0.05/0.15 MAYBE 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_0/3,eval_foo_1/4,eval_foo_3/5,eval_foo_4/6,eval_foo_bb1_in/3,eval_foo_bb2_in/3,eval_foo_bb3_in/4,eval_foo_bb4_in/4] 0.05/0.15 1. non_recursive : [eval_foo_stop/1] 0.05/0.15 2. non_recursive : [eval_foo_bb5_in/1] 0.05/0.15 3. non_recursive : [eval_foo_bb1_in_loop_cont/2] 0.05/0.15 4. non_recursive : [eval_foo_bb0_in/3] 0.05/0.15 5. non_recursive : [eval_foo_start/3] 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 completely evaluated into other SCCs 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 partially evaluated into eval_foo_bb0_in/3 0.05/0.15 5. SCC is partially evaluated into eval_foo_start/3 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 5 is refined into CE [7] 0.05/0.15 * CE 6 is refined into CE [8] 0.05/0.15 * CE 3 is refined into CE [9] 0.05/0.15 * CE 4 is refined into CE [10] 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 [9] --> Loop 7 0.05/0.15 * CEs [10] --> Loop 8 0.05/0.15 * CEs [7] --> Loop 9 0.05/0.15 * CEs [8] --> Loop 10 0.05/0.15 0.05/0.15 ### Ranking functions of CR eval_foo_bb1_in(V__01,V__0,B) 0.05/0.15 0.05/0.15 #### Partial ranking functions of CR eval_foo_bb1_in(V__01,V__0,B) 0.05/0.15 * Partial RF of phase [7,8]: 0.05/0.15 - RF of loop [7:1]: 0.05/0.15 V__0 0.05/0.15 - RF of loop [8:1]: 0.05/0.15 V__01 depends on loops [7:1] 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 2 is refined into CE [11,12,13] 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 [13] --> Loop 11 0.05/0.15 * CEs [11] --> Loop 12 0.05/0.15 * CEs [12] --> Loop 13 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/3 0.05/0.15 * CE 1 is refined into CE [14,15,16] 0.05/0.15 0.05/0.15 0.05/0.15 ### Cost equations --> "Loop" of eval_foo_start/3 0.05/0.15 * CEs [16] --> Loop 14 0.05/0.15 * CEs [15] --> Loop 15 0.05/0.15 * CEs [14] --> Loop 16 0.05/0.15 0.05/0.15 ### Ranking functions of CR eval_foo_start(V_x,V_y,B) 0.05/0.15 0.05/0.15 #### Partial ranking functions of CR eval_foo_start(V_x,V_y,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,V__0,B): 0.05/0.15 * Chain [[7,8],10]: 1*it(7)+1*it(8)+0 0.05/0.15 Such that:it(7) =< V__0 0.05/0.15 0.05/0.15 with precondition: [B=2,V__01>=1,V__0>=1] 0.05/0.15 0.05/0.15 * Chain [[7,8],9]: 1*it(7)+1*it(8)+0 0.05/0.15 Such that:it(7) =< V__0 0.05/0.15 0.05/0.15 with precondition: [B=2,V__01>=1,V__0>=1] 0.05/0.15 0.05/0.15 * Chain [10]: 0 0.05/0.15 with precondition: [B=2,0>=V__01] 0.05/0.15 0.05/0.15 * Chain [9]: 0 0.05/0.15 with precondition: [B=2,0>=V__0] 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 [13]: 0 0.05/0.15 with precondition: [0>=V_x] 0.05/0.15 0.05/0.15 * Chain [12]: 0 0.05/0.15 with precondition: [0>=V_y] 0.05/0.15 0.05/0.15 * Chain [11]: 2*s(6)+2*s(7)+0 0.05/0.15 Such that:s(5) =< V_x 0.05/0.15 s(6) =< s(5) 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,B): 0.05/0.15 * Chain [16]: 0 0.05/0.15 with precondition: [0>=V_x] 0.05/0.15 0.05/0.15 * Chain [15]: 0 0.05/0.15 with precondition: [0>=V_y] 0.05/0.15 0.05/0.15 * Chain [14]: 2*s(9)+2*s(10)+0 0.05/0.15 Such that:s(8) =< V_x 0.05/0.15 s(9) =< s(8) 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,B): 0.05/0.15 ------------------------------------- 0.05/0.15 * Chain [16] with precondition: [0>=V_x] 0.05/0.15 - Upper bound: 0 0.05/0.15 - Complexity: constant 0.05/0.15 * Chain [15] with precondition: [0>=V_y] 0.05/0.15 - Upper bound: 0 0.05/0.15 - Complexity: constant 0.05/0.15 * Chain [14] with precondition: [V_x>=1,V_y>=1] 0.05/0.15 - Upper bound: inf 0.05/0.15 - Complexity: infinity 0.05/0.15 0.05/0.15 ### Maximum cost of eval_foo_start(V_x,V_y,B): inf 0.05/0.15 Asymptotic class: infinity 0.05/0.15 * Total analysis performed in 78 ms. 0.05/0.15 0.05/0.25 EOF