0.05/0.15 WORST_CASE(?,O(n^1)) 0.05/0.15 0.05/0.15 Preprocessing Cost Relations 0.05/0.15 ===================================== 0.05/0.15 0.05/0.15 #### Computed strongly connected components 0.05/0.15 0. recursive : [eval_foo_bb1_in/3,eval_foo_bb2_in/3] 0.05/0.15 1. recursive : [eval_foo_bb3_in/3,eval_foo_bb4_in/3] 0.05/0.15 2. non_recursive : [eval_foo_stop/1] 0.05/0.15 3. non_recursive : [eval_foo_bb5_in/1] 0.05/0.15 4. non_recursive : [eval_foo_bb3_in_loop_cont/2] 0.05/0.15 5. non_recursive : [eval_foo_bb1_in_loop_cont/4] 0.05/0.15 6. non_recursive : [eval_foo_bb0_in/3] 0.05/0.15 7. non_recursive : [eval_foo_start/5] 0.05/0.15 0.05/0.15 #### Obtained direct recursion through partial evaluation 0.05/0.15 0. SCC is partially evaluated into eval_foo_bb1_in/3 0.05/0.15 1. SCC is partially evaluated into eval_foo_bb3_in/3 0.05/0.15 2. SCC is completely evaluated into other SCCs 0.05/0.15 3. SCC is completely evaluated into other SCCs 0.05/0.15 4. SCC is completely evaluated into other SCCs 0.05/0.15 5. SCC is partially evaluated into eval_foo_bb1_in_loop_cont/4 0.05/0.15 6. SCC is partially evaluated into eval_foo_bb0_in/3 0.05/0.15 7. SCC is partially evaluated into eval_foo_start/5 0.05/0.15 0.05/0.15 Control-Flow Refinement of Cost Relations 0.05/0.15 ===================================== 0.05/0.15 0.05/0.15 ### Specialization of cost equations eval_foo_bb1_in/3 0.05/0.15 * CE 6 is refined into CE [10] 0.05/0.15 * CE 5 is refined into CE [11] 0.05/0.15 0.05/0.15 0.05/0.15 ### Cost equations --> "Loop" of eval_foo_bb1_in/3 0.05/0.15 * CEs [11] --> Loop 10 0.05/0.15 * CEs [10] --> Loop 11 0.05/0.15 0.05/0.15 ### Ranking functions of CR eval_foo_bb1_in(V__01,B,C) 0.05/0.15 * RF of phase [10]: [V__01] 0.05/0.15 0.05/0.15 #### Partial ranking functions of CR eval_foo_bb1_in(V__01,B,C) 0.05/0.15 * Partial RF of phase [10]: 0.05/0.15 - RF of loop [10:1]: 0.05/0.15 V__01 0.05/0.15 0.05/0.15 0.05/0.15 ### Specialization of cost equations eval_foo_bb3_in/3 0.05/0.15 * CE 9 is refined into CE [12] 0.05/0.15 * CE 8 is refined into CE [13] 0.05/0.15 0.05/0.15 0.05/0.15 ### Cost equations --> "Loop" of eval_foo_bb3_in/3 0.05/0.15 * CEs [13] --> Loop 12 0.05/0.15 * CEs [12] --> Loop 13 0.05/0.15 0.05/0.15 ### Ranking functions of CR eval_foo_bb3_in(V_y,V__12,B) 0.05/0.15 * RF of phase [12]: [V_y-V__12] 0.05/0.15 0.05/0.15 #### Partial ranking functions of CR eval_foo_bb3_in(V_y,V__12,B) 0.05/0.15 * Partial RF of phase [12]: 0.05/0.15 - RF of loop [12:1]: 0.05/0.15 V_y-V__12 0.05/0.15 0.05/0.15 0.05/0.15 ### Specialization of cost equations eval_foo_bb1_in_loop_cont/4 0.05/0.15 * CE 7 is refined into CE [14,15] 0.05/0.15 0.05/0.15 0.05/0.15 ### Cost equations --> "Loop" of eval_foo_bb1_in_loop_cont/4 0.05/0.15 * CEs [15] --> Loop 14 0.05/0.15 * CEs [14] --> Loop 15 0.05/0.15 0.05/0.15 ### Ranking functions of CR eval_foo_bb1_in_loop_cont(A,B,C,D) 0.05/0.15 0.05/0.15 #### Partial ranking functions of CR eval_foo_bb1_in_loop_cont(A,B,C,D) 0.05/0.15 0.05/0.15 0.05/0.15 ### Specialization of cost equations eval_foo_bb0_in/3 0.05/0.15 * CE 4 is refined into CE [16] 0.05/0.15 * CE 2 is refined into CE [17] 0.05/0.15 * CE 3 is refined into CE [18] 0.05/0.15 0.05/0.15 0.05/0.15 ### Cost equations --> "Loop" of eval_foo_bb0_in/3 0.05/0.15 * CEs [16] --> Loop 16 0.05/0.15 * CEs [17] --> Loop 17 0.05/0.15 * CEs [18] --> Loop 18 0.05/0.15 0.05/0.15 ### Ranking functions of CR eval_foo_bb0_in(V_x,V_y,B) 0.05/0.15 0.05/0.15 #### Partial ranking functions of CR eval_foo_bb0_in(V_x,V_y,B) 0.05/0.15 0.05/0.15 0.05/0.15 ### Specialization of cost equations eval_foo_start/5 0.05/0.15 * CE 1 is refined into CE [19,20,21] 0.05/0.15 0.05/0.15 0.05/0.15 ### Cost equations --> "Loop" of eval_foo_start/5 0.05/0.15 * CEs [21] --> Loop 19 0.05/0.15 * CEs [20] --> Loop 20 0.05/0.15 * CEs [19] --> Loop 21 0.05/0.15 0.05/0.15 ### Ranking functions of CR eval_foo_start(V_x,V_y,V_z,V_i,B) 0.05/0.15 0.05/0.15 #### Partial ranking functions of CR eval_foo_start(V_x,V_y,V_z,V_i,B) 0.05/0.15 0.05/0.15 0.05/0.15 Computing Bounds 0.05/0.15 ===================================== 0.05/0.15 0.05/0.15 #### Cost of chains of eval_foo_bb1_in(V__01,B,C): 0.05/0.15 * Chain [[10],11]: 1*it(10)+0 0.05/0.15 Such that:it(10) =< V__01 0.05/0.15 0.05/0.15 with precondition: [B=3,C=0,V__01>=1] 0.05/0.15 0.05/0.15 0.05/0.15 #### Cost of chains of eval_foo_bb3_in(V_y,V__12,B): 0.05/0.15 * Chain [[12],13]: 1*it(12)+0 0.05/0.15 Such that:it(12) =< V_y-V__12 0.05/0.15 0.05/0.15 with precondition: [B=2,V_y>=1,V_y>=V__12+1] 0.05/0.15 0.05/0.15 * Chain [13]: 0 0.05/0.15 with precondition: [B=2,V_y>=1,V__12>=V_y] 0.05/0.15 0.05/0.15 0.05/0.15 #### Cost of chains of eval_foo_bb1_in_loop_cont(A,B,C,D): 0.05/0.15 * Chain [15]: 0 0.05/0.15 with precondition: [A=3,B>=1,C>=B] 0.05/0.15 0.05/0.15 * Chain [14]: 1*s(1)+0 0.05/0.15 Such that:s(1) =< B-C 0.05/0.15 0.05/0.15 with precondition: [A=3,B>=1,B>=C+1] 0.05/0.15 0.05/0.15 0.05/0.15 #### Cost of chains of eval_foo_bb0_in(V_x,V_y,B): 0.05/0.15 * Chain [18]: 0 0.05/0.15 with precondition: [0>=V_x] 0.05/0.15 0.05/0.15 * Chain [17]: 0 0.05/0.15 with precondition: [0>=V_y] 0.05/0.15 0.05/0.15 * Chain [16]: 1*s(2)+1*s(3)+0 0.05/0.15 Such that:s(2) =< V_x 0.05/0.15 s(3) =< V_y 0.05/0.15 0.05/0.15 with precondition: [V_x>=1,V_y>=1] 0.05/0.15 0.05/0.15 0.05/0.15 #### Cost of chains of eval_foo_start(V_x,V_y,V_z,V_i,B): 0.05/0.15 * Chain [21]: 0 0.05/0.15 with precondition: [0>=V_x] 0.05/0.15 0.05/0.15 * Chain [20]: 0 0.05/0.15 with precondition: [0>=V_y] 0.05/0.15 0.05/0.15 * Chain [19]: 1*s(4)+1*s(5)+0 0.05/0.15 Such that:s(4) =< V_x 0.05/0.15 s(5) =< V_y 0.05/0.15 0.05/0.15 with precondition: [V_x>=1,V_y>=1] 0.05/0.15 0.05/0.15 0.05/0.15 Closed-form bounds of eval_foo_start(V_x,V_y,V_z,V_i,B): 0.05/0.15 ------------------------------------- 0.05/0.15 * Chain [21] with precondition: [0>=V_x] 0.05/0.15 - Upper bound: 0 0.05/0.15 - Complexity: constant 0.05/0.15 * Chain [20] with precondition: [0>=V_y] 0.05/0.15 - Upper bound: 0 0.05/0.15 - Complexity: constant 0.05/0.15 * Chain [19] with precondition: [V_x>=1,V_y>=1] 0.05/0.15 - Upper bound: V_x+V_y 0.05/0.15 - Complexity: n 0.05/0.15 0.05/0.15 ### Maximum cost of eval_foo_start(V_x,V_y,V_z,V_i,B): nat(V_y)+nat(V_x) 0.05/0.15 Asymptotic class: n 0.05/0.15 * Total analysis performed in 84 ms. 0.05/0.15 0.05/0.26 EOF