0.05/0.18 WORST_CASE(?,O(n^1)) 0.05/0.18 0.05/0.18 Preprocessing Cost Relations 0.05/0.18 ===================================== 0.05/0.18 0.05/0.18 #### Computed strongly connected components 0.05/0.18 0. recursive : [eval_Loopus2011_ex3_bb1_in/3,eval_Loopus2011_ex3_bb2_in/3] 0.05/0.18 1. non_recursive : [eval_Loopus2011_ex3_stop/1] 0.05/0.18 2. non_recursive : [eval_Loopus2011_ex3_bb3_in/1] 0.05/0.18 3. non_recursive : [eval_Loopus2011_ex3_bb1_in_loop_cont/2] 0.05/0.18 4. non_recursive : [eval_Loopus2011_ex3_bb0_in/3] 0.05/0.18 5. non_recursive : [eval_Loopus2011_ex3_start/3] 0.05/0.18 0.05/0.18 #### Obtained direct recursion through partial evaluation 0.05/0.18 0. SCC is partially evaluated into eval_Loopus2011_ex3_bb1_in/3 0.05/0.18 1. SCC is completely evaluated into other SCCs 0.05/0.18 2. SCC is completely evaluated into other SCCs 0.05/0.18 3. SCC is completely evaluated into other SCCs 0.05/0.18 4. SCC is partially evaluated into eval_Loopus2011_ex3_bb0_in/3 0.05/0.18 5. SCC is partially evaluated into eval_Loopus2011_ex3_start/3 0.05/0.18 0.05/0.18 Control-Flow Refinement of Cost Relations 0.05/0.18 ===================================== 0.05/0.18 0.05/0.18 ### Specialization of cost equations eval_Loopus2011_ex3_bb1_in/3 0.05/0.18 * CE 7 is refined into CE [8] 0.05/0.18 * CE 6 is refined into CE [9] 0.05/0.18 * CE 4 is refined into CE [10] 0.05/0.18 * CE 5 is refined into CE [11] 0.05/0.18 * CE 3 is refined into CE [12] 0.05/0.18 0.05/0.18 0.05/0.18 ### Cost equations --> "Loop" of eval_Loopus2011_ex3_bb1_in/3 0.05/0.18 * CEs [10] --> Loop 8 0.05/0.18 * CEs [11] --> Loop 9 0.05/0.18 * CEs [12] --> Loop 10 0.05/0.18 * CEs [8] --> Loop 11 0.05/0.18 * CEs [9] --> Loop 12 0.05/0.18 0.05/0.18 ### Ranking functions of CR eval_Loopus2011_ex3_bb1_in(V_b,V__0,B) 0.05/0.18 * RF of phase [8]: [-V__0+255] 0.05/0.18 * RF of phase [9]: [-V__0+255] 0.05/0.18 * RF of phase [10]: [V__0] 0.05/0.18 0.05/0.18 #### Partial ranking functions of CR eval_Loopus2011_ex3_bb1_in(V_b,V__0,B) 0.05/0.18 * Partial RF of phase [8]: 0.05/0.18 - RF of loop [8:1]: 0.05/0.18 -V__0+255 0.05/0.18 * Partial RF of phase [9]: 0.05/0.18 - RF of loop [9:1]: 0.05/0.18 -V__0+255 0.05/0.18 * Partial RF of phase [10]: 0.05/0.18 - RF of loop [10:1]: 0.05/0.18 V__0 0.05/0.18 0.05/0.18 0.05/0.18 ### Specialization of cost equations eval_Loopus2011_ex3_bb0_in/3 0.05/0.18 * CE 2 is refined into CE [13,14,15,16,17] 0.05/0.18 0.05/0.18 0.05/0.18 ### Cost equations --> "Loop" of eval_Loopus2011_ex3_bb0_in/3 0.05/0.18 * CEs [17] --> Loop 13 0.05/0.18 * CEs [16] --> Loop 14 0.05/0.18 * CEs [15] --> Loop 15 0.05/0.18 * CEs [14] --> Loop 16 0.05/0.18 * CEs [13] --> Loop 17 0.05/0.18 0.05/0.18 ### Ranking functions of CR eval_Loopus2011_ex3_bb0_in(V_x,V_b,B) 0.05/0.18 0.05/0.18 #### Partial ranking functions of CR eval_Loopus2011_ex3_bb0_in(V_x,V_b,B) 0.05/0.18 0.05/0.18 0.05/0.18 ### Specialization of cost equations eval_Loopus2011_ex3_start/3 0.05/0.18 * CE 1 is refined into CE [18,19,20,21,22] 0.05/0.18 0.05/0.18 0.05/0.18 ### Cost equations --> "Loop" of eval_Loopus2011_ex3_start/3 0.05/0.18 * CEs [22] --> Loop 18 0.05/0.18 * CEs [21] --> Loop 19 0.05/0.18 * CEs [20] --> Loop 20 0.05/0.18 * CEs [19] --> Loop 21 0.05/0.18 * CEs [18] --> Loop 22 0.05/0.18 0.05/0.18 ### Ranking functions of CR eval_Loopus2011_ex3_start(V_x,V_b,B) 0.05/0.18 0.05/0.18 #### Partial ranking functions of CR eval_Loopus2011_ex3_start(V_x,V_b,B) 0.05/0.18 0.05/0.18 0.05/0.18 Computing Bounds 0.05/0.18 ===================================== 0.05/0.18 0.05/0.18 #### Cost of chains of eval_Loopus2011_ex3_bb1_in(V_b,V__0,B): 0.05/0.18 * Chain [[10],12]: 1*it(10)+0 0.05/0.18 Such that:it(10) =< V__0 0.05/0.18 0.05/0.18 with precondition: [V_b=0,B=2,254>=V__0,V__0>=1] 0.05/0.18 0.05/0.18 * Chain [[9],11]: 1*it(9)+0 0.05/0.18 Such that:it(9) =< -V__0+255 0.05/0.18 0.05/0.18 with precondition: [B=2,0>=V_b+1,254>=V__0,V__0>=1] 0.05/0.18 0.05/0.18 * Chain [[8],11]: 1*it(8)+0 0.05/0.18 Such that:it(8) =< -V__0+255 0.05/0.18 0.05/0.18 with precondition: [B=2,254>=V__0,V_b>=1,V__0>=1] 0.05/0.18 0.05/0.18 * Chain [12]: 0 0.05/0.18 with precondition: [B=2,0>=V__0] 0.05/0.18 0.05/0.18 * Chain [11]: 0 0.05/0.18 with precondition: [B=2,V__0>=255] 0.05/0.18 0.05/0.18 0.05/0.18 #### Cost of chains of eval_Loopus2011_ex3_bb0_in(V_x,V_b,B): 0.05/0.18 * Chain [17]: 1*s(1)+0 0.05/0.18 Such that:s(1) =< V_x 0.05/0.18 0.05/0.18 with precondition: [V_b=0,254>=V_x,V_x>=1] 0.05/0.18 0.05/0.18 * Chain [16]: 1*s(2)+0 0.05/0.18 Such that:s(2) =< -V_x+255 0.05/0.18 0.05/0.18 with precondition: [254>=V_x,0>=V_b+1,V_x>=1] 0.05/0.18 0.05/0.18 * Chain [15]: 1*s(3)+0 0.05/0.18 Such that:s(3) =< -V_x+255 0.05/0.18 0.05/0.18 with precondition: [254>=V_x,V_x>=1,V_b>=1] 0.05/0.18 0.05/0.18 * Chain [14]: 0 0.05/0.18 with precondition: [0>=V_x] 0.05/0.18 0.05/0.18 * Chain [13]: 0 0.05/0.18 with precondition: [V_x>=255] 0.05/0.18 0.05/0.18 0.05/0.18 #### Cost of chains of eval_Loopus2011_ex3_start(V_x,V_b,B): 0.05/0.18 * Chain [22]: 1*s(4)+0 0.05/0.18 Such that:s(4) =< V_x 0.05/0.18 0.05/0.18 with precondition: [V_b=0,254>=V_x,V_x>=1] 0.05/0.18 0.05/0.18 * Chain [21]: 1*s(5)+0 0.05/0.18 Such that:s(5) =< -V_x+255 0.05/0.18 0.05/0.18 with precondition: [254>=V_x,0>=V_b+1,V_x>=1] 0.05/0.18 0.05/0.18 * Chain [20]: 1*s(6)+0 0.05/0.18 Such that:s(6) =< -V_x+255 0.05/0.18 0.05/0.18 with precondition: [254>=V_x,V_x>=1,V_b>=1] 0.05/0.18 0.05/0.18 * Chain [19]: 0 0.05/0.18 with precondition: [0>=V_x] 0.05/0.18 0.05/0.18 * Chain [18]: 0 0.05/0.18 with precondition: [V_x>=255] 0.05/0.18 0.05/0.18 0.05/0.18 Closed-form bounds of eval_Loopus2011_ex3_start(V_x,V_b,B): 0.05/0.18 ------------------------------------- 0.05/0.18 * Chain [22] with precondition: [V_b=0,254>=V_x,V_x>=1] 0.05/0.18 - Upper bound: V_x 0.05/0.18 - Complexity: n 0.05/0.18 * Chain [21] with precondition: [254>=V_x,0>=V_b+1,V_x>=1] 0.05/0.18 - Upper bound: -V_x+255 0.05/0.18 - Complexity: n 0.05/0.18 * Chain [20] with precondition: [254>=V_x,V_x>=1,V_b>=1] 0.05/0.18 - Upper bound: -V_x+255 0.05/0.18 - Complexity: n 0.05/0.18 * Chain [19] with precondition: [0>=V_x] 0.05/0.18 - Upper bound: 0 0.05/0.18 - Complexity: constant 0.05/0.18 * Chain [18] with precondition: [V_x>=255] 0.05/0.18 - Upper bound: 0 0.05/0.18 - Complexity: constant 0.05/0.18 0.05/0.18 ### Maximum cost of eval_Loopus2011_ex3_start(V_x,V_b,B): max([nat(V_x),nat(-V_x+255)]) 0.05/0.18 Asymptotic class: n 0.05/0.18 * Total analysis performed in 110 ms. 0.05/0.18 0.05/0.28 EOF