0.04/0.24 WORST_CASE(?,O(n^1)) 0.04/0.24 0.04/0.24 Preprocessing Cost Relations 0.04/0.24 ===================================== 0.04/0.24 0.04/0.24 #### Computed strongly connected components 0.04/0.24 0. recursive : [eval_foo_bb2_in/4,eval_foo_bb3_in/4] 0.04/0.24 1. recursive : [eval_foo_bb1_in/4,eval_foo_bb2_in_loop_cont/6,eval_foo_bb4_in/5] 0.04/0.24 2. non_recursive : [eval_foo_stop/1] 0.04/0.24 3. non_recursive : [eval_foo_bb5_in/1] 0.04/0.24 4. non_recursive : [eval_foo_bb1_in_loop_cont/2] 0.04/0.24 5. non_recursive : [eval_foo_bb0_in/4] 0.04/0.24 6. non_recursive : [eval_foo_start/5] 0.04/0.24 0.04/0.24 #### Obtained direct recursion through partial evaluation 0.04/0.24 0. SCC is partially evaluated into eval_foo_bb2_in/4 0.04/0.24 1. SCC is partially evaluated into eval_foo_bb1_in/4 0.04/0.24 2. SCC is completely evaluated into other SCCs 0.04/0.24 3. SCC is completely evaluated into other SCCs 0.04/0.24 4. SCC is completely evaluated into other SCCs 0.04/0.24 5. SCC is partially evaluated into eval_foo_bb0_in/4 0.04/0.24 6. SCC is partially evaluated into eval_foo_start/5 0.04/0.24 0.04/0.24 Control-Flow Refinement of Cost Relations 0.04/0.24 ===================================== 0.04/0.24 0.04/0.24 ### Specialization of cost equations eval_foo_bb2_in/4 0.04/0.24 * CE 6 is refined into CE [7] 0.04/0.24 * CE 5 is refined into CE [8] 0.04/0.24 0.04/0.24 0.04/0.24 ### Cost equations --> "Loop" of eval_foo_bb2_in/4 0.04/0.24 * CEs [8] --> Loop 7 0.04/0.24 * CEs [7] --> Loop 8 0.04/0.24 0.04/0.24 ### Ranking functions of CR eval_foo_bb2_in(V_z,V__13,B,C) 0.04/0.24 * RF of phase [7]: [-V_z+V__13] 0.04/0.24 0.04/0.24 #### Partial ranking functions of CR eval_foo_bb2_in(V_z,V__13,B,C) 0.04/0.24 * Partial RF of phase [7]: 0.04/0.24 - RF of loop [7:1]: 0.04/0.24 -V_z+V__13 0.04/0.24 0.04/0.24 0.04/0.24 ### Specialization of cost equations eval_foo_bb1_in/4 0.04/0.24 * CE 4 is refined into CE [9] 0.04/0.24 * CE 3 is refined into CE [10,11] 0.04/0.24 0.04/0.24 0.04/0.24 ### Cost equations --> "Loop" of eval_foo_bb1_in/4 0.04/0.24 * CEs [11] --> Loop 9 0.04/0.24 * CEs [10] --> Loop 10 0.04/0.24 * CEs [9] --> Loop 11 0.04/0.24 0.04/0.24 ### Ranking functions of CR eval_foo_bb1_in(V_z,V__02,V__01,B) 0.04/0.24 * RF of phase [9]: [-V__02+V__01,-V_z+V__01] 0.04/0.24 0.04/0.24 #### Partial ranking functions of CR eval_foo_bb1_in(V_z,V__02,V__01,B) 0.04/0.24 * Partial RF of phase [9]: 0.04/0.24 - RF of loop [9:1]: 0.04/0.24 -V__02+V__01 0.04/0.24 -V_z+V__01 0.04/0.24 0.04/0.24 0.04/0.24 ### Specialization of cost equations eval_foo_bb0_in/4 0.04/0.24 * CE 2 is refined into CE [12,13,14,15] 0.04/0.24 0.04/0.24 0.04/0.24 ### Cost equations --> "Loop" of eval_foo_bb0_in/4 0.04/0.24 * CEs [13] --> Loop 12 0.04/0.24 * CEs [14] --> Loop 13 0.04/0.24 * CEs [15] --> Loop 14 0.04/0.24 * CEs [12] --> Loop 15 0.04/0.24 0.04/0.24 ### Ranking functions of CR eval_foo_bb0_in(V_x,V_y,V_z,B) 0.04/0.24 0.04/0.24 #### Partial ranking functions of CR eval_foo_bb0_in(V_x,V_y,V_z,B) 0.04/0.24 0.04/0.24 0.04/0.24 ### Specialization of cost equations eval_foo_start/5 0.04/0.24 * CE 1 is refined into CE [16,17,18,19] 0.04/0.24 0.04/0.24 0.04/0.24 ### Cost equations --> "Loop" of eval_foo_start/5 0.04/0.24 * CEs [19] --> Loop 16 0.04/0.24 * CEs [18] --> Loop 17 0.04/0.24 * CEs [17] --> Loop 18 0.04/0.24 * CEs [16] --> Loop 19 0.04/0.24 0.04/0.24 ### Ranking functions of CR eval_foo_start(V_c,V_x,V_y,V_z,B) 0.04/0.24 0.04/0.24 #### Partial ranking functions of CR eval_foo_start(V_c,V_x,V_y,V_z,B) 0.04/0.24 0.04/0.24 0.04/0.24 Computing Bounds 0.04/0.24 ===================================== 0.04/0.24 0.04/0.24 #### Cost of chains of eval_foo_bb2_in(V_z,V__13,B,C): 0.04/0.24 * Chain [[7],8]: 1*it(7)+0 0.04/0.24 Such that:it(7) =< -V_z+V__13 0.04/0.24 0.04/0.24 with precondition: [B=2,V_z=C,V__13>=V_z+1] 0.04/0.24 0.04/0.24 * Chain [8]: 0 0.04/0.24 with precondition: [B=2,V__13=C,V_z>=V__13] 0.04/0.24 0.04/0.24 0.04/0.24 #### Cost of chains of eval_foo_bb1_in(V_z,V__02,V__01,B): 0.04/0.24 * Chain [[9],11]: 1*it(9)+0 0.04/0.24 Such that:it(9) =< -V_z+V__01 0.04/0.24 0.04/0.24 with precondition: [B=3,V__01>=V_z+1,V_z>=V__02] 0.04/0.24 0.04/0.24 * Chain [11]: 0 0.04/0.24 with precondition: [B=3,V_z>=V__01] 0.04/0.24 0.04/0.24 * Chain [10,[9],11]: 1*it(9)+1*s(1)+1 0.04/0.24 Such that:s(1) =< -V_z+V__02 0.04/0.24 it(9) =< -V_z+V__01 0.04/0.24 0.04/0.24 with precondition: [B=3,V__02>=V_z+1,V__01>=V_z+2] 0.04/0.24 0.04/0.24 * Chain [10,11]: 1*s(1)+1 0.04/0.24 Such that:s(1) =< -V_z+V__02 0.04/0.24 0.04/0.24 with precondition: [B=3,V_z+1=V__01,V__02>=V_z+1] 0.04/0.24 0.04/0.24 0.04/0.24 #### Cost of chains of eval_foo_bb0_in(V_x,V_y,V_z,B): 0.04/0.24 * Chain [15]: 1*s(2)+1 0.04/0.24 Such that:s(2) =< -V_x+V_y+1 0.04/0.24 0.04/0.24 with precondition: [V_x=V_z+1,V_y>=V_x] 0.04/0.24 0.04/0.24 * Chain [14]: 0 0.04/0.24 with precondition: [V_z>=V_x] 0.04/0.24 0.04/0.24 * Chain [13]: 1*s(3)+0 0.04/0.24 Such that:s(3) =< V_x-V_z 0.04/0.24 0.04/0.24 with precondition: [V_z>=V_y,V_x>=V_z+1] 0.04/0.24 0.04/0.24 * Chain [12]: 1*s(4)+1*s(5)+1 0.04/0.24 Such that:s(5) =< V_x-V_z 0.04/0.24 s(4) =< V_y-V_z 0.04/0.24 0.04/0.24 with precondition: [V_x>=V_z+2,V_y>=V_z+1] 0.04/0.24 0.04/0.24 0.04/0.24 #### Cost of chains of eval_foo_start(V_c,V_x,V_y,V_z,B): 0.04/0.24 * Chain [19]: 1*s(6)+1 0.04/0.24 Such that:s(6) =< -V_x+V_y+1 0.04/0.24 0.04/0.24 with precondition: [V_x=V_z+1,V_y>=V_x] 0.04/0.24 0.04/0.24 * Chain [18]: 0 0.04/0.24 with precondition: [V_z>=V_x] 0.04/0.24 0.04/0.24 * Chain [17]: 1*s(7)+0 0.04/0.24 Such that:s(7) =< V_x-V_z 0.04/0.24 0.04/0.24 with precondition: [V_z>=V_y,V_x>=V_z+1] 0.04/0.24 0.04/0.24 * Chain [16]: 1*s(8)+1*s(9)+1 0.04/0.24 Such that:s(8) =< V_x-V_z 0.04/0.24 s(9) =< V_y-V_z 0.04/0.24 0.04/0.24 with precondition: [V_x>=V_z+2,V_y>=V_z+1] 0.04/0.24 0.04/0.24 0.04/0.24 Closed-form bounds of eval_foo_start(V_c,V_x,V_y,V_z,B): 0.04/0.24 ------------------------------------- 0.04/0.24 * Chain [19] with precondition: [V_x=V_z+1,V_y>=V_x] 0.04/0.24 - Upper bound: -V_x+V_y+2 0.04/0.24 - Complexity: n 0.04/0.24 * Chain [18] with precondition: [V_z>=V_x] 0.04/0.24 - Upper bound: 0 0.04/0.24 - Complexity: constant 0.04/0.24 * Chain [17] with precondition: [V_z>=V_y,V_x>=V_z+1] 0.04/0.24 - Upper bound: V_x-V_z 0.04/0.24 - Complexity: n 0.04/0.24 * Chain [16] with precondition: [V_x>=V_z+2,V_y>=V_z+1] 0.04/0.24 - Upper bound: V_x+V_y-2*V_z+1 0.04/0.24 - Complexity: n 0.04/0.24 0.04/0.24 ### Maximum cost of eval_foo_start(V_c,V_x,V_y,V_z,B): max([nat(-V_x+V_y+1)+1,nat(V_y-V_z)+1+nat(V_x-V_z)]) 0.04/0.24 Asymptotic class: n 0.04/0.24 * Total analysis performed in 124 ms. 0.04/0.24 0.04/0.34 EOF