0.05/0.19 WORST_CASE(?,O(n^1)) 0.05/0.19 0.05/0.19 Preprocessing Cost Relations 0.05/0.19 ===================================== 0.05/0.19 0.05/0.19 #### Computed strongly connected components 0.05/0.19 0. recursive : [eval_foo_bb1_in/4,eval_foo_bb2_in/4,eval_foo_bb3_in/4,eval_foo_bb4_in/4,eval_foo_bb5_in/6] 0.05/0.19 1. non_recursive : [eval_foo_stop/1] 0.05/0.19 2. non_recursive : [eval_foo_bb6_in/1] 0.05/0.19 3. non_recursive : [eval_foo_bb1_in_loop_cont/2] 0.05/0.19 4. non_recursive : [eval_foo_bb0_in/4] 0.05/0.19 5. non_recursive : [eval_foo_start/5] 0.05/0.19 0.05/0.19 #### Obtained direct recursion through partial evaluation 0.05/0.19 0. SCC is partially evaluated into eval_foo_bb1_in/4 0.05/0.19 1. SCC is completely evaluated into other SCCs 0.05/0.19 2. SCC is completely evaluated into other SCCs 0.05/0.19 3. SCC is completely evaluated into other SCCs 0.05/0.19 4. SCC is partially evaluated into eval_foo_bb0_in/4 0.05/0.19 5. SCC is partially evaluated into eval_foo_start/5 0.05/0.19 0.05/0.19 Control-Flow Refinement of Cost Relations 0.05/0.19 ===================================== 0.05/0.19 0.05/0.19 ### Specialization of cost equations eval_foo_bb1_in/4 0.05/0.19 * CE 5 is refined into CE [6] 0.05/0.19 * CE 4 is refined into CE [7] 0.05/0.19 * CE 3 is refined into CE [8] 0.05/0.19 0.05/0.19 0.05/0.19 ### Cost equations --> "Loop" of eval_foo_bb1_in/4 0.05/0.19 * CEs [7] --> Loop 6 0.05/0.19 * CEs [8] --> Loop 7 0.05/0.19 * CEs [6] --> Loop 8 0.05/0.19 0.05/0.19 ### Ranking functions of CR eval_foo_bb1_in(V_z,V__02,V__01,B) 0.05/0.19 * RF of phase [6]: [V__02-V__01,-V_z+V__02] 0.05/0.19 * RF of phase [7]: [-V_z+V__01] 0.05/0.19 0.05/0.19 #### Partial ranking functions of CR eval_foo_bb1_in(V_z,V__02,V__01,B) 0.05/0.19 * Partial RF of phase [6]: 0.05/0.19 - RF of loop [6:1]: 0.05/0.19 V__02-V__01 0.05/0.19 -V_z+V__02 0.05/0.20 * Partial RF of phase [7]: 0.05/0.20 - RF of loop [7:1]: 0.05/0.20 -V_z+V__01 0.05/0.20 0.05/0.20 0.05/0.20 ### Specialization of cost equations eval_foo_bb0_in/4 0.05/0.20 * CE 2 is refined into CE [9,10,11,12] 0.05/0.20 0.05/0.20 0.05/0.20 ### Cost equations --> "Loop" of eval_foo_bb0_in/4 0.05/0.20 * CEs [9] --> Loop 9 0.05/0.20 * CEs [11] --> Loop 10 0.05/0.20 * CEs [10] --> Loop 11 0.05/0.20 * CEs [12] --> Loop 12 0.05/0.20 0.05/0.20 ### Ranking functions of CR eval_foo_bb0_in(V_x,V_y,V_z,B) 0.05/0.20 0.05/0.20 #### Partial ranking functions of CR eval_foo_bb0_in(V_x,V_y,V_z,B) 0.05/0.20 0.05/0.20 0.05/0.20 ### Specialization of cost equations eval_foo_start/5 0.05/0.20 * CE 1 is refined into CE [13,14,15,16] 0.05/0.20 0.05/0.20 0.05/0.20 ### Cost equations --> "Loop" of eval_foo_start/5 0.05/0.20 * CEs [16] --> Loop 13 0.05/0.20 * CEs [15] --> Loop 14 0.05/0.20 * CEs [14] --> Loop 15 0.05/0.20 * CEs [13] --> Loop 16 0.05/0.20 0.05/0.20 ### Ranking functions of CR eval_foo_start(V_c,V_x,V_y,V_z,B) 0.05/0.20 0.05/0.20 #### Partial ranking functions of CR eval_foo_start(V_c,V_x,V_y,V_z,B) 0.05/0.20 0.05/0.20 0.05/0.20 Computing Bounds 0.05/0.20 ===================================== 0.05/0.20 0.05/0.20 #### Cost of chains of eval_foo_bb1_in(V_z,V__02,V__01,B): 0.05/0.20 * Chain [[7],[6],8]: 1*it(6)+1*it(7)+0 0.05/0.20 Such that:it(6) =< -V_z+V__02 0.05/0.20 it(7) =< -V_z+V__01 0.05/0.20 0.05/0.20 with precondition: [B=2,V__02>=V_z+1,V__01>=V_z+1] 0.05/0.20 0.05/0.20 * Chain [[7],8]: 1*it(7)+0 0.05/0.20 Such that:it(7) =< -V_z+V__01 0.05/0.20 0.05/0.20 with precondition: [B=2,V__01>=V_z+1,V_z>=V__02] 0.05/0.20 0.05/0.20 * Chain [[6],8]: 1*it(6)+0 0.05/0.20 Such that:it(6) =< -V_z+V__02 0.05/0.20 0.05/0.20 with precondition: [B=2,V__02>=V_z+1,V_z>=V__01] 0.05/0.20 0.05/0.20 * Chain [8]: 0 0.05/0.20 with precondition: [B=2,V_z>=V__02,V_z>=V__01] 0.05/0.20 0.05/0.20 0.05/0.20 #### Cost of chains of eval_foo_bb0_in(V_x,V_y,V_z,B): 0.05/0.20 * Chain [12]: 0 0.05/0.20 with precondition: [V_z>=V_x,V_z>=V_y] 0.05/0.20 0.05/0.20 * Chain [11]: 1*s(1)+0 0.05/0.20 Such that:s(1) =< V_y-V_z 0.05/0.20 0.05/0.20 with precondition: [V_z>=V_x,V_y>=V_z+1] 0.05/0.20 0.05/0.20 * Chain [10]: 1*s(2)+0 0.05/0.20 Such that:s(2) =< V_x-V_z 0.05/0.20 0.05/0.20 with precondition: [V_z>=V_y,V_x>=V_z+1] 0.05/0.20 0.05/0.20 * Chain [9]: 1*s(3)+1*s(4)+0 0.05/0.20 Such that:s(4) =< V_x-V_z 0.05/0.20 s(3) =< V_y-V_z 0.05/0.20 0.05/0.20 with precondition: [V_x>=V_z+1,V_y>=V_z+1] 0.05/0.20 0.05/0.20 0.05/0.20 #### Cost of chains of eval_foo_start(V_c,V_x,V_y,V_z,B): 0.05/0.20 * Chain [16]: 0 0.05/0.20 with precondition: [V_z>=V_x,V_z>=V_y] 0.05/0.20 0.05/0.20 * Chain [15]: 1*s(5)+0 0.05/0.20 Such that:s(5) =< V_y-V_z 0.05/0.20 0.05/0.20 with precondition: [V_z>=V_x,V_y>=V_z+1] 0.05/0.20 0.05/0.20 * Chain [14]: 1*s(6)+0 0.05/0.20 Such that:s(6) =< V_x-V_z 0.05/0.20 0.05/0.20 with precondition: [V_z>=V_y,V_x>=V_z+1] 0.05/0.20 0.05/0.20 * Chain [13]: 1*s(7)+1*s(8)+0 0.05/0.20 Such that:s(7) =< V_x-V_z 0.05/0.20 s(8) =< V_y-V_z 0.05/0.20 0.05/0.20 with precondition: [V_x>=V_z+1,V_y>=V_z+1] 0.05/0.20 0.05/0.20 0.05/0.20 Closed-form bounds of eval_foo_start(V_c,V_x,V_y,V_z,B): 0.05/0.20 ------------------------------------- 0.05/0.20 * Chain [16] with precondition: [V_z>=V_x,V_z>=V_y] 0.05/0.20 - Upper bound: 0 0.05/0.20 - Complexity: constant 0.05/0.20 * Chain [15] with precondition: [V_z>=V_x,V_y>=V_z+1] 0.05/0.20 - Upper bound: V_y-V_z 0.05/0.20 - Complexity: n 0.05/0.20 * Chain [14] with precondition: [V_z>=V_y,V_x>=V_z+1] 0.05/0.20 - Upper bound: V_x-V_z 0.05/0.20 - Complexity: n 0.05/0.20 * Chain [13] with precondition: [V_x>=V_z+1,V_y>=V_z+1] 0.05/0.20 - Upper bound: V_x+V_y-2*V_z 0.05/0.20 - Complexity: n 0.05/0.20 0.05/0.20 ### Maximum cost of eval_foo_start(V_c,V_x,V_y,V_z,B): nat(V_y-V_z)+nat(V_x-V_z) 0.05/0.20 Asymptotic class: n 0.05/0.20 * Total analysis performed in 120 ms. 0.05/0.20 0.05/0.30 EOF