0.05/0.20 WORST_CASE(?,O(n^1)) 0.05/0.20 0.05/0.20 Preprocessing Cost Relations 0.05/0.20 ===================================== 0.05/0.20 0.05/0.20 #### Computed strongly connected components 0.05/0.20 0. recursive : [eval_foo_bb2_in/5,eval_foo_bb3_in/5,eval_foo_bb4_in/5,eval_foo_bb5_in/5] 0.05/0.20 1. recursive : [eval_foo_bb1_in/3,eval_foo_bb2_in_loop_cont/6,eval_foo_bb6_in/5] 0.05/0.20 2. non_recursive : [eval_foo_stop/1] 0.05/0.20 3. non_recursive : [eval_foo_bb7_in/1] 0.05/0.20 4. non_recursive : [eval_foo_bb1_in_loop_cont/2] 0.05/0.20 5. non_recursive : [eval_foo_bb0_in/3] 0.05/0.20 6. non_recursive : [eval_foo_start/5] 0.05/0.20 0.05/0.20 #### Obtained direct recursion through partial evaluation 0.05/0.20 0. SCC is partially evaluated into eval_foo_bb2_in/5 0.05/0.20 1. SCC is partially evaluated into eval_foo_bb1_in/3 0.05/0.20 2. SCC is completely evaluated into other SCCs 0.05/0.20 3. SCC is completely evaluated into other SCCs 0.05/0.20 4. SCC is completely evaluated into other SCCs 0.05/0.20 5. SCC is partially evaluated into eval_foo_bb0_in/3 0.05/0.20 6. SCC is partially evaluated into eval_foo_start/5 0.05/0.20 0.05/0.20 Control-Flow Refinement of Cost Relations 0.05/0.20 ===================================== 0.05/0.20 0.05/0.20 ### Specialization of cost equations eval_foo_bb2_in/5 0.05/0.20 * CE 8 is refined into CE [9] 0.05/0.20 * CE 6 is refined into CE [10] 0.05/0.20 * CE 7 is discarded (unfeasible) 0.05/0.20 0.05/0.20 0.05/0.20 ### Cost equations --> "Loop" of eval_foo_bb2_in/5 0.05/0.20 * CEs [10] --> Loop 9 0.05/0.20 * CEs [9] --> Loop 10 0.05/0.20 0.05/0.20 ### Ranking functions of CR eval_foo_bb2_in(V__01,V__1,B,C,D) 0.05/0.20 * RF of phase [9]: [V__01,V__1] 0.05/0.20 0.05/0.20 #### Partial ranking functions of CR eval_foo_bb2_in(V__01,V__1,B,C,D) 0.05/0.20 * Partial RF of phase [9]: 0.05/0.20 - RF of loop [9:1]: 0.05/0.20 V__01 0.05/0.20 V__1 0.05/0.20 0.05/0.20 0.05/0.20 ### Specialization of cost equations eval_foo_bb1_in/3 0.05/0.20 * CE 4 is refined into CE [11] 0.05/0.20 * CE 5 is refined into CE [12] 0.05/0.20 * CE 3 is refined into CE [13] 0.05/0.20 0.05/0.20 0.05/0.20 ### Cost equations --> "Loop" of eval_foo_bb1_in/3 0.05/0.20 * CEs [13] --> Loop 11 0.05/0.20 * CEs [11] --> Loop 12 0.05/0.20 * CEs [12] --> Loop 13 0.05/0.20 0.05/0.20 ### Ranking functions of CR eval_foo_bb1_in(V_y,V__0,B) 0.05/0.20 * RF of phase [11]: [V__0,-V_y+V__0+1] 0.05/0.20 0.05/0.20 #### Partial ranking functions of CR eval_foo_bb1_in(V_y,V__0,B) 0.05/0.20 * Partial RF of phase [11]: 0.05/0.20 - RF of loop [11:1]: 0.05/0.20 V__0 0.05/0.20 -V_y+V__0+1 0.05/0.20 0.05/0.20 0.05/0.20 ### Specialization of cost equations eval_foo_bb0_in/3 0.05/0.20 * CE 2 is refined into CE [14,15,16] 0.05/0.20 0.05/0.20 0.05/0.20 ### Cost equations --> "Loop" of eval_foo_bb0_in/3 0.05/0.20 * CEs [16] --> Loop 14 0.05/0.20 * CEs [15] --> Loop 15 0.05/0.20 * CEs [14] --> Loop 16 0.05/0.20 0.05/0.20 ### Ranking functions of CR eval_foo_bb0_in(V_x,V_y,B) 0.05/0.20 0.05/0.20 #### Partial ranking functions of CR eval_foo_bb0_in(V_x,V_y,B) 0.05/0.20 0.05/0.20 0.05/0.20 ### Specialization of cost equations eval_foo_start/5 0.05/0.20 * CE 1 is refined into CE [17,18,19] 0.05/0.20 0.05/0.20 0.05/0.20 ### Cost equations --> "Loop" of eval_foo_start/5 0.05/0.20 * CEs [19] --> Loop 17 0.05/0.20 * CEs [18] --> Loop 18 0.05/0.20 * CEs [17] --> Loop 19 0.05/0.20 0.05/0.20 ### Ranking functions of CR eval_foo_start(V_x,V_y,V_ytmp,V_res,B) 0.05/0.20 0.05/0.20 #### Partial ranking functions of CR eval_foo_start(V_x,V_y,V_ytmp,V_res,B) 0.05/0.20 0.05/0.20 0.05/0.20 Computing Bounds 0.05/0.20 ===================================== 0.05/0.20 0.05/0.20 #### Cost of chains of eval_foo_bb2_in(V__01,V__1,B,C,D): 0.05/0.20 * Chain [[9],10]: 1*it(9)+0 0.05/0.20 Such that:it(9) =< V__01 0.05/0.20 0.05/0.20 with precondition: [B=2,C=0,V__01+D=V__1,V__01>=1,V__1>=V__01] 0.05/0.20 0.05/0.20 0.05/0.20 #### Cost of chains of eval_foo_bb1_in(V_y,V__0,B): 0.05/0.20 * Chain [[11],12]: 1*it(11)+1*s(3)+0 0.05/0.20 Such that:it(11) =< -V_y+V__0+1 0.05/0.20 aux(3) =< V__0 0.05/0.20 it(11) =< aux(3) 0.05/0.20 s(3) =< aux(3) 0.05/0.20 0.05/0.20 with precondition: [B=3,V_y>=1,V__0>=V_y] 0.05/0.20 0.05/0.20 * Chain [13]: 0 0.05/0.20 with precondition: [B=3,0>=V_y] 0.05/0.20 0.05/0.20 * Chain [12]: 0 0.05/0.20 with precondition: [B=3,V_y>=V__0+1] 0.05/0.20 0.05/0.20 0.05/0.20 #### Cost of chains of eval_foo_bb0_in(V_x,V_y,B): 0.05/0.20 * Chain [16]: 0 0.05/0.20 with precondition: [0>=V_y] 0.05/0.20 0.05/0.20 * Chain [15]: 1*s(4)+1*s(6)+0 0.05/0.20 Such that:s(5) =< V_x 0.05/0.20 s(4) =< V_x-V_y+1 0.05/0.20 s(4) =< s(5) 0.05/0.20 s(6) =< s(5) 0.05/0.20 0.05/0.20 with precondition: [V_y>=1,V_x>=V_y] 0.05/0.20 0.05/0.20 * Chain [14]: 0 0.05/0.20 with precondition: [V_y>=V_x+1] 0.05/0.20 0.05/0.20 0.05/0.20 #### Cost of chains of eval_foo_start(V_x,V_y,V_ytmp,V_res,B): 0.05/0.20 * Chain [19]: 0 0.05/0.20 with precondition: [0>=V_y] 0.05/0.20 0.05/0.20 * Chain [18]: 1*s(8)+1*s(9)+0 0.05/0.20 Such that:s(7) =< V_x 0.05/0.20 s(8) =< V_x-V_y+1 0.05/0.20 s(8) =< s(7) 0.05/0.20 s(9) =< s(7) 0.05/0.20 0.05/0.20 with precondition: [V_y>=1,V_x>=V_y] 0.05/0.20 0.05/0.20 * Chain [17]: 0 0.05/0.20 with precondition: [V_y>=V_x+1] 0.05/0.20 0.05/0.20 0.05/0.20 Closed-form bounds of eval_foo_start(V_x,V_y,V_ytmp,V_res,B): 0.05/0.20 ------------------------------------- 0.05/0.20 * Chain [19] with precondition: [0>=V_y] 0.05/0.20 - Upper bound: 0 0.05/0.20 - Complexity: constant 0.05/0.20 * Chain [18] with precondition: [V_y>=1,V_x>=V_y] 0.05/0.20 - Upper bound: 2*V_x-V_y+1 0.05/0.20 - Complexity: n 0.05/0.20 * Chain [17] with precondition: [V_y>=V_x+1] 0.05/0.20 - Upper bound: 0 0.05/0.20 - Complexity: constant 0.05/0.20 0.05/0.20 ### Maximum cost of eval_foo_start(V_x,V_y,V_ytmp,V_res,B): nat(V_x-V_y+1)+nat(V_x) 0.05/0.20 Asymptotic class: n 0.05/0.20 * Total analysis performed in 120 ms. 0.05/0.20 0.05/0.30 EOF