/0.17 * CEs [8] --> Loop 9 0.04/0.17 0.04/0.17 ### Ranking functions of CR eval_t16_bb3_in(V__0,V_z_0,B) 0.04/0.17 * RF of phase [8]: [V_z_0] 0.04/0.17 0.04/0.17 #### Partial ranking functions of CR eval_t16_bb3_in(V__0,V_z_0,B) 0.04/0.17 * Partial RF of phase [8]: 0.04/0.17 - RF of loop [8:1]: 0.04/0.17 V_z_0 0.04/0.17 0.04/0.17 0.04/0.17 ### Specialization of cost equations eval_t16_bb1_in/3 0.04/0.17 * CE 5 is refined into CE [10] 0.04/0.17 * CE 4 is refined into CE [11] 0.04/0.17 0.04/0.17 0.04/0.17 ### Cost equations --> "Loop" of eval_t16_bb1_in/3 0.04/0.17 * CEs [11] --> Loop 10 0.04/0.17 * CEs [10] --> Loop 11 0.04/0.17 0.04/0.17 ### Ranking functions of CR eval_t16_bb1_in(V_y,V__0,B) 0.04/0.17 * RF of phase [10]: [V__0,-V_y+V__0] 0.04/0.17 0.04/0.17 #### Partial ranking functions of CR eval_t16_bb1_in(V_y,V__0,B) 0.04/0.17 * Partial RF of phase [10]: 0.04/0.17 - RF of loop [10:1]: 0.04/0.17 V__0 0.04/0.17 -V_y+V__0 0.04/0.17 0.04/0.17 0.04/0.17 ### Specialization of cost equations eval_t16_bb0_in/3 0.04/0.17 * CE 3 is refined into CE [12,13] 0.04/0.17 * CE 2 is refined into CE [14] 0.04/0.17 0.04/0.17 0.04/0.17 ### Cost equations --> "Loop" of eval_t16_bb0_in/3 0.04/0.17 * CEs [12] --> Loop 12 0.04/0.17 * CEs [13] --> Loop 13 0.04/0.17 * CEs [14] --> Loop 14 0.04/0.17 0.04/0.17 ### Ranking functions of CR eval_t16_bb0_in(V_x,V_y,B) 0.04/0.17 0.04/0.17 #### Partial ranking functions of CR eval_t16_bb0_in(V_x,V_y,B) 0.04/0.17 0.04/0.17 0.04/0.17 ### Specialization of cost equations eval_t16_start/3 0.04/0.17 * CE 1 is refined into CE [15,16,17] 0.04/0.17 0.04/0.17 0.04/0.17 ### Cost equations --> "Loop" of eval_t16_start/3 0.04/0.17 * CEs [17] --> Loop 15 0.04/0.17 * CEs [16] --> Loop 16 0.04/0.17 * CEs [15] --> Loop 17 0.04/0.17 0.04/0.17 ### Ranking functions of CR eval_t16_start(V_x,V_y,B) 0.04/0.17 0.04/0.17 #### Partial ranking functions of CR eval_t16_start(V_x,V_y,B) 0.04/0.17 0.04/0.17 0.04/0.17 Computing Bounds 0.04/0.17 ===================================== 0.04/0.17 0.04/0.17 #### Cost of chains of eval_t16_bb3_in(V__0,V_z_0,B): 0.04/0.17 * Chain [[8],9]: 1*it(8)+0 0.04/0.17 Such that:it(8) =< V_z_0 0.04/0.17 0.04/0.17 with precondition: [B=2,V__0>=1,V_z_0>=1,2*V__0+98>=V_z_0] 0.04/0.17 0.04/0.17 0.04/0.17 #### Cost of chains of eval_t16_bb1_in(V_y,V__0,B): 0.04/0.17 * Chain [[10],11]: 1*it(10)+1*s(3)+0 0.04/0.17 Such that:s(3) =< -98*V_y+100*V__0 0.04/0.17 it(10) =< -V_y+V__0 0.04/0.17 0.04/0.17 with precondition: [B=3,V_y>=0,V__0>=V_y+1] 0.04/0.17 0.04/0.17 * Chain [11]: 0 0.04/0.17 with precondition: [B=3,V_y>=0,V_y>=V__0] 0.04/0.17 0.04/0.17 0.04/0.17 #### Cost of chains of eval_t16_bb0_in(V_x,V_y,B): 0.04/0.17 * Chain [14]: 0 0.04/0.17 with precondition: [0>=V_y+1] 0.04/0.17 0.04/0.17 * Chain [13]: 0 0.04/0.17 with precondition: [V_y>=0,V_y>=V_x] 0.04/0.17 0.04/0.17 * Chain [12]: 1*s(4)+1*s(5)+0 0.04/0.17 Such that:s(5) =< V_x-V_y 0.04/0.17 s(4) =< 100*V_x-98*V_y 0.04/0.17 0.04/0.17 with precondition: [V_y>=0,V_x>=V_y+1] 0.04/0.17 0.04/0.17 0.04/0.17 #### Cost of chains of eval_t16_start(V_x,V_y,B): 0.04/0.17 * Chain [17]: 0 0.04/0.17 with precondition: [0>=V_y+1] 0.04/0.17 0.04/0.17 * Chain [16]: 0 0.04/0.17 with precondition: [V_y>=0,V_y>=V_x] 0.04/0.17 0.04/0.17 * Chain [15]: 1*s(6)+1*s(7)+0 0.04/0.17 Such that:s(6) =< V_x-V_y 0.04/0.17 s(7) =< 100*V_x-98*V_y 0.04/0.17 0.04/0.17 with precondition: [V_y>=0,V_x>=V_y+1] 0.04/0.17 0.04/0.17 0.04/0.17 Closed-form bounds of eval_t16_start(V_x,V_y,B): 0.04/0.17 ------------------------------------- 0.04/0.17 * Chain [17] with precondition: [0>=V_y+1] 0.04/0.17 - Upper bound: 0 0.04/0.17 - Complexity: constant 0.04/0.17 * Chain [16] with precondition: [V_y>=0,V_y>=V_x] 0.04/0.17 - Upper bound: 0 0.04/0.17 - Complexity: constant 0.04/0.17 * Chain [15] with precondition: [V_y>=0,V_x>=V_y+1] 0.04/0.17 - Upper bound: 101*V_x-99*V_y 0.04/0.17 - Complexity: n 0.04/0.17 0.04/0.17 ### Maximum cost of eval_t16_start(V_x,V_y,B): nat(100*V_x-98*V_y)+nat(V_x-V_y) 0.04/0.17 Asymptotic class: n 0.04/0.17 * Total analysis performed in 96 ms. 0.04/0.17 0.04/0.27 EOF