0.03/0.26 WORST_CASE(?,O(n^1)) 0.03/0.26 0.03/0.26 Preprocessing Cost Relations 0.03/0.26 ===================================== 0.03/0.26 0.03/0.26 #### Computed strongly connected components 0.03/0.26 0. recursive : [eval_terminate_bb1_in/7,eval_terminate_bb2_in/7] 0.03/0.26 1. non_recursive : [eval_terminate_stop/7] 0.03/0.26 2. non_recursive : [eval_terminate_bb3_in/7] 0.03/0.26 3. non_recursive : [exit_location/1] 0.03/0.26 4. non_recursive : [eval_terminate_bb1_in_loop_cont/8] 0.03/0.26 5. non_recursive : [eval_terminate_7/7] 0.03/0.26 6. non_recursive : [eval_terminate_6/7] 0.03/0.26 7. non_recursive : [eval_terminate_5/7] 0.03/0.26 8. non_recursive : [eval_terminate_4/7] 0.03/0.26 9. non_recursive : [eval_terminate_3/7] 0.03/0.26 10. non_recursive : [eval_terminate_2/7] 0.03/0.26 11. non_recursive : [eval_terminate_1/7] 0.03/0.26 12. non_recursive : [eval_terminate_0/7] 0.03/0.26 13. non_recursive : [eval_terminate_bb0_in/7] 0.03/0.26 14. non_recursive : [eval_terminate_start/7] 0.03/0.26 0.03/0.26 #### Obtained direct recursion through partial evaluation 0.03/0.26 0. SCC is partially evaluated into eval_terminate_bb1_in/7 0.03/0.26 1. SCC is completely evaluated into other SCCs 0.03/0.26 2. SCC is completely evaluated into other SCCs 0.03/0.26 3. SCC is completely evaluated into other SCCs 0.03/0.26 4. SCC is partially evaluated into eval_terminate_bb1_in_loop_cont/8 0.03/0.26 5. SCC is partially evaluated into eval_terminate_7/7 0.03/0.26 6. SCC is completely evaluated into other SCCs 0.03/0.26 7. SCC is completely evaluated into other SCCs 0.03/0.26 8. SCC is completely evaluated into other SCCs 0.03/0.26 9. SCC is completely evaluated into other SCCs 0.03/0.26 10. SCC is completely evaluated into other SCCs 0.03/0.26 11. SCC is completely evaluated into other SCCs 0.03/0.26 12. SCC is completely evaluated into other SCCs 0.03/0.26 13. SCC is completely evaluated into other SCCs 0.03/0.26 14. SCC is partially evaluated into eval_terminate_start/7 0.03/0.26 0.03/0.26 Control-Flow Refinement of Cost Relations 0.03/0.26 ===================================== 0.03/0.26 0.03/0.26 ### Specialization of cost equations eval_terminate_bb1_in/7 0.03/0.26 * CE 6 is refined into CE [9] 0.03/0.26 * CE 5 is refined into CE [10] 0.03/0.26 * CE 4 is refined into CE [11] 0.03/0.26 * CE 3 is refined into CE [12] 0.03/0.26 0.03/0.26 0.03/0.26 ### Cost equations --> "Loop" of eval_terminate_bb1_in/7 0.03/0.26 * CEs [12] --> Loop 9 0.03/0.26 * CEs [9] --> Loop 10 0.03/0.26 * CEs [10] --> Loop 11 0.03/0.26 * CEs [11] --> Loop 12 0.03/0.26 0.03/0.26 ### Ranking functions of CR eval_terminate_bb1_in(V__0,V__01,V__02,B,C,D,E) 0.03/0.26 * RF of phase [9]: [-V__0/2-V__01/2+V__02/2+101/2] 0.03/0.26 0.03/0.26 #### Partial ranking functions of CR eval_terminate_bb1_in(V__0,V__01,V__02,B,C,D,E) 0.03/0.26 * Partial RF of phase [9]: 0.03/0.26 - RF of loop [9:1]: 0.03/0.26 -V__0/2-V__01/2+V__02/2+101/2 0.03/0.26 0.03/0.26 0.03/0.26 ### Specialization of cost equations eval_terminate_bb1_in_loop_cont/8 0.03/0.26 * CE 8 is refined into CE [13] 0.03/0.26 * CE 7 is refined into CE [14] 0.03/0.26 0.03/0.26 0.03/0.26 ### Cost equations --> "Loop" of eval_terminate_bb1_in_loop_cont/8 0.03/0.26 * CEs [13] --> Loop 13 0.03/0.26 * CEs [14] --> Loop 14 0.03/0.26 0.03/0.26 ### Ranking functions of CR eval_terminate_bb1_in_loop_cont(A,B,C,D,E,F,G,H) 0.03/0.26 0.03/0.26 #### Partial ranking functions of CR eval_terminate_bb1_in_loop_cont(A,B,C,D,E,F,G,H) 0.03/0.26 0.03/0.26 0.03/0.26 ### Specialization of cost equations eval_terminate_7/7 0.03/0.26 * CE 2 is refined into CE [15,16,17,18,19,20] 0.03/0.26 0.03/0.26 0.03/0.26 ### Cost equations --> "Loop" of eval_terminate_7/7 0.03/0.26 * CEs [15] --> Loop 15 0.03/0.26 * CEs [16] --> Loop 16 0.03/0.26 * CEs [17] --> Loop 17 0.03/0.26 * CEs [20] --> Loop 18 0.03/0.26 * CEs [18] --> Loop 19 0.03/0.26 * CEs [19] --> Loop 20 0.03/0.26 0.03/0.26 ### Ranking functions of CR eval_terminate_7(V__0,V__01,V__02,V_i,V_j,V_k,B) 0.03/0.26 0.03/0.26 #### Partial ranking functions of CR eval_terminate_7(V__0,V__01,V__02,V_i,V_j,V_k,B) 0.03/0.26 0.03/0.26 0.03/0.26 ### Specialization of cost equations eval_terminate_start/7 0.03/0.26 * CE 1 is refined into CE [21,22,23,24,25,26] 0.03/0.26 0.03/0.26 0.03/0.26 ### Cost equations --> "Loop" of eval_terminate_start/7 0.03/0.26 * CEs [26] --> Loop 21 0.03/0.26 * CEs [25] --> Loop 22 0.03/0.26 * CEs [24] --> Loop 23 0.03/0.26 * CEs [23] --> Loop 24 0.03/0.26 * CEs [22] --> Loop 25 0.03/0.26 * CEs [21] --> Loop 26 0.03/0.26 0.03/0.26 ### Ranking functions of CR eval_terminate_start(V__0,V__01,V__02,V_i,V_j,V_k,B) 0.03/0.26 0.03/0.26 #### Partial ranking functions of CR eval_terminate_start(V__0,V__01,V__02,V_i,V_j,V_k,B) 0.03/0.26 0.03/0.26 0.03/0.26 Computing Bounds 0.03/0.26 ===================================== 0.03/0.26 0.03/0.26 #### Cost of chains of eval_terminate_bb1_in(V__0,V__01,V__02,B,C,D,E): 0.03/0.26 * Chain [[9],12]: 1*it(9)+0 0.03/0.26 Such that:it(9) =< V__02-C/2-D/2-E/2+101/2 0.03/0.26 it(9) =< V__02-E 0.03/0.26 0.03/0.26 with precondition: [B=2,V__0+V__01+V__02=C+D+E,100>=V__0,C>=101,V__02>=V__01,C+D>=V__0+V__01+1,V__0+V__01+V__02+1>=2*C+D] 0.03/0.26 0.03/0.26 * Chain [[9],11]: 1*it(9)+0 0.03/0.26 Such that:it(9) =< V__02-C/2-D/2-E/2+101/2 0.03/0.26 it(9) =< V__02-E 0.03/0.26 0.03/0.26 with precondition: [B=2,V__0+V__01+V__02=C+D+E,100>=V__0,101>=D,V__02>=V__01,C+2*D>=2*V__0+V__01+2,C+D>=V__0+V__01+1,V__0+V__01+V__02+1>=2*C+D,C+2*D>=V__0+V__01+V__02+1] 0.03/0.26 0.03/0.26 * Chain [[9],10]: 1*it(9)+0 0.03/0.26 Such that:it(9) =< -V__0/2-V__01/2+V__02/2+101/2 0.03/0.26 0.03/0.26 with precondition: [B=3,100>=V__0,V__02>=V__01] 0.03/0.26 0.03/0.26 * Chain [12]: 0 0.03/0.26 with precondition: [B=2,D=V__01,E=V__02,V__0=C,V__0>=101] 0.03/0.26 0.03/0.26 * Chain [11]: 0 0.03/0.26 with precondition: [B=2,C=V__0,V__01=D,V__02=E,V__01>=V__02+1] 0.03/0.26 0.03/0.26 * Chain [10]: 0 0.03/0.26 with precondition: [B=3] 0.03/0.26 0.03/0.26 0.03/0.26 #### Cost of chains of eval_terminate_bb1_in_loop_cont(A,B,C,D,E,F,G,H): 0.03/0.26 * Chain [14]: 0 0.03/0.26 with precondition: [A=2] 0.03/0.26 0.03/0.26 * Chain [13]: 0 0.03/0.26 with precondition: [A=3] 0.03/0.26 0.03/0.26 0.03/0.26 #### Cost of chains of eval_terminate_7(V__0,V__01,V__02,V_i,V_j,V_k,B): 0.03/0.26 * Chain [20]: 0 0.03/0.26 with precondition: [] 0.03/0.26 0.03/0.26 * Chain [19]: 1*s(1)+0 0.03/0.26 Such that:s(1) =< -V_i/2-V_j/2+V_k/2+101/2 0.03/0.26 s(1) =< V_k 0.03/0.26 0.03/0.26 with precondition: [100>=V_i,V_k>=101,V_k>=V_j] 0.03/0.26 0.03/0.26 * Chain [18]: 1*s(2)+0 0.03/0.26 Such that:s(2) =< -V_i/2-V_j/2+V_k/2+101/2 0.03/0.26 0.03/0.26 with precondition: [100>=V_i,V_k>=V_j] 0.03/0.26 0.03/0.26 * Chain [17]: 1*s(3)+0 0.03/0.26 Such that:s(3) =< -V_i/2-V_j/2+V_k/2+101/2 0.03/0.26 0.03/0.26 with precondition: [100>=V_i,V_k>=V_j,302>=V_i+V_j+V_k] 0.03/0.26 0.03/0.26 * Chain [16]: 0 0.03/0.26 with precondition: [V_i>=101] 0.03/0.26 0.03/0.26 * Chain [15]: 0 0.03/0.26 with precondition: [V_j>=V_k+1] 0.03/0.26 0.03/0.26 0.03/0.26 #### Cost of chains of eval_terminate_start(V__0,V__01,V__02,V_i,V_j,V_k,B): 0.03/0.26 * Chain [26]: 0 0.03/0.26 with precondition: [] 0.03/0.26 0.03/0.26 * Chain [25]: 1*s(4)+0 0.03/0.26 Such that:s(4) =< -V_i/2-V_j/2+V_k/2+101/2 0.03/0.26 s(4) =< V_k 0.03/0.26 0.03/0.26 with precondition: [100>=V_i,V_k>=101,V_k>=V_j] 0.03/0.26 0.03/0.26 * Chain [24]: 1*s(5)+0 0.03/0.26 Such that:s(5) =< -V_i/2-V_j/2+V_k/2+101/2 0.03/0.26 0.03/0.26 with precondition: [100>=V_i,V_k>=V_j] 0.03/0.26 0.03/0.26 * Chain [23]: 1*s(6)+0 0.03/0.26 Such that:s(6) =< -V_i/2-V_j/2+V_k/2+101/2 0.03/0.26 0.03/0.26 with precondition: [100>=V_i,V_k>=V_j,302>=V_i+V_j+V_k] 0.03/0.26 0.03/0.26 * Chain [22]: 0 0.03/0.26 with precondition: [V_i>=101] 0.03/0.26 0.03/0.26 * Chain [21]: 0 0.03/0.26 with precondition: [V_j>=V_k+1] 0.03/0.26 0.03/0.26 0.03/0.26 Closed-form bounds of eval_terminate_start(V__0,V__01,V__02,V_i,V_j,V_k,B): 0.03/0.26 ------------------------------------- 0.03/0.26 * Chain [26] with precondition: [] 0.03/0.26 - Upper bound: 0 0.03/0.26 - Complexity: constant 0.03/0.26 * Chain [25] with precondition: [100>=V_i,V_k>=101,V_k>=V_j] 0.03/0.26 - Upper bound: -V_i/2-V_j/2+V_k/2+101/2 0.03/0.26 - Complexity: n 0.03/0.26 * Chain [24] with precondition: [100>=V_i,V_k>=V_j] 0.03/0.26 - Upper bound: -V_i/2-V_j/2+V_k/2+101/2 0.03/0.26 - Complexity: n 0.03/0.26 * Chain [23] with precondition: [100>=V_i,V_k>=V_j,302>=V_i+V_j+V_k] 0.03/0.26 - Upper bound: -V_i/2-V_j/2+V_k/2+101/2 0.03/0.26 - Complexity: n 0.03/0.26 * Chain [22] with precondition: [V_i>=101] 0.03/0.26 - Upper bound: 0 0.03/0.26 - Complexity: constant 0.03/0.26 * Chain [21] with precondition: [V_j>=V_k+1] 0.03/0.26 - Upper bound: 0 0.03/0.26 - Complexity: constant 0.03/0.26 0.03/0.26 ### Maximum cost of eval_terminate_start(V__0,V__01,V__02,V_i,V_j,V_k,B): nat(-V_i/2-V_j/2+V_k/2+101/2) 0.03/0.26 Asymptotic class: n 0.03/0.26 * Total analysis performed in 189 ms. 0.03/0.26 0.03/0.36 EOF