0.04/0.24 WORST_CASE(?,O(n^1)) 0.04/0.24 0.04/0.24 Preprocessing Cost Relations 0.04/0.24 ===================================== 0.04/0.24 0.04/0.24 #### Computed strongly connected components 0.04/0.24 0. recursive : [eval_start_bb1_in/4,eval_start_bb2_in/4] 0.04/0.24 1. non_recursive : [eval_start_stop/4] 0.04/0.24 2. non_recursive : [eval_start_bb3_in/4] 0.04/0.24 3. non_recursive : [exit_location/1] 0.04/0.24 4. non_recursive : [eval_start_bb1_in_loop_cont/5] 0.04/0.24 5. non_recursive : [eval_start_9/4] 0.04/0.24 6. non_recursive : [eval_start_8/4] 0.04/0.24 7. non_recursive : [eval_start_bb4_in/4] 0.04/0.24 8. non_recursive : [eval_start_3/4] 0.04/0.24 9. non_recursive : [eval_start_2/4] 0.04/0.24 10. non_recursive : [eval_start_1/4] 0.04/0.24 11. non_recursive : [eval_start_0/4] 0.04/0.24 12. non_recursive : [eval_start_bb0_in/4] 0.04/0.24 13. non_recursive : [eval_start_start/4] 0.04/0.24 0.04/0.24 #### Obtained direct recursion through partial evaluation 0.04/0.24 0. SCC is partially evaluated into eval_start_bb1_in/4 0.04/0.24 1. SCC is completely evaluated into other SCCs 0.04/0.24 2. SCC is completely evaluated into other SCCs 0.04/0.24 3. SCC is completely evaluated into other SCCs 0.04/0.24 4. SCC is partially evaluated into eval_start_bb1_in_loop_cont/5 0.04/0.24 5. SCC is completely evaluated into other SCCs 0.04/0.24 6. SCC is completely evaluated into other SCCs 0.04/0.24 7. SCC is completely evaluated into other SCCs 0.04/0.24 8. SCC is partially evaluated into eval_start_3/4 0.04/0.24 9. SCC is completely evaluated into other SCCs 0.04/0.24 10. SCC is completely evaluated into other SCCs 0.04/0.24 11. SCC is completely evaluated into other SCCs 0.04/0.24 12. SCC is completely evaluated into other SCCs 0.04/0.24 13. SCC is partially evaluated into eval_start_start/4 0.04/0.24 0.04/0.24 Control-Flow Refinement of Cost Relations 0.04/0.24 ===================================== 0.04/0.24 0.04/0.24 ### Specialization of cost equations eval_start_bb1_in/4 0.04/0.24 * CE 7 is refined into CE [10] 0.04/0.24 * CE 6 is refined into CE [11] 0.04/0.24 * CE 4 is refined into CE [12] 0.04/0.24 * CE 5 is refined into CE [13] 0.04/0.24 0.04/0.24 0.04/0.24 ### Cost equations --> "Loop" of eval_start_bb1_in/4 0.04/0.24 * CEs [12] --> Loop 10 0.04/0.24 * CEs [13] --> Loop 11 0.04/0.24 * CEs [10] --> Loop 12 0.04/0.24 * CEs [11] --> Loop 13 0.04/0.24 0.04/0.24 ### Ranking functions of CR eval_start_bb1_in(V_i_0,V_m,B,C) 0.04/0.24 * RF of phase [10]: [V_i_0,V_i_0-V_m+1] 0.04/0.24 * RF of phase [11]: [V_i_0] 0.04/0.24 0.04/0.24 #### Partial ranking functions of CR eval_start_bb1_in(V_i_0,V_m,B,C) 0.04/0.24 * Partial RF of phase [10]: 0.04/0.24 - RF of loop [10:1]: 0.04/0.24 V_i_0 0.04/0.24 V_i_0-V_m+1 0.04/0.24 * Partial RF of phase [11]: 0.04/0.24 - RF of loop [11:1]: 0.04/0.24 V_i_0 0.04/0.24 0.04/0.24 0.04/0.24 ### Specialization of cost equations eval_start_bb1_in_loop_cont/5 0.04/0.24 * CE 9 is refined into CE [14] 0.04/0.24 * CE 8 is refined into CE [15] 0.04/0.24 0.04/0.24 0.04/0.24 ### Cost equations --> "Loop" of eval_start_bb1_in_loop_cont/5 0.04/0.24 * CEs [14] --> Loop 14 0.04/0.24 * CEs [15] --> Loop 15 0.04/0.24 0.04/0.24 ### Ranking functions of CR eval_start_bb1_in_loop_cont(A,B,C,D,E) 0.04/0.24 0.04/0.24 #### Partial ranking functions of CR eval_start_bb1_in_loop_cont(A,B,C,D,E) 0.04/0.24 0.04/0.24 0.04/0.24 ### Specialization of cost equations eval_start_3/4 0.04/0.24 * CE 3 is refined into CE [16,17,18,19,20,21,22,23] 0.04/0.24 * CE 2 is refined into CE [24] 0.04/0.24 0.04/0.24 0.04/0.24 ### Cost equations --> "Loop" of eval_start_3/4 0.04/0.24 * CEs [16,20] --> Loop 16 0.04/0.24 * CEs [18,23] --> Loop 17 0.04/0.24 * CEs [17,22] --> Loop 18 0.04/0.24 * CEs [21] --> Loop 19 0.04/0.24 * CEs [19] --> Loop 20 0.04/0.24 * CEs [24] --> Loop 21 0.04/0.24 0.04/0.24 ### Ranking functions of CR eval_start_3(V_i_0,V_m,V_n,B) 0.04/0.24 0.04/0.24 #### Partial ranking functions of CR eval_start_3(V_i_0,V_m,V_n,B) 0.04/0.24 0.04/0.24 0.04/0.24 ### Specialization of cost equations eval_start_start/4 0.04/0.24 * CE 1 is refined into CE [25,26,27,28,29,30] 0.04/0.24 0.04/0.24 0.04/0.24 ### Cost equations --> "Loop" of eval_start_start/4 0.04/0.24 * CEs [30] --> Loop 22 0.04/0.24 * CEs [29] --> Loop 23 0.04/0.24 * CEs [28] --> Loop 24 0.04/0.24 * CEs [27] --> Loop 25 0.04/0.24 * CEs [26] --> Loop 26 0.04/0.24 * CEs [25] --> Loop 27 0.04/0.24 0.04/0.24 ### Ranking functions of CR eval_start_start(V_i_0,V_m,V_n,B) 0.04/0.24 0.04/0.24 #### Partial ranking functions of CR eval_start_start(V_i_0,V_m,V_n,B) 0.04/0.24 0.04/0.24 0.04/0.24 Computing Bounds 0.04/0.24 ===================================== 0.04/0.24 0.04/0.24 #### Cost of chains of eval_start_bb1_in(V_i_0,V_m,B,C): 0.04/0.24 * Chain [[11],13]: 1*it(11)+0 0.04/0.24 Such that:it(11) =< V_i_0 0.04/0.24 0.04/0.24 with precondition: [B=2,C=0,V_i_0>=1,V_m>=V_i_0+1] 0.04/0.24 0.04/0.24 * Chain [[11],12]: 1*it(11)+0 0.04/0.24 Such that:it(11) =< V_i_0 0.04/0.24 0.04/0.24 with precondition: [B=3,V_i_0>=1,V_m>=V_i_0+1] 0.04/0.24 0.04/0.24 * Chain [[10],[11],13]: 1*it(10)+1*it(11)+0 0.04/0.24 Such that:it(11) =< V_i_0-V_m 0.04/0.24 it(10) =< V_i_0-V_m+1 0.04/0.24 it(11) =< V_m 0.04/0.24 0.04/0.24 with precondition: [B=2,C=0,V_m>=2,V_i_0>=V_m+1] 0.04/0.24 0.04/0.24 * Chain [[10],[11],12]: 1*it(10)+1*it(11)+0 0.04/0.24 Such that:it(11) =< V_i_0-V_m 0.04/0.24 it(10) =< V_i_0-V_m+1 0.04/0.24 it(11) =< V_m 0.04/0.24 0.04/0.24 with precondition: [B=3,V_m>=2,V_i_0>=V_m+1] 0.04/0.24 0.04/0.24 * Chain [[10],13]: 1*it(10)+0 0.04/0.24 Such that:it(10) =< V_i_0-V_m+1 0.04/0.24 0.04/0.24 with precondition: [B=2,C=0,V_m>=1,V_i_0>=V_m] 0.04/0.24 0.04/0.24 * Chain [[10],12]: 1*it(10)+0 0.04/0.24 Such that:it(10) =< V_i_0-V_m+1 0.04/0.24 0.04/0.24 with precondition: [B=3,V_m>=1,V_i_0>=V_m] 0.04/0.24 0.04/0.24 * Chain [13]: 0 0.04/0.24 with precondition: [B=2,V_i_0=C,0>=V_i_0,V_m>=1] 0.04/0.24 0.04/0.24 * Chain [12]: 0 0.04/0.24 with precondition: [B=3,V_m>=1] 0.04/0.24 0.04/0.24 0.04/0.24 #### Cost of chains of eval_start_bb1_in_loop_cont(A,B,C,D,E): 0.04/0.24 * Chain [15]: 0 0.04/0.24 with precondition: [A=2,C>=1] 0.04/0.24 0.04/0.24 * Chain [14]: 0 0.04/0.24 with precondition: [A=3,C>=1] 0.04/0.24 0.04/0.24 0.04/0.24 #### Cost of chains of eval_start_3(V_i_0,V_m,V_n,B): 0.04/0.24 * Chain [21]: 0 0.04/0.24 with precondition: [0>=V_m] 0.04/0.24 0.04/0.24 * Chain [20]: 0 0.04/0.24 with precondition: [0>=V_n,V_m>=1] 0.04/0.24 0.04/0.24 * Chain [19]: 0 0.04/0.24 with precondition: [V_m>=1] 0.04/0.24 0.04/0.24 * Chain [18]: 2*s(1)+0 0.04/0.24 Such that:aux(1) =< -V_m+V_n+1 0.04/0.24 s(1) =< aux(1) 0.04/0.24 0.04/0.24 with precondition: [V_m>=1,V_n>=V_m] 0.04/0.24 0.04/0.24 * Chain [17]: 2*s(3)+2*s(4)+0 0.04/0.24 Such that:aux(2) =< -V_m+V_n 0.04/0.24 aux(3) =< -V_m+V_n+1 0.04/0.24 aux(4) =< V_m 0.04/0.24 s(3) =< aux(2) 0.04/0.24 s(4) =< aux(3) 0.04/0.24 s(3) =< aux(4) 0.04/0.24 0.04/0.24 with precondition: [V_m>=2,V_n>=V_m+1] 0.04/0.24 0.04/0.24 * Chain [16]: 2*s(7)+0 0.04/0.24 Such that:aux(5) =< V_n 0.04/0.24 s(7) =< aux(5) 0.04/0.24 0.04/0.24 with precondition: [V_n>=1,V_m>=V_n+1] 0.04/0.24 0.04/0.24 0.04/0.24 #### Cost of chains of eval_start_start(V_i_0,V_m,V_n,B): 0.04/0.24 * Chain [27]: 0 0.04/0.24 with precondition: [0>=V_m] 0.04/0.24 0.04/0.24 * Chain [26]: 0 0.04/0.24 with precondition: [0>=V_n,V_m>=1] 0.04/0.24 0.04/0.24 * Chain [25]: 0 0.04/0.24 with precondition: [V_m>=1] 0.04/0.24 0.04/0.24 * Chain [24]: 2*s(10)+0 0.04/0.24 Such that:s(9) =< -V_m+V_n+1 0.04/0.24 s(10) =< s(9) 0.04/0.24 0.04/0.24 with precondition: [V_m>=1,V_n>=V_m] 0.04/0.24 0.04/0.24 * Chain [23]: 2*s(14)+2*s(15)+0 0.04/0.24 Such that:s(11) =< -V_m+V_n 0.04/0.24 s(12) =< -V_m+V_n+1 0.04/0.24 s(13) =< V_m 0.04/0.24 s(14) =< s(11) 0.04/0.24 s(15) =< s(12) 0.04/0.24 s(14) =< s(13) 0.04/0.24 0.04/0.24 with precondition: [V_m>=2,V_n>=V_m+1] 0.04/0.24 0.04/0.24 * Chain [22]: 2*s(17)+0 0.04/0.24 Such that:s(16) =< V_n 0.04/0.24 s(17) =< s(16) 0.04/0.24 0.04/0.24 with precondition: [V_n>=1,V_m>=V_n+1] 0.04/0.24 0.04/0.24 0.04/0.24 Closed-form bounds of eval_start_start(V_i_0,V_m,V_n,B): 0.04/0.24 ------------------------------------- 0.04/0.24 * Chain [27] with precondition: [0>=V_m] 0.04/0.24 - Upper bound: 0 0.04/0.24 - Complexity: constant 0.04/0.24 * Chain [26] with precondition: [0>=V_n,V_m>=1] 0.04/0.24 - Upper bound: 0 0.04/0.24 - Complexity: constant 0.04/0.24 * Chain [25] with precondition: [V_m>=1] 0.04/0.24 - Upper bound: 0 0.04/0.24 - Complexity: constant 0.04/0.24 * Chain [24] with precondition: [V_m>=1,V_n>=V_m] 0.04/0.24 - Upper bound: -2*V_m+2*V_n+2 0.04/0.24 - Complexity: n 0.04/0.24 * Chain [23] with precondition: [V_m>=2,V_n>=V_m+1] 0.04/0.24 - Upper bound: -4*V_m+4*V_n+2 0.04/0.24 - Complexity: n 0.04/0.24 * Chain [22] with precondition: [V_n>=1,V_m>=V_n+1] 0.04/0.24 - Upper bound: 2*V_n 0.04/0.24 - Complexity: n 0.04/0.24 0.04/0.24 ### Maximum cost of eval_start_start(V_i_0,V_m,V_n,B): max([nat(V_n)*2,nat(-V_m+V_n+1)*2+nat(-V_m+V_n)*2]) 0.04/0.24 Asymptotic class: n 0.04/0.24 * Total analysis performed in 179 ms. 0.04/0.24 0.04/0.34 EOF