0.04/0.27 WORST_CASE(?,O(n^1)) 0.04/0.27 0.04/0.27 Preprocessing Cost Relations 0.04/0.27 ===================================== 0.04/0.27 0.04/0.27 #### Computed strongly connected components 0.04/0.27 0. recursive : [eval_aaron2_4/8,eval_aaron2_5/8,eval_aaron2_bb1_in/8,eval_aaron2_bb2_in/8,eval_aaron2_bb3_in/8,eval_aaron2_bb4_in/8] 0.04/0.27 1. non_recursive : [eval_aaron2_stop/7] 0.04/0.27 2. non_recursive : [eval_aaron2_bb5_in/7] 0.04/0.27 3. non_recursive : [exit_location/1] 0.04/0.27 4. non_recursive : [eval_aaron2_bb1_in_loop_cont/8] 0.04/0.27 5. non_recursive : [eval_aaron2_3/7] 0.04/0.27 6. non_recursive : [eval_aaron2_2/7] 0.04/0.27 7. non_recursive : [eval_aaron2_1/7] 0.04/0.27 8. non_recursive : [eval_aaron2_0/7] 0.04/0.27 9. non_recursive : [eval_aaron2_bb0_in/7] 0.04/0.27 10. non_recursive : [eval_aaron2_start/7] 0.04/0.27 0.04/0.27 #### Obtained direct recursion through partial evaluation 0.04/0.27 0. SCC is partially evaluated into eval_aaron2_bb1_in/8 0.04/0.27 1. SCC is completely evaluated into other SCCs 0.04/0.27 2. SCC is completely evaluated into other SCCs 0.04/0.27 3. SCC is completely evaluated into other SCCs 0.04/0.27 4. SCC is partially evaluated into eval_aaron2_bb1_in_loop_cont/8 0.04/0.27 5. SCC is partially evaluated into eval_aaron2_3/7 0.04/0.27 6. SCC is completely evaluated into other SCCs 0.04/0.27 7. SCC is completely evaluated into other SCCs 0.04/0.27 8. SCC is completely evaluated into other SCCs 0.04/0.27 9. SCC is completely evaluated into other SCCs 0.04/0.27 10. SCC is partially evaluated into eval_aaron2_start/7 0.04/0.27 0.04/0.27 Control-Flow Refinement of Cost Relations 0.04/0.27 ===================================== 0.04/0.27 0.04/0.27 ### Specialization of cost equations eval_aaron2_bb1_in/8 0.04/0.27 * CE 8 is refined into CE [11] 0.04/0.27 * CE 6 is refined into CE [12] 0.04/0.27 * CE 7 is discarded (unfeasible) 0.04/0.27 * CE 4 is refined into CE [13] 0.04/0.27 * CE 5 is refined into CE [14] 0.04/0.27 0.04/0.27 0.04/0.27 ### Cost equations --> "Loop" of eval_aaron2_bb1_in/8 0.04/0.27 * CEs [13] --> Loop 11 0.04/0.27 * CEs [14] --> Loop 12 0.04/0.27 * CEs [11] --> Loop 13 0.04/0.27 * CEs [12] --> Loop 14 0.04/0.27 0.04/0.27 ### Ranking functions of CR eval_aaron2_bb1_in(V__01,V__02,V_3,V_tx,B,C,D,E) 0.04/0.27 * RF of phase [11,12]: [V__01-V__02+1] 0.04/0.27 0.04/0.27 #### Partial ranking functions of CR eval_aaron2_bb1_in(V__01,V__02,V_3,V_tx,B,C,D,E) 0.04/0.27 * Partial RF of phase [11,12]: 0.04/0.27 - RF of loop [11:1,12:1]: 0.04/0.27 V__01-V__02+1 0.04/0.27 0.04/0.27 0.04/0.27 ### Specialization of cost equations eval_aaron2_bb1_in_loop_cont/8 0.04/0.27 * CE 10 is refined into CE [15] 0.04/0.27 * CE 9 is refined into CE [16] 0.04/0.27 0.04/0.27 0.04/0.27 ### Cost equations --> "Loop" of eval_aaron2_bb1_in_loop_cont/8 0.04/0.27 * CEs [15] --> Loop 15 0.04/0.27 * CEs [16] --> Loop 16 0.04/0.27 0.04/0.27 ### Ranking functions of CR eval_aaron2_bb1_in_loop_cont(A,B,C,D,E,F,G,H) 0.04/0.27 0.04/0.27 #### Partial ranking functions of CR eval_aaron2_bb1_in_loop_cont(A,B,C,D,E,F,G,H) 0.04/0.27 0.04/0.27 0.04/0.27 ### Specialization of cost equations eval_aaron2_3/7 0.04/0.27 * CE 3 is refined into CE [17,18,19,20] 0.04/0.27 * CE 2 is refined into CE [21] 0.04/0.27 0.04/0.27 0.04/0.27 ### Cost equations --> "Loop" of eval_aaron2_3/7 0.04/0.27 * CEs [18,20] --> Loop 17 0.04/0.27 * CEs [17] --> Loop 18 0.04/0.27 * CEs [19] --> Loop 19 0.04/0.27 * CEs [21] --> Loop 20 0.04/0.27 0.04/0.27 ### Ranking functions of CR eval_aaron2_3(V__01,V__02,V_3,V_tx,V_x,V_y,B) 0.04/0.27 0.04/0.27 #### Partial ranking functions of CR eval_aaron2_3(V__01,V__02,V_3,V_tx,V_x,V_y,B) 0.04/0.27 0.04/0.27 0.04/0.27 ### Specialization of cost equations eval_aaron2_start/7 0.04/0.27 * CE 1 is refined into CE [22,23,24,25] 0.04/0.27 0.04/0.27 0.04/0.27 ### Cost equations --> "Loop" of eval_aaron2_start/7 0.04/0.27 * CEs [25] --> Loop 21 0.04/0.27 * CEs [24] --> Loop 22 0.04/0.27 * CEs [23] --> Loop 23 0.04/0.27 * CEs [22] --> Loop 24 0.04/0.27 0.04/0.27 ### Ranking functions of CR eval_aaron2_start(V__01,V__02,V_3,V_tx,V_x,V_y,B) 0.04/0.27 0.04/0.27 #### Partial ranking functions of CR eval_aaron2_start(V__01,V__02,V_3,V_tx,V_x,V_y,B) 0.04/0.27 0.04/0.27 0.04/0.27 Computing Bounds 0.04/0.27 ===================================== 0.04/0.27 0.04/0.27 #### Cost of chains of eval_aaron2_bb1_in(V__01,V__02,V_3,V_tx,B,C,D,E): 0.04/0.27 * Chain [[11,12],14]: 2*it(11)+0 0.04/0.27 Such that:aux(1) =< V__01-V__02+1 0.04/0.27 aux(2) =< V__01-V__02-C+D 0.04/0.27 it(11) =< aux(1) 0.04/0.27 it(11) =< aux(2) 0.04/0.27 0.04/0.27 with precondition: [B=2,D>=V__02,V__01>=C,D>=C+1,V_tx+C+1>=D,V__01+D>=V__02+V_tx+C+1] 0.04/0.27 0.04/0.27 * Chain [[11,12],13]: 2*it(11)+0 0.04/0.27 Such that:aux(1) =< V__01-V__02+1 0.04/0.27 aux(2) =< V__01-V__02+V_tx+1 0.04/0.27 it(11) =< aux(1) 0.04/0.27 it(11) =< aux(2) 0.04/0.27 0.04/0.27 with precondition: [B=3,V_tx>=0,V__01>=V__02] 0.04/0.27 0.04/0.27 * Chain [14]: 0 0.04/0.27 with precondition: [B=2,E=V_3,V__01=C,V__02=D,V_tx>=0,V__02>=V__01+1] 0.04/0.27 0.04/0.27 * Chain [13]: 0 0.04/0.27 with precondition: [B=3,V_tx>=0] 0.04/0.27 0.04/0.27 0.04/0.27 #### Cost of chains of eval_aaron2_bb1_in_loop_cont(A,B,C,D,E,F,G,H): 0.04/0.27 * Chain [16]: 0 0.04/0.27 with precondition: [A=2,E>=0] 0.04/0.27 0.04/0.27 * Chain [15]: 0 0.04/0.27 with precondition: [A=3,E>=0] 0.04/0.27 0.04/0.27 0.04/0.27 #### Cost of chains of eval_aaron2_3(V__01,V__02,V_3,V_tx,V_x,V_y,B): 0.04/0.27 * Chain [20]: 0 0.04/0.27 with precondition: [0>=V_tx+1] 0.04/0.27 0.04/0.27 * Chain [19]: 0 0.04/0.27 with precondition: [V_tx>=0] 0.04/0.27 0.04/0.27 * Chain [18]: 0 0.04/0.27 with precondition: [V_tx>=0,V_y>=V_x+1] 0.04/0.27 0.04/0.27 * Chain [17]: 4*s(3)+0 0.04/0.27 Such that:aux(3) =< V_tx+V_x-V_y+1 0.04/0.27 aux(4) =< V_x-V_y+1 0.04/0.27 s(3) =< aux(4) 0.04/0.27 s(3) =< aux(3) 0.04/0.27 0.04/0.27 with precondition: [V_tx>=0,V_x>=V_y] 0.04/0.27 0.04/0.27 0.04/0.27 #### Cost of chains of eval_aaron2_start(V__01,V__02,V_3,V_tx,V_x,V_y,B): 0.04/0.27 * Chain [24]: 0 0.04/0.27 with precondition: [0>=V_tx+1] 0.04/0.27 0.04/0.27 * Chain [23]: 0 0.04/0.27 with precondition: [V_tx>=0] 0.04/0.27 0.04/0.27 * Chain [22]: 0 0.04/0.27 with precondition: [V_tx>=0,V_y>=V_x+1] 0.04/0.27 0.04/0.27 * Chain [21]: 4*s(9)+0 0.04/0.27 Such that:s(7) =< V_tx+V_x-V_y+1 0.04/0.27 s(8) =< V_x-V_y+1 0.04/0.27 s(9) =< s(8) 0.04/0.27 s(9) =< s(7) 0.04/0.27 0.04/0.27 with precondition: [V_tx>=0,V_x>=V_y] 0.04/0.27 0.04/0.27 0.04/0.27 Closed-form bounds of eval_aaron2_start(V__01,V__02,V_3,V_tx,V_x,V_y,B): 0.04/0.27 ------------------------------------- 0.04/0.27 * Chain [24] with precondition: [0>=V_tx+1] 0.04/0.27 - Upper bound: 0 0.04/0.27 - Complexity: constant 0.04/0.27 * Chain [23] with precondition: [V_tx>=0] 0.04/0.27 - Upper bound: 0 0.04/0.27 - Complexity: constant 0.04/0.27 * Chain [22] with precondition: [V_tx>=0,V_y>=V_x+1] 0.04/0.27 - Upper bound: 0 0.04/0.27 - Complexity: constant 0.04/0.27 * Chain [21] with precondition: [V_tx>=0,V_x>=V_y] 0.04/0.27 - Upper bound: 4*V_x-4*V_y+4 0.04/0.27 - Complexity: n 0.04/0.27 0.04/0.27 ### Maximum cost of eval_aaron2_start(V__01,V__02,V_3,V_tx,V_x,V_y,B): nat(V_x-V_y+1)*4 0.04/0.27 Asymptotic class: n 0.04/0.27 * Total analysis performed in 193 ms. 0.04/0.27 0.04/0.37 EOF