0.05/0.19 WORST_CASE(?,O(n^1)) 0.05/0.19 0.05/0.19 Preprocessing Cost Relations 0.05/0.19 ===================================== 0.05/0.19 0.05/0.19 #### Computed strongly connected components 0.05/0.19 0. recursive : [eval_t15_bb3_in/3,eval_t15_bb4_in/3] 0.05/0.19 1. recursive : [eval_t15_bb1_in/3,eval_t15_bb2_in/3,eval_t15_bb3_in_loop_cont/4] 0.05/0.19 2. non_recursive : [eval_t15_stop/1] 0.05/0.19 3. non_recursive : [eval_t15_bb5_in/1] 0.05/0.19 4. non_recursive : [eval_t15_bb1_in_loop_cont/2] 0.05/0.19 5. non_recursive : [eval_t15_bb0_in/3] 0.05/0.19 6. non_recursive : [eval_t15_start/3] 0.05/0.19 0.05/0.19 #### Obtained direct recursion through partial evaluation 0.05/0.19 0. SCC is partially evaluated into eval_t15_bb3_in/3 0.05/0.19 1. SCC is partially evaluated into eval_t15_bb1_in/3 0.05/0.19 2. SCC is completely evaluated into other SCCs 0.05/0.19 3. SCC is completely evaluated into other SCCs 0.05/0.19 4. SCC is completely evaluated into other SCCs 0.05/0.19 5. SCC is partially evaluated into eval_t15_bb0_in/3 0.05/0.19 6. SCC is partially evaluated into eval_t15_start/3 0.05/0.19 0.05/0.19 Control-Flow Refinement of Cost Relations 0.05/0.19 ===================================== 0.05/0.19 0.05/0.19 ### Specialization of cost equations eval_t15_bb3_in/3 0.05/0.19 * CE 7 is refined into CE [8] 0.05/0.19 * CE 6 is refined into CE [9] 0.05/0.19 0.05/0.19 0.05/0.19 ### Cost equations --> "Loop" of eval_t15_bb3_in/3 0.05/0.19 * CEs [9] --> Loop 8 0.05/0.19 * CEs [8] --> Loop 9 0.05/0.19 0.05/0.19 ### Ranking functions of CR eval_t15_bb3_in(V__0,V_z_0,B) 0.05/0.19 * RF of phase [8]: [V_z_0] 0.05/0.19 0.05/0.19 #### Partial ranking functions of CR eval_t15_bb3_in(V__0,V_z_0,B) 0.05/0.19 * Partial RF of phase [8]: 0.05/0.19 - RF of loop [8:1]: 0.05/0.19 V_z_0 0.05/0.19 0.05/0.19 0.05/0.19 ### Specialization of cost equations eval_t15_bb1_in/3 0.05/0.19 * CE 5 is refined into CE [10] 0.05/0.19 * CE 4 is refined into CE [11,12] 0.05/0.19 0.05/0.19 0.05/0.19 ### Cost equations --> "Loop" of eval_t15_bb1_in/3 0.05/0.19 * CEs [12] --> Loop 10 0.05/0.19 * CEs [11] --> Loop 11 0.05/0.19 * CEs [10] --> Loop 12 0.05/0.19 0.05/0.19 ### Ranking functions of CR eval_t15_bb1_in(V_y,V__0,B) 0.05/0.19 * RF of phase [10]: [V__0/2-1/2,-V_y/2+V__0/2] 0.05/0.19 * RF of phase [11]: [V__0] 0.05/0.19 0.05/0.19 #### Partial ranking functions of CR eval_t15_bb1_in(V_y,V__0,B) 0.05/0.19 * Partial RF of phase [10]: 0.05/0.19 - RF of loop [10:1]: 0.05/0.19 V__0/2-1/2 0.05/0.19 -V_y/2+V__0/2 0.05/0.19 * Partial RF of phase [11]: 0.05/0.19 - RF of loop [11:1]: 0.05/0.19 V__0 0.05/0.19 0.05/0.19 0.05/0.19 ### Specialization of cost equations eval_t15_bb0_in/3 0.05/0.19 * CE 3 is refined into CE [13,14,15] 0.05/0.19 * CE 2 is refined into CE [16] 0.05/0.19 0.05/0.19 0.05/0.19 ### Cost equations --> "Loop" of eval_t15_bb0_in/3 0.05/0.19 * CEs [15] --> Loop 13 0.05/0.19 * CEs [14] --> Loop 14 0.05/0.19 * CEs [16] --> Loop 15 0.05/0.19 * CEs [13] --> Loop 16 0.05/0.19 0.05/0.19 ### Ranking functions of CR eval_t15_bb0_in(V_x,V_y,B) 0.05/0.19 0.05/0.19 #### Partial ranking functions of CR eval_t15_bb0_in(V_x,V_y,B) 0.05/0.19 0.05/0.19 0.05/0.19 ### Specialization of cost equations eval_t15_start/3 0.05/0.19 * CE 1 is refined into CE [17,18,19,20] 0.05/0.19 0.05/0.19 0.05/0.19 ### Cost equations --> "Loop" of eval_t15_start/3 0.05/0.19 * CEs [20] --> Loop 17 0.05/0.19 * CEs [19] --> Loop 18 0.05/0.19 * CEs [18] --> Loop 19 0.05/0.19 * CEs [17] --> Loop 20 0.05/0.19 0.05/0.19 ### Ranking functions of CR eval_t15_start(V_x,V_y,B) 0.05/0.19 0.05/0.19 #### Partial ranking functions of CR eval_t15_start(V_x,V_y,B) 0.05/0.19 0.05/0.19 0.05/0.19 Computing Bounds 0.05/0.19 ===================================== 0.05/0.19 0.05/0.19 #### Cost of chains of eval_t15_bb3_in(V__0,V_z_0,B): 0.05/0.19 * Chain [[8],9]: 1*it(8)+0 0.05/0.19 Such that:it(8) =< V_z_0 0.05/0.19 0.05/0.19 with precondition: [B=2,V_z_0>=1,V__0>=V_z_0+1] 0.05/0.19 0.05/0.19 * Chain [9]: 0 0.05/0.19 with precondition: [V_z_0=0,B=2,V__0>=1] 0.05/0.19 0.05/0.19 0.05/0.19 #### Cost of chains of eval_t15_bb1_in(V_y,V__0,B): 0.05/0.19 * Chain [[11],12]: 1*it(11)+0 0.05/0.19 Such that:it(11) =< V__0 0.05/0.19 0.05/0.19 with precondition: [V_y=0,B=3,V__0>=1] 0.05/0.19 0.05/0.19 * Chain [[10],12]: 1*it(10)+1*s(3)+0 0.05/0.19 Such that:it(10) =< -V_y/2+V__0/2 0.05/0.19 s(3) =< V__0 0.05/0.19 0.05/0.19 with precondition: [B=3,V_y>=1,V__0>=V_y+1] 0.05/0.19 0.05/0.19 * Chain [12]: 0 0.05/0.19 with precondition: [B=3,V_y>=0,V_y>=V__0] 0.05/0.19 0.05/0.19 0.05/0.19 #### Cost of chains of eval_t15_bb0_in(V_x,V_y,B): 0.05/0.19 * Chain [16]: 1*s(4)+0 0.05/0.19 Such that:s(4) =< V_x 0.05/0.19 0.05/0.19 with precondition: [V_y=0,V_x>=1] 0.05/0.19 0.05/0.19 * Chain [15]: 0 0.05/0.19 with precondition: [0>=V_y+1] 0.05/0.19 0.05/0.19 * Chain [14]: 0 0.05/0.19 with precondition: [V_y>=0,V_y>=V_x] 0.05/0.19 0.05/0.19 * Chain [13]: 1*s(5)+1*s(6)+0 0.05/0.19 Such that:s(6) =< V_x 0.05/0.19 s(5) =< V_x/2-V_y/2 0.05/0.19 0.05/0.19 with precondition: [V_y>=1,V_x>=V_y+1] 0.05/0.19 0.05/0.19 0.05/0.19 #### Cost of chains of eval_t15_start(V_x,V_y,B): 0.05/0.19 * Chain [20]: 1*s(7)+0 0.05/0.19 Such that:s(7) =< V_x 0.05/0.19 0.05/0.19 with precondition: [V_y=0,V_x>=1] 0.05/0.19 0.05/0.19 * Chain [19]: 0 0.05/0.19 with precondition: [0>=V_y+1] 0.05/0.19 0.05/0.19 * Chain [18]: 0 0.05/0.19 with precondition: [V_y>=0,V_y>=V_x] 0.05/0.19 0.05/0.19 * Chain [17]: 1*s(8)+1*s(9)+0 0.05/0.19 Such that:s(8) =< V_x 0.05/0.19 s(9) =< V_x/2-V_y/2 0.05/0.19 0.05/0.19 with precondition: [V_y>=1,V_x>=V_y+1] 0.05/0.19 0.05/0.19 0.05/0.19 Closed-form bounds of eval_t15_start(V_x,V_y,B): 0.05/0.19 ------------------------------------- 0.05/0.19 * Chain [20] with precondition: [V_y=0,V_x>=1] 0.05/0.19 - Upper bound: V_x 0.05/0.19 - Complexity: n 0.05/0.19 * Chain [19] with precondition: [0>=V_y+1] 0.05/0.19 - Upper bound: 0 0.05/0.19 - Complexity: constant 0.05/0.19 * Chain [18] with precondition: [V_y>=0,V_y>=V_x] 0.05/0.19 - Upper bound: 0 0.05/0.19 - Complexity: constant 0.05/0.19 * Chain [17] with precondition: [V_y>=1,V_x>=V_y+1] 0.05/0.19 - Upper bound: 3/2*V_x-V_y/2 0.05/0.19 - Complexity: n 0.05/0.19 0.05/0.19 ### Maximum cost of eval_t15_start(V_x,V_y,B): nat(V_x/2-V_y/2)+nat(V_x) 0.05/0.19 Asymptotic class: n 0.05/0.19 * Total analysis performed in 116 ms. 0.05/0.19 0.05/0.29 EOF