0.04/0.12 WORST_CASE(?,O(n^1)) 0.04/0.12 0.04/0.12 Preprocessing Cost Relations 0.04/0.12 ===================================== 0.04/0.12 0.04/0.12 #### Computed strongly connected components 0.04/0.12 0. recursive : [eval_easy2_bb1_in/3,eval_easy2_bb2_in/3] 0.04/0.12 1. non_recursive : [eval_easy2_stop/3] 0.04/0.12 2. non_recursive : [eval_easy2_bb3_in/3] 0.04/0.12 3. non_recursive : [exit_location/1] 0.04/0.12 4. non_recursive : [eval_easy2_bb1_in_loop_cont/4] 0.04/0.12 5. non_recursive : [eval_easy2_6/3] 0.04/0.12 6. non_recursive : [eval_easy2_5/3] 0.04/0.12 7. non_recursive : [eval_easy2_4/3] 0.04/0.12 8. non_recursive : [eval_easy2_3/3] 0.04/0.12 9. non_recursive : [eval_easy2_2/3] 0.04/0.12 10. non_recursive : [eval_easy2_1/3] 0.04/0.12 11. non_recursive : [eval_easy2_0/3] 0.04/0.12 12. non_recursive : [eval_easy2_bb0_in/3] 0.04/0.12 13. non_recursive : [eval_easy2_start/3] 0.04/0.12 0.04/0.12 #### Obtained direct recursion through partial evaluation 0.04/0.12 0. SCC is partially evaluated into eval_easy2_bb1_in/3 0.04/0.12 1. SCC is completely evaluated into other SCCs 0.04/0.12 2. SCC is completely evaluated into other SCCs 0.04/0.12 3. SCC is completely evaluated into other SCCs 0.04/0.12 4. SCC is partially evaluated into eval_easy2_bb1_in_loop_cont/4 0.04/0.12 5. SCC is partially evaluated into eval_easy2_6/3 0.04/0.12 6. SCC is completely evaluated into other SCCs 0.04/0.12 7. SCC is completely evaluated into other SCCs 0.04/0.12 8. SCC is completely evaluated into other SCCs 0.04/0.12 9. SCC is completely evaluated into other SCCs 0.04/0.12 10. SCC is completely evaluated into other SCCs 0.04/0.12 11. SCC is completely evaluated into other SCCs 0.04/0.12 12. SCC is completely evaluated into other SCCs 0.04/0.12 13. SCC is partially evaluated into eval_easy2_start/3 0.04/0.12 0.04/0.12 Control-Flow Refinement of Cost Relations 0.04/0.12 ===================================== 0.04/0.12 0.04/0.12 ### Specialization of cost equations eval_easy2_bb1_in/3 0.04/0.12 * CE 5 is refined into CE [8] 0.04/0.12 * CE 4 is refined into CE [9] 0.04/0.12 * CE 3 is refined into CE [10] 0.04/0.12 0.04/0.12 0.04/0.12 ### Cost equations --> "Loop" of eval_easy2_bb1_in/3 0.04/0.12 * CEs [10] --> Loop 8 0.04/0.12 * CEs [8] --> Loop 9 0.04/0.12 * CEs [9] --> Loop 10 0.04/0.12 0.04/0.12 ### Ranking functions of CR eval_easy2_bb1_in(V__0,B,C) 0.04/0.12 * RF of phase [8]: [V__0] 0.04/0.12 0.04/0.12 #### Partial ranking functions of CR eval_easy2_bb1_in(V__0,B,C) 0.04/0.12 * Partial RF of phase [8]: 0.04/0.12 - RF of loop [8:1]: 0.04/0.12 V__0 0.04/0.12 0.04/0.12 0.04/0.12 ### Specialization of cost equations eval_easy2_bb1_in_loop_cont/4 0.04/0.12 * CE 7 is refined into CE [11] 0.04/0.12 * CE 6 is refined into CE [12] 0.04/0.12 0.04/0.12 0.04/0.12 ### Cost equations --> "Loop" of eval_easy2_bb1_in_loop_cont/4 0.04/0.12 * CEs [11] --> Loop 11 0.04/0.12 * CEs [12] --> Loop 12 0.04/0.12 0.04/0.12 ### Ranking functions of CR eval_easy2_bb1_in_loop_cont(A,B,C,D) 0.04/0.12 0.04/0.12 #### Partial ranking functions of CR eval_easy2_bb1_in_loop_cont(A,B,C,D) 0.04/0.12 0.04/0.12 0.04/0.12 ### Specialization of cost equations eval_easy2_6/3 0.04/0.12 * CE 2 is refined into CE [13,14,15,16] 0.04/0.12 0.04/0.12 0.04/0.12 ### Cost equations --> "Loop" of eval_easy2_6/3 0.04/0.12 * CEs [13,16] --> Loop 13 0.04/0.12 * CEs [14] --> Loop 14 0.04/0.12 * CEs [15] --> Loop 15 0.04/0.12 0.04/0.12 ### Ranking functions of CR eval_easy2_6(V__0,V_z,B) 0.04/0.12 0.04/0.12 #### Partial ranking functions of CR eval_easy2_6(V__0,V_z,B) 0.04/0.12 0.04/0.12 0.04/0.12 ### Specialization of cost equations eval_easy2_start/3 0.04/0.12 * CE 1 is refined into CE [17,18,19] 0.04/0.12 0.04/0.12 0.04/0.12 ### Cost equations --> "Loop" of eval_easy2_start/3 0.04/0.12 * CEs [19] --> Loop 16 0.04/0.12 * CEs [18] --> Loop 17 0.04/0.12 * CEs [17] --> Loop 18 0.04/0.12 0.04/0.12 ### Ranking functions of CR eval_easy2_start(V__0,V_z,B) 0.04/0.12 0.04/0.12 #### Partial ranking functions of CR eval_easy2_start(V__0,V_z,B) 0.04/0.12 0.04/0.12 0.04/0.12 Computing Bounds 0.04/0.12 ===================================== 0.04/0.12 0.04/0.12 #### Cost of chains of eval_easy2_bb1_in(V__0,B,C): 0.04/0.12 * Chain [[8],10]: 1*it(8)+0 0.04/0.12 Such that:it(8) =< V__0 0.04/0.12 0.04/0.12 with precondition: [B=2,C=0,V__0>=1] 0.04/0.12 0.04/0.12 * Chain [[8],9]: 1*it(8)+0 0.04/0.12 Such that:it(8) =< V__0 0.04/0.12 0.04/0.12 with precondition: [B=3,V__0>=1] 0.04/0.12 0.04/0.12 * Chain [10]: 0 0.04/0.12 with precondition: [B=2,V__0=C,0>=V__0] 0.04/0.12 0.04/0.12 * Chain [9]: 0 0.04/0.12 with precondition: [B=3] 0.04/0.12 0.04/0.12 0.04/0.12 #### Cost of chains of eval_easy2_bb1_in_loop_cont(A,B,C,D): 0.04/0.12 * Chain [12]: 0 0.04/0.12 with precondition: [A=2] 0.04/0.12 0.04/0.12 * Chain [11]: 0 0.04/0.12 with precondition: [A=3] 0.04/0.12 0.04/0.12 0.04/0.12 #### Cost of chains of eval_easy2_6(V__0,V_z,B): 0.04/0.12 * Chain [15]: 0 0.04/0.12 with precondition: [] 0.04/0.12 0.04/0.12 * Chain [14]: 0 0.04/0.12 with precondition: [0>=V_z] 0.04/0.12 0.04/0.12 * Chain [13]: 2*s(1)+0 0.04/0.12 Such that:aux(1) =< V_z 0.04/0.12 s(1) =< aux(1) 0.04/0.12 0.04/0.12 with precondition: [V_z>=1] 0.04/0.12 0.04/0.12 0.04/0.12 #### Cost of chains of eval_easy2_start(V__0,V_z,B): 0.04/0.12 * Chain [18]: 0 0.04/0.12 with precondition: [] 0.04/0.12 0.04/0.12 * Chain [17]: 0 0.04/0.12 with precondition: [0>=V_z] 0.04/0.12 0.04/0.12 * Chain [16]: 2*s(4)+0 0.04/0.12 Such that:s(3) =< V_z 0.04/0.12 s(4) =< s(3) 0.04/0.12 0.04/0.12 with precondition: [V_z>=1] 0.04/0.12 0.04/0.12 0.04/0.12 Closed-form bounds of eval_easy2_start(V__0,V_z,B): 0.04/0.12 ------------------------------------- 0.04/0.12 * Chain [18] with precondition: [] 0.04/0.12 - Upper bound: 0 0.04/0.12 - Complexity: constant 0.04/0.12 * Chain [17] with precondition: [0>=V_z] 0.04/0.12 - Upper bound: 0 0.04/0.12 - Complexity: constant 0.04/0.12 * Chain [16] with precondition: [V_z>=1] 0.04/0.12 - Upper bound: 2*V_z 0.04/0.12 - Complexity: n 0.04/0.12 0.04/0.12 ### Maximum cost of eval_easy2_start(V__0,V_z,B): nat(V_z)*2 0.04/0.12 Asymptotic class: n 0.04/0.12 * Total analysis performed in 63 ms. 0.04/0.12 0.04/0.22 EOF