0.05/0.17 WORST_CASE(?,O(n^1)) 0.05/0.17 0.05/0.17 Preprocessing Cost Relations 0.05/0.17 ===================================== 0.05/0.17 0.05/0.17 #### Computed strongly connected components 0.05/0.17 0. recursive : [eval_foo_bb1_in/3,eval_foo_bb2_in/3,eval_foo_bb3_in/3,eval_foo_bb4_in/3,eval_foo_bb5_in/5] 0.05/0.17 1. non_recursive : [eval_foo_stop/1] 0.05/0.17 2. non_recursive : [eval_foo_bb6_in/1] 0.05/0.17 3. non_recursive : [eval_foo_bb1_in_loop_cont/2] 0.05/0.17 4. non_recursive : [eval_foo_bb0_in/3] 0.05/0.17 5. non_recursive : [eval_foo_start/4] 0.05/0.17 0.05/0.17 #### Obtained direct recursion through partial evaluation 0.05/0.17 0. SCC is partially evaluated into eval_foo_bb1_in/3 0.05/0.17 1. SCC is completely evaluated into other SCCs 0.05/0.17 2. SCC is completely evaluated into other SCCs 0.05/0.17 3. SCC is completely evaluated into other SCCs 0.05/0.17 4. SCC is partially evaluated into eval_foo_bb0_in/3 0.05/0.17 5. SCC is partially evaluated into eval_foo_start/4 0.05/0.17 0.05/0.17 Control-Flow Refinement of Cost Relations 0.05/0.17 ===================================== 0.05/0.17 0.05/0.17 ### Specialization of cost equations eval_foo_bb1_in/3 0.05/0.17 * CE 5 is refined into CE [6] 0.05/0.17 * CE 4 is refined into CE [7] 0.05/0.17 * CE 3 is refined into CE [8] 0.05/0.17 0.05/0.17 0.05/0.17 ### Cost equations --> "Loop" of eval_foo_bb1_in/3 0.05/0.17 * CEs [7] --> Loop 6 0.05/0.17 * CEs [8] --> Loop 7 0.05/0.17 * CEs [6] --> Loop 8 0.05/0.17 0.05/0.17 ### Ranking functions of CR eval_foo_bb1_in(V__02,V__01,B) 0.05/0.17 * RF of phase [6]: [V__02,V__02+V__01] 0.05/0.17 * RF of phase [7]: [V__01,V__02+V__01] 0.05/0.17 0.05/0.17 #### Partial ranking functions of CR eval_foo_bb1_in(V__02,V__01,B) 0.05/0.17 * Partial RF of phase [6]: 0.05/0.17 - RF of loop [6:1]: 0.05/0.17 V__02 0.05/0.17 V__02+V__01 0.05/0.17 * Partial RF of phase [7]: 0.05/0.17 - RF of loop [7:1]: 0.05/0.17 V__01 0.05/0.17 V__02+V__01 0.05/0.17 0.05/0.17 0.05/0.17 ### Specialization of cost equations eval_foo_bb0_in/3 0.05/0.17 * CE 2 is refined into CE [9,10,11,12] 0.05/0.17 0.05/0.17 0.05/0.17 ### Cost equations --> "Loop" of eval_foo_bb0_in/3 0.05/0.17 * CEs [12] --> Loop 9 0.05/0.17 * CEs [11] --> Loop 10 0.05/0.17 * CEs [9] --> Loop 11 0.05/0.17 * CEs [10] --> Loop 12 0.05/0.17 0.05/0.17 ### Ranking functions of CR eval_foo_bb0_in(V_x,V_y,B) 0.05/0.17 0.05/0.17 #### Partial ranking functions of CR eval_foo_bb0_in(V_x,V_y,B) 0.05/0.17 0.05/0.17 0.05/0.17 ### Specialization of cost equations eval_foo_start/4 0.05/0.17 * CE 1 is refined into CE [13,14,15,16] 0.05/0.17 0.05/0.17 0.05/0.17 ### Cost equations --> "Loop" of eval_foo_start/4 0.05/0.17 * CEs [16] --> Loop 13 0.05/0.17 * CEs [15] --> Loop 14 0.05/0.17 * CEs [14] --> Loop 15 0.05/0.17 * CEs [13] --> Loop 16 0.05/0.17 0.05/0.17 ### Ranking functions of CR eval_foo_start(V_c,V_x,V_y,B) 0.05/0.17 0.05/0.17 #### Partial ranking functions of CR eval_foo_start(V_c,V_x,V_y,B) 0.05/0.17 0.05/0.17 0.05/0.17 Computing Bounds 0.05/0.17 ===================================== 0.05/0.17 0.05/0.17 #### Cost of chains of eval_foo_bb1_in(V__02,V__01,B): 0.05/0.17 * Chain [[7],[6],8]: 1*it(6)+1*it(7)+0 0.05/0.17 Such that:it(6) =< V__02 0.05/0.17 it(7) =< V__01 0.05/0.17 0.05/0.17 with precondition: [B=2,V__02>=1,V__01>=1] 0.05/0.17 0.05/0.17 * Chain [[7],8]: 1*it(7)+0 0.05/0.17 Such that:it(7) =< V__02+V__01 0.05/0.17 0.05/0.17 with precondition: [B=2,0>=V__02,V__01+V__02>=1] 0.05/0.17 0.05/0.17 * Chain [[6],8]: 1*it(6)+0 0.05/0.17 Such that:it(6) =< V__02+V__01 0.05/0.17 0.05/0.17 with precondition: [B=2,0>=V__01,V__01+V__02>=1] 0.05/0.17 0.05/0.17 * Chain [8]: 0 0.05/0.17 with precondition: [B=2,0>=V__01+V__02] 0.05/0.17 0.05/0.17 0.05/0.17 #### Cost of chains of eval_foo_bb0_in(V_x,V_y,B): 0.05/0.17 * Chain [12]: 1*s(1)+0 0.05/0.17 Such that:s(1) =< V_x+V_y 0.05/0.17 0.05/0.17 with precondition: [0>=V_x,V_x+V_y>=1] 0.05/0.17 0.05/0.17 * Chain [11]: 1*s(2)+0 0.05/0.17 Such that:s(2) =< V_x+V_y 0.05/0.17 0.05/0.17 with precondition: [0>=V_y,V_x+V_y>=1] 0.05/0.17 0.05/0.17 * Chain [10]: 1*s(3)+1*s(4)+0 0.05/0.17 Such that:s(4) =< V_x 0.05/0.17 s(3) =< V_y 0.05/0.17 0.05/0.17 with precondition: [V_x>=1,V_y>=1] 0.05/0.17 0.05/0.17 * Chain [9]: 0 0.05/0.17 with precondition: [0>=V_x+V_y] 0.05/0.17 0.05/0.17 0.05/0.17 #### Cost of chains of eval_foo_start(V_c,V_x,V_y,B): 0.05/0.17 * Chain [16]: 1*s(5)+0 0.05/0.17 Such that:s(5) =< V_x+V_y 0.05/0.17 0.05/0.17 with precondition: [0>=V_x,V_x+V_y>=1] 0.05/0.17 0.05/0.17 * Chain [15]: 1*s(6)+0 0.05/0.17 Such that:s(6) =< V_x+V_y 0.05/0.17 0.05/0.17 with precondition: [0>=V_y,V_x+V_y>=1] 0.05/0.17 0.05/0.17 * Chain [14]: 1*s(7)+1*s(8)+0 0.05/0.17 Such that:s(7) =< V_x 0.05/0.17 s(8) =< V_y 0.05/0.17 0.05/0.17 with precondition: [V_x>=1,V_y>=1] 0.05/0.17 0.05/0.17 * Chain [13]: 0 0.05/0.17 with precondition: [0>=V_x+V_y] 0.05/0.17 0.05/0.17 0.05/0.17 Closed-form bounds of eval_foo_start(V_c,V_x,V_y,B): 0.05/0.17 ------------------------------------- 0.05/0.17 * Chain [16] with precondition: [0>=V_x,V_x+V_y>=1] 0.05/0.17 - Upper bound: V_x+V_y 0.05/0.17 - Complexity: n 0.05/0.17 * Chain [15] with precondition: [0>=V_y,V_x+V_y>=1] 0.05/0.17 - Upper bound: V_x+V_y 0.05/0.17 - Complexity: n 0.05/0.17 * Chain [14] with precondition: [V_x>=1,V_y>=1] 0.05/0.17 - Upper bound: V_x+V_y 0.05/0.17 - Complexity: n 0.05/0.17 * Chain [13] with precondition: [0>=V_x+V_y] 0.05/0.17 - Upper bound: 0 0.05/0.17 - Complexity: constant 0.05/0.17 0.05/0.17 ### Maximum cost of eval_foo_start(V_c,V_x,V_y,B): max([nat(V_x+V_y),nat(V_y)+nat(V_x)]) 0.05/0.17 Asymptotic class: n 0.05/0.17 * Total analysis performed in 99 ms. 0.05/0.17 0.05/0.27 EOF