0.03/0.24 WORST_CASE(?,O(n^1)) 0.03/0.24 0.03/0.24 Preprocessing Cost Relations 0.03/0.24 ===================================== 0.03/0.24 0.03/0.24 #### Computed strongly connected components 0.03/0.24 0. recursive : [eval_ex3_bb1_in/4,eval_ex3_bb2_in/4] 0.03/0.24 1. non_recursive : [eval_ex3_stop/4] 0.03/0.24 2. non_recursive : [eval_ex3_bb3_in/4] 0.03/0.24 3. non_recursive : [exit_location/1] 0.03/0.24 4. non_recursive : [eval_ex3_bb1_in_loop_cont/5] 0.03/0.24 5. non_recursive : [eval_ex3_4/4] 0.03/0.24 6. non_recursive : [eval_ex3_3/4] 0.03/0.24 7. non_recursive : [eval_ex3_2/4] 0.03/0.24 8. non_recursive : [eval_ex3_1/4] 0.03/0.24 9. non_recursive : [eval_ex3_0/4] 0.03/0.24 10. non_recursive : [eval_ex3_bb0_in/4] 0.03/0.24 11. non_recursive : [eval_ex3_start/4] 0.03/0.24 0.03/0.24 #### Obtained direct recursion through partial evaluation 0.03/0.24 0. SCC is partially evaluated into eval_ex3_bb1_in/4 0.03/0.24 1. SCC is completely evaluated into other SCCs 0.03/0.24 2. SCC is completely evaluated into other SCCs 0.03/0.24 3. SCC is completely evaluated into other SCCs 0.03/0.24 4. SCC is partially evaluated into eval_ex3_bb1_in_loop_cont/5 0.03/0.24 5. SCC is partially evaluated into eval_ex3_4/4 0.03/0.24 6. SCC is completely evaluated into other SCCs 0.03/0.24 7. SCC is completely evaluated into other SCCs 0.03/0.24 8. SCC is completely evaluated into other SCCs 0.03/0.24 9. SCC is completely evaluated into other SCCs 0.03/0.24 10. SCC is completely evaluated into other SCCs 0.03/0.24 11. SCC is partially evaluated into eval_ex3_start/4 0.03/0.24 0.03/0.24 Control-Flow Refinement of Cost Relations 0.03/0.24 ===================================== 0.03/0.24 0.03/0.24 ### Specialization of cost equations eval_ex3_bb1_in/4 0.03/0.24 * CE 8 is refined into CE [11] 0.03/0.24 * CE 7 is refined into CE [12] 0.03/0.24 * CE 6 is refined into CE [13] 0.03/0.24 * CE 4 is refined into CE [14] 0.03/0.24 * CE 5 is refined into CE [15] 0.03/0.24 * CE 3 is refined into CE [16] 0.03/0.24 0.03/0.24 0.03/0.24 ### Cost equations --> "Loop" of eval_ex3_bb1_in/4 0.03/0.24 * CEs [14] --> Loop 11 0.03/0.24 * CEs [15] --> Loop 12 0.03/0.24 * CEs [16] --> Loop 13 0.03/0.24 * CEs [11] --> Loop 14 0.03/0.24 * CEs [12] --> Loop 15 0.03/0.24 * CEs [13] --> Loop 16 0.03/0.24 0.03/0.24 ### Ranking functions of CR eval_ex3_bb1_in(V__0,V_b,B,C) 0.03/0.24 * RF of phase [11]: [-V__0+255] 0.03/0.24 * RF of phase [12]: [-V__0+255] 0.03/0.24 * RF of phase [13]: [V__0] 0.03/0.24 0.03/0.24 #### Partial ranking functions of CR eval_ex3_bb1_in(V__0,V_b,B,C) 0.03/0.24 * Partial RF of phase [11]: 0.03/0.24 - RF of loop [11:1]: 0.03/0.24 -V__0+255 0.03/0.24 * Partial RF of phase [12]: 0.03/0.24 - RF of loop [12:1]: 0.03/0.24 -V__0+255 0.03/0.24 * Partial RF of phase [13]: 0.03/0.24 - RF of loop [13:1]: 0.03/0.24 V__0 0.03/0.24 0.03/0.24 0.03/0.24 ### Specialization of cost equations eval_ex3_bb1_in_loop_cont/5 0.03/0.24 * CE 10 is refined into CE [17] 0.03/0.24 * CE 9 is refined into CE [18] 0.03/0.24 0.03/0.24 0.03/0.24 ### Cost equations --> "Loop" of eval_ex3_bb1_in_loop_cont/5 0.03/0.24 * CEs [17] --> Loop 17 0.03/0.24 * CEs [18] --> Loop 18 0.03/0.24 0.03/0.24 ### Ranking functions of CR eval_ex3_bb1_in_loop_cont(A,B,C,D,E) 0.03/0.24 0.03/0.24 #### Partial ranking functions of CR eval_ex3_bb1_in_loop_cont(A,B,C,D,E) 0.03/0.24 0.03/0.24 0.03/0.24 ### Specialization of cost equations eval_ex3_4/4 0.03/0.24 * CE 2 is refined into CE [19,20,21,22,23,24,25,26,27] 0.03/0.24 0.03/0.24 0.03/0.24 ### Cost equations --> "Loop" of eval_ex3_4/4 0.03/0.24 * CEs [24] --> Loop 19 0.03/0.24 * CEs [23] --> Loop 20 0.03/0.24 * CEs [22,27] --> Loop 21 0.03/0.24 * CEs [21,26] --> Loop 22 0.03/0.24 * CEs [19,20] --> Loop 23 0.03/0.24 * CEs [25] --> Loop 24 0.03/0.24 0.03/0.24 ### Ranking functions of CR eval_ex3_4(V__0,V_b,V_x,B) 0.03/0.24 0.03/0.24 #### Partial ranking functions of CR eval_ex3_4(V__0,V_b,V_x,B) 0.03/0.24 0.03/0.24 0.03/0.24 ### Specialization of cost equations eval_ex3_start/4 0.03/0.24 * CE 1 is refined into CE [28,29,30,31,32,33] 0.03/0.24 0.03/0.24 0.03/0.24 ### Cost equations --> "Loop" of eval_ex3_start/4 0.03/0.24 * CEs [33] --> Loop 25 0.03/0.24 * CEs [32] --> Loop 26 0.03/0.24 * CEs [31] --> Loop 27 0.03/0.24 * CEs [30] --> Loop 28 0.03/0.24 * CEs [29] --> Loop 29 0.03/0.24 * CEs [28] --> Loop 30 0.03/0.24 0.03/0.24 ### Ranking functions of CR eval_ex3_start(V__0,V_b,V_x,B) 0.03/0.24 0.03/0.24 #### Partial ranking functions of CR eval_ex3_start(V__0,V_b,V_x,B) 0.03/0.24 0.03/0.24 0.03/0.24 Computing Bounds 0.03/0.24 ===================================== 0.03/0.24 0.03/0.24 #### Cost of chains of eval_ex3_bb1_in(V__0,V_b,B,C): 0.03/0.24 * Chain [[13],16]: 1*it(13)+0 0.03/0.24 Such that:it(13) =< V__0 0.03/0.24 0.03/0.24 with precondition: [V_b=0,B=2,C=0,254>=V__0,V__0>=1] 0.03/0.24 0.03/0.24 * Chain [[13],14]: 1*it(13)+0 0.03/0.24 Such that:it(13) =< V__0 0.03/0.24 0.03/0.24 with precondition: [V_b=0,B=3,254>=V__0,V__0>=1] 0.03/0.24 0.03/0.24 * Chain [[12],15]: 1*it(12)+0 0.03/0.24 Such that:it(12) =< -V__0+255 0.03/0.24 0.03/0.24 with precondition: [B=2,C=255,254>=V__0,0>=V_b+1,V__0>=1] 0.03/0.24 0.03/0.24 * Chain [[12],14]: 1*it(12)+0 0.03/0.24 Such that:it(12) =< -V__0+255 0.03/0.24 0.03/0.24 with precondition: [B=3,254>=V__0,0>=V_b+1,V__0>=1] 0.03/0.24 0.03/0.24 * Chain [[11],15]: 1*it(11)+0 0.03/0.24 Such that:it(11) =< -V__0+255 0.03/0.24 0.03/0.24 with precondition: [B=2,C=255,254>=V__0,V__0>=1,V_b>=1] 0.03/0.24 0.03/0.24 * Chain [[11],14]: 1*it(11)+0 0.03/0.24 Such that:it(11) =< -V__0+255 0.03/0.24 0.03/0.24 with precondition: [B=3,254>=V__0,V__0>=1,V_b>=1] 0.03/0.24 0.03/0.24 * Chain [16]: 0 0.03/0.24 with precondition: [B=2,V__0=C,0>=V__0] 0.03/0.24 0.03/0.24 * Chain [15]: 0 0.03/0.24 with precondition: [B=2,V__0=C,V__0>=255] 0.03/0.24 0.03/0.24 * Chain [14]: 0 0.03/0.24 with precondition: [B=3] 0.03/0.24 0.03/0.24 0.03/0.24 #### Cost of chains of eval_ex3_bb1_in_loop_cont(A,B,C,D,E): 0.03/0.24 * Chain [18]: 0 0.03/0.24 with precondition: [A=2] 0.03/0.24 0.03/0.24 * Chain [17]: 0 0.03/0.24 with precondition: [A=3] 0.03/0.24 0.03/0.24 0.03/0.24 #### Cost of chains of eval_ex3_4(V__0,V_b,V_x,B): 0.03/0.24 * Chain [24]: 0 0.03/0.24 with precondition: [] 0.03/0.24 0.03/0.24 * Chain [23]: 2*s(1)+0 0.03/0.24 Such that:aux(1) =< V_x 0.03/0.24 s(1) =< aux(1) 0.03/0.24 0.03/0.24 with precondition: [V_b=0,254>=V_x,V_x>=1] 0.03/0.24 0.03/0.24 * Chain [22]: 2*s(3)+0 0.03/0.24 Such that:aux(2) =< -V_x+255 0.03/0.24 s(3) =< aux(2) 0.03/0.24 0.03/0.24 with precondition: [0>=V_b+1,254>=V_x,V_x>=1] 0.03/0.24 0.03/0.24 * Chain [21]: 2*s(5)+0 0.03/0.24 Such that:aux(3) =< -V_x+255 0.03/0.24 s(5) =< aux(3) 0.03/0.24 0.03/0.24 with precondition: [254>=V_x,V_b>=1,V_x>=1] 0.03/0.24 0.03/0.24 * Chain [20]: 0 0.03/0.24 with precondition: [0>=V_x] 0.03/0.24 0.03/0.24 * Chain [19]: 0 0.03/0.24 with precondition: [V_x>=255] 0.03/0.24 0.03/0.24 0.03/0.24 #### Cost of chains of eval_ex3_start(V__0,V_b,V_x,B): 0.03/0.24 * Chain [30]: 0 0.03/0.24 with precondition: [] 0.03/0.24 0.03/0.24 * Chain [29]: 2*s(8)+0 0.03/0.24 Such that:s(7) =< V_x 0.03/0.24 s(8) =< s(7) 0.03/0.24 0.03/0.24 with precondition: [V_b=0,254>=V_x,V_x>=1] 0.03/0.24 0.03/0.24 * Chain [28]: 2*s(10)+0 0.03/0.24 Such that:s(9) =< -V_x+255 0.03/0.24 s(10) =< s(9) 0.03/0.24 0.03/0.24 with precondition: [0>=V_b+1,254>=V_x,V_x>=1] 0.03/0.24 0.03/0.24 * Chain [27]: 2*s(12)+0 0.03/0.24 Such that:s(11) =< -V_x+255 0.03/0.24 s(12) =< s(11) 0.03/0.24 0.03/0.24 with precondition: [254>=V_x,V_b>=1,V_x>=1] 0.03/0.24 0.03/0.24 * Chain [26]: 0 0.03/0.24 with precondition: [0>=V_x] 0.03/0.24 0.03/0.24 * Chain [25]: 0 0.03/0.24 with precondition: [V_x>=255] 0.03/0.24 0.03/0.24 0.03/0.24 Closed-form bounds of eval_ex3_start(V__0,V_b,V_x,B): 0.03/0.24 ------------------------------------- 0.03/0.24 * Chain [30] with precondition: [] 0.03/0.24 - Upper bound: 0 0.03/0.24 - Complexity: constant 0.03/0.24 * Chain [29] with precondition: [V_b=0,254>=V_x,V_x>=1] 0.03/0.24 - Upper bound: 2*V_x 0.03/0.24 - Complexity: n 0.03/0.24 * Chain [28] with precondition: [0>=V_b+1,254>=V_x,V_x>=1] 0.03/0.24 - Upper bound: -2*V_x+510 0.03/0.24 - Complexity: n 0.03/0.24 * Chain [27] with precondition: [254>=V_x,V_b>=1,V_x>=1] 0.03/0.24 - Upper bound: -2*V_x+510 0.03/0.24 - Complexity: n 0.03/0.24 * Chain [26] with precondition: [0>=V_x] 0.03/0.24 - Upper bound: 0 0.03/0.24 - Complexity: constant 0.03/0.24 * Chain [25] with precondition: [V_x>=255] 0.03/0.24 - Upper bound: 0 0.03/0.24 - Complexity: constant 0.03/0.24 0.03/0.24 ### Maximum cost of eval_ex3_start(V__0,V_b,V_x,B): max([nat(V_x)*2,nat(-V_x+255)*2]) 0.03/0.24 Asymptotic class: n 0.03/0.24 * Total analysis performed in 179 ms. 0.03/0.24 0.03/0.34 EOF