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_foo_bb2_in/7,eval_foo_bb3_in/7] 0.05/0.18 1. recursive : [eval_foo_bb1_in/3,eval_foo_bb2_in_loop_cont/4] 0.05/0.18 2. non_recursive : [eval_foo_stop/1] 0.05/0.18 3. non_recursive : [eval_foo_bb4_in/1] 0.05/0.18 4. non_recursive : [eval_foo_bb1_in_loop_cont/2] 0.05/0.18 5. non_recursive : [eval_foo_bb0_in/3] 0.05/0.18 6. non_recursive : [eval_foo_start/4] 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_foo_bb2_in/7 0.05/0.18 1. SCC is partially evaluated into eval_foo_bb1_in/3 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 completely evaluated into other SCCs 0.05/0.18 5. SCC is partially evaluated into eval_foo_bb0_in/3 0.05/0.18 6. SCC is partially evaluated into eval_foo_start/4 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_foo_bb2_in/7 0.05/0.18 * CE 8 is refined into CE [9] 0.05/0.18 * CE 7 is refined into CE [10] 0.05/0.18 0.05/0.18 0.05/0.18 ### Cost equations --> "Loop" of eval_foo_bb2_in/7 0.05/0.18 * CEs [10] --> Loop 9 0.05/0.18 * CEs [9] --> Loop 10 0.05/0.18 0.05/0.18 ### Ranking functions of CR eval_foo_bb2_in(V__03,V__01,V__14,V__12,B,C,D) 0.05/0.18 * RF of phase [9]: [V__12,V__14] 0.05/0.18 0.05/0.18 #### Partial ranking functions of CR eval_foo_bb2_in(V__03,V__01,V__14,V__12,B,C,D) 0.05/0.18 * Partial RF of phase [9]: 0.05/0.18 - RF of loop [9:1]: 0.05/0.18 V__12 0.05/0.18 V__14 0.05/0.18 0.05/0.18 0.05/0.18 ### Specialization of cost equations eval_foo_bb1_in/3 0.05/0.18 * CE 4 is refined into CE [11] 0.05/0.18 * CE 5 is refined into CE [12] 0.05/0.18 * CE 6 is refined into CE [13] 0.05/0.18 * CE 3 is refined into CE [14] 0.05/0.18 0.05/0.18 0.05/0.18 ### Cost equations --> "Loop" of eval_foo_bb1_in/3 0.05/0.18 * CEs [14] --> Loop 11 0.05/0.18 * CEs [11] --> Loop 12 0.05/0.18 * CEs [12] --> Loop 13 0.05/0.18 * CEs [13] --> Loop 14 0.05/0.18 0.05/0.18 ### Ranking functions of CR eval_foo_bb1_in(V__03,V__01,B) 0.05/0.18 0.05/0.18 #### Partial ranking functions of CR eval_foo_bb1_in(V__03,V__01,B) 0.05/0.18 0.05/0.18 0.05/0.18 ### Specialization of cost equations eval_foo_bb0_in/3 0.05/0.18 * CE 2 is refined into CE [15,16,17,18] 0.05/0.18 0.05/0.18 0.05/0.18 ### Cost equations --> "Loop" of eval_foo_bb0_in/3 0.05/0.18 * CEs [17] --> Loop 15 0.05/0.18 * CEs [18] --> Loop 16 0.05/0.18 * CEs [16] --> Loop 17 0.05/0.18 * CEs [15] --> Loop 18 0.05/0.18 0.05/0.18 ### Ranking functions of CR eval_foo_bb0_in(V_x,V_y,B) 0.05/0.18 0.05/0.18 #### Partial ranking functions of CR eval_foo_bb0_in(V_x,V_y,B) 0.05/0.18 0.05/0.18 0.05/0.18 ### Specialization of cost equations eval_foo_start/4 0.05/0.18 * CE 1 is refined into CE [19,20,21,22] 0.05/0.18 0.05/0.18 0.05/0.18 ### Cost equations --> "Loop" of eval_foo_start/4 0.05/0.18 * CEs [22] --> Loop 19 0.05/0.18 * CEs [21] --> Loop 20 0.05/0.18 * CEs [20] --> Loop 21 0.05/0.18 * CEs [19] --> Loop 22 0.05/0.18 0.05/0.18 ### Ranking functions of CR eval_foo_start(V_c,V_x,V_y,B) 0.05/0.18 0.05/0.18 #### Partial ranking functions of CR eval_foo_start(V_c,V_x,V_y,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_foo_bb2_in(V__03,V__01,V__14,V__12,B,C,D): 0.05/0.18 * Chain [[9],10]: 1*it(9)+0 0.05/0.18 Such that:it(9) =< V__14 0.05/0.18 0.05/0.18 with precondition: [B=2,C=0,D=0,V__03=V__01,V__14=V__12,V__14>=1,V__03>=V__14] 0.05/0.18 0.05/0.18 0.05/0.18 #### Cost of chains of eval_foo_bb1_in(V__03,V__01,B): 0.05/0.18 * Chain [14]: 0 0.05/0.18 with precondition: [B=3,0>=V__01] 0.05/0.18 0.05/0.18 * Chain [13]: 0 0.05/0.18 with precondition: [B=3,V__01>=V__03+1] 0.05/0.18 0.05/0.18 * Chain [12]: 0 0.05/0.18 with precondition: [B=3,V__03>=V__01+1] 0.05/0.18 0.05/0.18 * Chain [11,14]: 1*s(1)+1 0.05/0.18 Such that:s(1) =< V__03 0.05/0.18 0.05/0.18 with precondition: [B=3,V__03=V__01,V__03>=1] 0.05/0.18 0.05/0.18 0.05/0.18 #### Cost of chains of eval_foo_bb0_in(V_x,V_y,B): 0.05/0.18 * Chain [18]: 1*s(2)+1 0.05/0.18 Such that:s(2) =< V_y 0.05/0.18 0.05/0.18 with precondition: [V_x=V_y,V_x>=1] 0.05/0.18 0.05/0.18 * Chain [17]: 0 0.05/0.18 with precondition: [0>=V_x] 0.05/0.18 0.05/0.18 * Chain [16]: 0 0.05/0.18 with precondition: [V_y>=V_x+1] 0.05/0.18 0.05/0.18 * Chain [15]: 0 0.05/0.18 with precondition: [V_x>=V_y+1] 0.05/0.18 0.05/0.18 0.05/0.18 #### Cost of chains of eval_foo_start(V_c,V_x,V_y,B): 0.05/0.18 * Chain [22]: 1*s(3)+1 0.05/0.18 Such that:s(3) =< V_x 0.05/0.18 0.05/0.18 with precondition: [V_x=V_y,V_x>=1] 0.05/0.18 0.05/0.18 * Chain [21]: 0 0.05/0.18 with precondition: [0>=V_x] 0.05/0.18 0.05/0.18 * Chain [20]: 0 0.05/0.18 with precondition: [V_y>=V_x+1] 0.05/0.18 0.05/0.18 * Chain [19]: 0 0.05/0.18 with precondition: [V_x>=V_y+1] 0.05/0.18 0.05/0.18 0.05/0.18 Closed-form bounds of eval_foo_start(V_c,V_x,V_y,B): 0.05/0.18 ------------------------------------- 0.05/0.18 * Chain [22] with precondition: [V_x=V_y,V_x>=1] 0.05/0.18 - Upper bound: V_x+1 0.05/0.18 - Complexity: n 0.05/0.18 * Chain [21] with precondition: [0>=V_x] 0.05/0.18 - Upper bound: 0 0.05/0.18 - Complexity: constant 0.05/0.18 * Chain [20] with precondition: [V_y>=V_x+1] 0.05/0.18 - Upper bound: 0 0.05/0.18 - Complexity: constant 0.05/0.18 * Chain [19] with precondition: [V_x>=V_y+1] 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_foo_start(V_c,V_x,V_y,B): nat(V_x)+1 0.05/0.18 Asymptotic class: n 0.05/0.18 * Total analysis performed in 112 ms. 0.05/0.18 0.05/0.29 EOF