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/8,eval_foo_bb3_in/8] 0.05/0.20 1. recursive : [eval_foo_bb1_in/4,eval_foo_bb2_in_loop_cont/5] 0.05/0.20 2. non_recursive : [eval_foo_stop/1] 0.05/0.20 3. non_recursive : [eval_foo_bb4_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/4] 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/8 0.05/0.20 1. SCC is partially evaluated into eval_foo_bb1_in/4 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/4 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/8 0.05/0.20 * CE 8 is refined into CE [9] 0.05/0.20 * CE 7 is refined into CE [10] 0.05/0.20 0.05/0.20 0.05/0.21 ### Cost equations --> "Loop" of eval_foo_bb2_in/8 0.05/0.21 * CEs [10] --> Loop 9 0.05/0.21 * CEs [9] --> Loop 10 0.05/0.21 0.05/0.21 ### Ranking functions of CR eval_foo_bb2_in(V_z,V__03,V__01,V__14,V__12,B,C,D) 0.05/0.21 * RF of phase [9]: [-V_z+V__12,-V_z+V__14] 0.05/0.21 0.05/0.21 #### Partial ranking functions of CR eval_foo_bb2_in(V_z,V__03,V__01,V__14,V__12,B,C,D) 0.05/0.21 * Partial RF of phase [9]: 0.05/0.21 - RF of loop [9:1]: 0.05/0.21 -V_z+V__12 0.05/0.21 -V_z+V__14 0.05/0.21 0.05/0.21 0.05/0.21 ### Specialization of cost equations eval_foo_bb1_in/4 0.05/0.21 * CE 4 is refined into CE [11] 0.05/0.21 * CE 6 is refined into CE [12] 0.05/0.21 * CE 5 is refined into CE [13] 0.05/0.21 * CE 3 is refined into CE [14] 0.05/0.21 0.05/0.21 0.05/0.21 ### Cost equations --> "Loop" of eval_foo_bb1_in/4 0.05/0.21 * CEs [14] --> Loop 11 0.05/0.21 * CEs [11] --> Loop 12 0.05/0.21 * CEs [12] --> Loop 13 0.05/0.21 * CEs [13] --> Loop 14 0.05/0.21 0.05/0.21 ### Ranking functions of CR eval_foo_bb1_in(V_z,V__03,V__01,B) 0.05/0.21 0.05/0.21 #### Partial ranking functions of CR eval_foo_bb1_in(V_z,V__03,V__01,B) 0.05/0.21 0.05/0.21 0.05/0.21 ### Specialization of cost equations eval_foo_bb0_in/4 0.05/0.21 * CE 2 is refined into CE [15,16,17,18] 0.05/0.21 0.05/0.21 0.05/0.21 ### Cost equations --> "Loop" of eval_foo_bb0_in/4 0.05/0.21 * CEs [16] --> Loop 15 0.05/0.21 * CEs [17] --> Loop 16 0.05/0.21 * CEs [18] --> Loop 17 0.05/0.21 * CEs [15] --> Loop 18 0.05/0.21 0.05/0.21 ### Ranking functions of CR eval_foo_bb0_in(V_x,V_y,V_z,B) 0.05/0.21 0.05/0.21 #### Partial ranking functions of CR eval_foo_bb0_in(V_x,V_y,V_z,B) 0.05/0.21 0.05/0.21 0.05/0.21 ### Specialization of cost equations eval_foo_start/5 0.05/0.21 * CE 1 is refined into CE [19,20,21,22] 0.05/0.21 0.05/0.21 0.05/0.21 ### Cost equations --> "Loop" of eval_foo_start/5 0.05/0.21 * CEs [22] --> Loop 19 0.05/0.21 * CEs [21] --> Loop 20 0.05/0.21 * CEs [20] --> Loop 21 0.05/0.21 * CEs [19] --> Loop 22 0.05/0.21 0.05/0.21 ### Ranking functions of CR eval_foo_start(V_c,V_x,V_y,V_z,B) 0.05/0.21 0.05/0.21 #### Partial ranking functions of CR eval_foo_start(V_c,V_x,V_y,V_z,B) 0.05/0.21 0.05/0.21 0.05/0.21 Computing Bounds 0.05/0.21 ===================================== 0.05/0.21 0.05/0.21 #### Cost of chains of eval_foo_bb2_in(V_z,V__03,V__01,V__14,V__12,B,C,D): 0.05/0.21 * Chain [[9],10]: 1*it(9)+0 0.05/0.21 Such that:it(9) =< -V_z+V__14 0.05/0.21 0.05/0.21 with precondition: [B=2,V__03=V__01,V__14=V__12,V_z=C,V_z=D,V__14>=V_z+1,V__03>=V__14] 0.05/0.21 0.05/0.21 0.05/0.21 #### Cost of chains of eval_foo_bb1_in(V_z,V__03,V__01,B): 0.05/0.21 * Chain [14]: 0 0.05/0.21 with precondition: [B=3,V__01>=V__03+1] 0.05/0.21 0.05/0.21 * Chain [13]: 0 0.05/0.21 with precondition: [B=3,V_z>=V__01] 0.05/0.21 0.05/0.21 * Chain [12]: 0 0.05/0.21 with precondition: [B=3,V__03>=V__01+1] 0.05/0.21 0.05/0.21 * Chain [11,13]: 1*s(1)+1 0.05/0.21 Such that:s(1) =< -V_z+V__01 0.05/0.21 0.05/0.21 with precondition: [B=3,V__03=V__01,V__03>=V_z+1] 0.05/0.21 0.05/0.21 0.05/0.21 #### Cost of chains of eval_foo_bb0_in(V_x,V_y,V_z,B): 0.05/0.21 * Chain [18]: 1*s(2)+1 0.05/0.21 Such that:s(2) =< V_x-V_z 0.05/0.21 0.05/0.21 with precondition: [V_x=V_y,V_x>=V_z+1] 0.05/0.21 0.05/0.21 * Chain [17]: 0 0.05/0.21 with precondition: [V_y>=V_x+1] 0.05/0.21 0.05/0.21 * Chain [16]: 0 0.05/0.21 with precondition: [V_z>=V_x] 0.05/0.21 0.05/0.21 * Chain [15]: 0 0.05/0.21 with precondition: [V_x>=V_y+1] 0.05/0.21 0.05/0.21 0.05/0.21 #### Cost of chains of eval_foo_start(V_c,V_x,V_y,V_z,B): 0.05/0.21 * Chain [22]: 1*s(3)+1 0.05/0.21 Such that:s(3) =< V_x-V_z 0.05/0.21 0.05/0.21 with precondition: [V_x=V_y,V_x>=V_z+1] 0.05/0.21 0.05/0.21 * Chain [21]: 0 0.05/0.21 with precondition: [V_y>=V_x+1] 0.05/0.21 0.05/0.21 * Chain [20]: 0 0.05/0.21 with precondition: [V_z>=V_x] 0.05/0.21 0.05/0.21 * Chain [19]: 0 0.05/0.21 with precondition: [V_x>=V_y+1] 0.05/0.21 0.05/0.21 0.05/0.21 Closed-form bounds of eval_foo_start(V_c,V_x,V_y,V_z,B): 0.05/0.21 ------------------------------------- 0.05/0.21 * Chain [22] with precondition: [V_x=V_y,V_x>=V_z+1] 0.05/0.21 - Upper bound: V_x-V_z+1 0.05/0.21 - Complexity: n 0.05/0.21 * Chain [21] with precondition: [V_y>=V_x+1] 0.05/0.21 - Upper bound: 0 0.05/0.21 - Complexity: constant 0.05/0.21 * Chain [20] with precondition: [V_z>=V_x] 0.05/0.21 - Upper bound: 0 0.05/0.21 - Complexity: constant 0.05/0.21 * Chain [19] with precondition: [V_x>=V_y+1] 0.05/0.21 - Upper bound: 0 0.05/0.21 - Complexity: constant 0.05/0.21 0.05/0.21 ### Maximum cost of eval_foo_start(V_c,V_x,V_y,V_z,B): nat(V_x-V_z)+1 0.05/0.21 Asymptotic class: n 0.05/0.21 * Total analysis performed in 132 ms. 0.05/0.21 0.05/0.31 EOF