0.03/0.14 WORST_CASE(?,O(n^1)) 0.03/0.14 0.03/0.14 Preprocessing Cost Relations 0.03/0.14 ===================================== 0.03/0.14 0.03/0.14 #### Computed strongly connected components 0.03/0.14 0. recursive : [eval_abc_bb1_in/4,eval_abc_bb2_in/4] 0.03/0.14 1. non_recursive : [eval_abc_stop/4] 0.03/0.14 2. non_recursive : [eval_abc_bb3_in/4] 0.03/0.14 3. non_recursive : [exit_location/1] 0.03/0.14 4. non_recursive : [eval_abc_bb1_in_loop_cont/5] 0.03/0.14 5. non_recursive : [eval_abc_4/4] 0.03/0.14 6. non_recursive : [eval_abc_3/4] 0.03/0.14 7. non_recursive : [eval_abc_2/4] 0.03/0.14 8. non_recursive : [eval_abc_1/4] 0.03/0.14 9. non_recursive : [eval_abc_0/4] 0.03/0.14 10. non_recursive : [eval_abc_bb0_in/4] 0.03/0.14 11. non_recursive : [eval_abc_start/4] 0.03/0.14 0.03/0.14 #### Obtained direct recursion through partial evaluation 0.03/0.14 0. SCC is partially evaluated into eval_abc_bb1_in/4 0.03/0.14 1. SCC is completely evaluated into other SCCs 0.03/0.14 2. SCC is completely evaluated into other SCCs 0.03/0.14 3. SCC is completely evaluated into other SCCs 0.03/0.14 4. SCC is partially evaluated into eval_abc_bb1_in_loop_cont/5 0.03/0.14 5. SCC is partially evaluated into eval_abc_4/4 0.03/0.14 6. SCC is completely evaluated into other SCCs 0.03/0.14 7. SCC is completely evaluated into other SCCs 0.03/0.14 8. SCC is completely evaluated into other SCCs 0.03/0.14 9. SCC is completely evaluated into other SCCs 0.03/0.14 10. SCC is completely evaluated into other SCCs 0.03/0.14 11. SCC is partially evaluated into eval_abc_start/4 0.03/0.14 0.03/0.14 Control-Flow Refinement of Cost Relations 0.03/0.14 ===================================== 0.03/0.14 0.03/0.14 ### Specialization of cost equations eval_abc_bb1_in/4 0.03/0.14 * CE 5 is refined into CE [8] 0.03/0.14 * CE 4 is refined into CE [9] 0.03/0.14 * CE 3 is refined into CE [10] 0.03/0.14 0.03/0.14 0.03/0.14 ### Cost equations --> "Loop" of eval_abc_bb1_in/4 0.03/0.14 * CEs [10] --> Loop 8 0.03/0.14 * CEs [8] --> Loop 9 0.03/0.14 * CEs [9] --> Loop 10 0.03/0.14 0.03/0.14 ### Ranking functions of CR eval_abc_bb1_in(V_b,V_i_0,B,C) 0.03/0.14 * RF of phase [8]: [V_b-V_i_0+1] 0.03/0.14 0.03/0.14 #### Partial ranking functions of CR eval_abc_bb1_in(V_b,V_i_0,B,C) 0.03/0.14 * Partial RF of phase [8]: 0.03/0.14 - RF of loop [8:1]: 0.03/0.14 V_b-V_i_0+1 0.03/0.14 0.03/0.14 0.03/0.14 ### Specialization of cost equations eval_abc_bb1_in_loop_cont/5 0.03/0.14 * CE 7 is refined into CE [11] 0.03/0.14 * CE 6 is refined into CE [12] 0.03/0.14 0.03/0.14 0.03/0.14 ### Cost equations --> "Loop" of eval_abc_bb1_in_loop_cont/5 0.03/0.14 * CEs [11] --> Loop 11 0.03/0.14 * CEs [12] --> Loop 12 0.03/0.14 0.03/0.14 ### Ranking functions of CR eval_abc_bb1_in_loop_cont(A,B,C,D,E) 0.03/0.14 0.03/0.14 #### Partial ranking functions of CR eval_abc_bb1_in_loop_cont(A,B,C,D,E) 0.03/0.14 0.03/0.14 0.03/0.14 ### Specialization of cost equations eval_abc_4/4 0.03/0.14 * CE 2 is refined into CE [13,14,15,16] 0.03/0.14 0.03/0.14 0.03/0.14 ### Cost equations --> "Loop" of eval_abc_4/4 0.03/0.14 * CEs [14] --> Loop 13 0.03/0.14 * CEs [13,16] --> Loop 14 0.03/0.14 * CEs [15] --> Loop 15 0.03/0.14 0.03/0.14 ### Ranking functions of CR eval_abc_4(V_a,V_b,V_i_0,B) 0.03/0.14 0.03/0.14 #### Partial ranking functions of CR eval_abc_4(V_a,V_b,V_i_0,B) 0.03/0.14 0.03/0.14 0.03/0.14 ### Specialization of cost equations eval_abc_start/4 0.03/0.14 * CE 1 is refined into CE [17,18,19] 0.03/0.14 0.03/0.14 0.03/0.14 ### Cost equations --> "Loop" of eval_abc_start/4 0.03/0.14 * CEs [19] --> Loop 16 0.03/0.14 * CEs [18] --> Loop 17 0.03/0.14 * CEs [17] --> Loop 18 0.03/0.14 0.03/0.14 ### Ranking functions of CR eval_abc_start(V_a,V_b,V_i_0,B) 0.03/0.14 0.03/0.14 #### Partial ranking functions of CR eval_abc_start(V_a,V_b,V_i_0,B) 0.03/0.14 0.03/0.14 0.03/0.14 Computing Bounds 0.03/0.14 ===================================== 0.03/0.14 0.03/0.14 #### Cost of chains of eval_abc_bb1_in(V_b,V_i_0,B,C): 0.03/0.14 * Chain [[8],10]: 1*it(8)+0 0.03/0.14 Such that:it(8) =< V_b-V_i_0+1 0.03/0.14 0.03/0.14 with precondition: [B=2,V_b+1=C,V_b>=V_i_0] 0.03/0.14 0.03/0.14 * Chain [[8],9]: 1*it(8)+0 0.03/0.14 Such that:it(8) =< V_b-V_i_0+1 0.03/0.14 0.03/0.14 with precondition: [B=3,V_b>=V_i_0] 0.03/0.14 0.03/0.14 * Chain [10]: 0 0.03/0.14 with precondition: [B=2,V_i_0=C,V_i_0>=V_b+1] 0.03/0.14 0.03/0.14 * Chain [9]: 0 0.03/0.14 with precondition: [B=3] 0.03/0.14 0.03/0.14 0.03/0.14 #### Cost of chains of eval_abc_bb1_in_loop_cont(A,B,C,D,E): 0.03/0.14 * Chain [12]: 0 0.03/0.14 with precondition: [A=2] 0.03/0.14 0.03/0.14 * Chain [11]: 0 0.03/0.14 with precondition: [A=3] 0.03/0.14 0.03/0.14 0.03/0.14 #### Cost of chains of eval_abc_4(V_a,V_b,V_i_0,B): 0.03/0.14 * Chain [15]: 0 0.03/0.14 with precondition: [] 0.03/0.14 0.03/0.14 * Chain [14]: 2*s(1)+0 0.03/0.14 Such that:aux(1) =< -V_a+V_b+1 0.03/0.14 s(1) =< aux(1) 0.03/0.14 0.03/0.14 with precondition: [V_b>=V_a] 0.03/0.14 0.03/0.14 * Chain [13]: 0 0.03/0.14 with precondition: [V_a>=V_b+1] 0.03/0.14 0.03/0.14 0.03/0.14 #### Cost of chains of eval_abc_start(V_a,V_b,V_i_0,B): 0.03/0.14 * Chain [18]: 0 0.03/0.14 with precondition: [] 0.03/0.14 0.03/0.14 * Chain [17]: 2*s(4)+0 0.03/0.14 Such that:s(3) =< -V_a+V_b+1 0.03/0.14 s(4) =< s(3) 0.03/0.14 0.03/0.14 with precondition: [V_b>=V_a] 0.03/0.14 0.03/0.14 * Chain [16]: 0 0.03/0.14 with precondition: [V_a>=V_b+1] 0.03/0.14 0.03/0.14 0.03/0.14 Closed-form bounds of eval_abc_start(V_a,V_b,V_i_0,B): 0.03/0.14 ------------------------------------- 0.03/0.14 * Chain [18] with precondition: [] 0.03/0.14 - Upper bound: 0 0.03/0.14 - Complexity: constant 0.03/0.14 * Chain [17] with precondition: [V_b>=V_a] 0.03/0.14 - Upper bound: -2*V_a+2*V_b+2 0.03/0.14 - Complexity: n 0.03/0.14 * Chain [16] with precondition: [V_a>=V_b+1] 0.03/0.14 - Upper bound: 0 0.03/0.14 - Complexity: constant 0.03/0.14 0.03/0.14 ### Maximum cost of eval_abc_start(V_a,V_b,V_i_0,B): nat(-V_a+V_b+1)*2 0.03/0.14 Asymptotic class: n 0.03/0.14 * Total analysis performed in 77 ms. 0.03/0.14 0.03/0.24 EOF