0.04/0.19 WORST_CASE(?,O(n^1)) 0.04/0.19 0.04/0.19 Preprocessing Cost Relations 0.04/0.19 ===================================== 0.04/0.19 0.04/0.19 #### Computed strongly connected components 0.04/0.19 0. recursive : [eval_t07_bb1_in/4,eval_t07_bb2_in/4] 0.04/0.19 1. recursive : [eval_t07_bb3_in/3,eval_t07_bb4_in/3] 0.04/0.19 2. recursive : [eval_t07_bb5_in/2,eval_t07_bb6_in/2] 0.04/0.19 3. non_recursive : [eval_t07_stop/1] 0.04/0.19 4. non_recursive : [eval_t07_bb7_in/1] 0.04/0.19 5. non_recursive : [eval_t07_bb5_in_loop_cont/2] 0.04/0.19 6. non_recursive : [eval_t07_bb3_in_loop_cont/3] 0.04/0.19 7. non_recursive : [eval_t07_bb1_in_loop_cont/3] 0.04/0.19 8. non_recursive : [eval_t07_bb0_in/3] 0.04/0.19 9. non_recursive : [eval_t07_start/3] 0.04/0.19 0.04/0.19 #### Obtained direct recursion through partial evaluation 0.04/0.19 0. SCC is partially evaluated into eval_t07_bb1_in/4 0.04/0.19 1. SCC is partially evaluated into eval_t07_bb3_in/3 0.04/0.19 2. SCC is partially evaluated into eval_t07_bb5_in/2 0.04/0.19 3. SCC is completely evaluated into other SCCs 0.04/0.19 4. SCC is completely evaluated into other SCCs 0.04/0.19 5. SCC is completely evaluated into other SCCs 0.04/0.19 6. SCC is partially evaluated into eval_t07_bb3_in_loop_cont/3 0.04/0.19 7. SCC is partially evaluated into eval_t07_bb1_in_loop_cont/3 0.04/0.19 8. SCC is partially evaluated into eval_t07_bb0_in/3 0.04/0.19 9. SCC is partially evaluated into eval_t07_start/3 0.04/0.19 0.04/0.19 Control-Flow Refinement of Cost Relations 0.04/0.19 ===================================== 0.04/0.19 0.04/0.19 ### Specialization of cost equations eval_t07_bb1_in/4 0.04/0.19 * CE 4 is refined into CE [11] 0.04/0.19 * CE 3 is refined into CE [12] 0.04/0.19 0.04/0.19 0.04/0.19 ### Cost equations --> "Loop" of eval_t07_bb1_in/4 0.04/0.19 * CEs [12] --> Loop 11 0.04/0.19 * CEs [11] --> Loop 12 0.04/0.19 0.04/0.19 ### Ranking functions of CR eval_t07_bb1_in(V__01,V__0,B,C) 0.04/0.19 * RF of phase [11]: [V__0] 0.04/0.19 0.04/0.19 #### Partial ranking functions of CR eval_t07_bb1_in(V__01,V__0,B,C) 0.04/0.19 * Partial RF of phase [11]: 0.04/0.19 - RF of loop [11:1]: 0.04/0.19 V__0 0.04/0.19 0.04/0.19 0.04/0.19 ### Specialization of cost equations eval_t07_bb3_in/3 0.04/0.19 * CE 7 is refined into CE [13] 0.04/0.19 * CE 6 is refined into CE [14] 0.04/0.19 0.04/0.19 0.04/0.19 ### Cost equations --> "Loop" of eval_t07_bb3_in/3 0.04/0.19 * CEs [14] --> Loop 13 0.04/0.19 * CEs [13] --> Loop 14 0.04/0.19 0.04/0.19 ### Ranking functions of CR eval_t07_bb3_in(V__1,B,C) 0.04/0.19 * RF of phase [13]: [V__1] 0.04/0.19 0.04/0.19 #### Partial ranking functions of CR eval_t07_bb3_in(V__1,B,C) 0.04/0.19 * Partial RF of phase [13]: 0.04/0.19 - RF of loop [13:1]: 0.04/0.19 V__1 0.04/0.19 0.04/0.19 0.04/0.19 ### Specialization of cost equations eval_t07_bb5_in/2 0.04/0.19 * CE 10 is refined into CE [15] 0.04/0.19 * CE 9 is refined into CE [16] 0.04/0.19 0.04/0.19 0.04/0.19 ### Cost equations --> "Loop" of eval_t07_bb5_in/2 0.04/0.19 * CEs [16] --> Loop 15 0.04/0.19 * CEs [15] --> Loop 16 0.04/0.19 0.04/0.19 ### Ranking functions of CR eval_t07_bb5_in(V__2,B) 0.04/0.19 * RF of phase [15]: [V__2] 0.04/0.19 0.04/0.19 #### Partial ranking functions of CR eval_t07_bb5_in(V__2,B) 0.04/0.19 * Partial RF of phase [15]: 0.04/0.19 - RF of loop [15:1]: 0.04/0.19 V__2 0.04/0.19 0.04/0.19 0.04/0.19 ### Specialization of cost equations eval_t07_bb3_in_loop_cont/3 0.04/0.19 * CE 8 is refined into CE [17,18] 0.04/0.19 0.04/0.19 0.04/0.19 ### Cost equations --> "Loop" of eval_t07_bb3_in_loop_cont/3 0.04/0.19 * CEs [18] --> Loop 17 0.04/0.19 * CEs [17] --> Loop 18 0.04/0.19 0.04/0.19 ### Ranking functions of CR eval_t07_bb3_in_loop_cont(A,B,C) 0.04/0.19 0.04/0.19 #### Partial ranking functions of CR eval_t07_bb3_in_loop_cont(A,B,C) 0.04/0.19 0.04/0.19 0.04/0.19 ### Specialization of cost equations eval_t07_bb1_in_loop_cont/3 0.04/0.19 * CE 5 is refined into CE [19,20] 0.04/0.19 0.04/0.19 0.04/0.19 ### Cost equations --> "Loop" of eval_t07_bb1_in_loop_cont/3 0.04/0.19 * CEs [19] --> Loop 19 0.04/0.19 * CEs [20] --> Loop 20 0.04/0.19 0.04/0.19 ### Ranking functions of CR eval_t07_bb1_in_loop_cont(A,B,C) 0.04/0.19 0.04/0.19 #### Partial ranking functions of CR eval_t07_bb1_in_loop_cont(A,B,C) 0.04/0.19 0.04/0.19 0.04/0.19 ### Specialization of cost equations eval_t07_bb0_in/3 0.04/0.19 * CE 2 is refined into CE [21,22,23,24] 0.04/0.19 0.04/0.19 0.04/0.19 ### Cost equations --> "Loop" of eval_t07_bb0_in/3 0.04/0.19 * CEs [24] --> Loop 21 0.04/0.19 * CEs [23] --> Loop 22 0.04/0.19 * CEs [22] --> Loop 23 0.04/0.19 * CEs [21] --> Loop 24 0.04/0.19 0.04/0.19 ### Ranking functions of CR eval_t07_bb0_in(V_x,V_y,B) 0.04/0.19 0.04/0.19 #### Partial ranking functions of CR eval_t07_bb0_in(V_x,V_y,B) 0.04/0.19 0.04/0.19 0.04/0.19 ### Specialization of cost equations eval_t07_start/3 0.04/0.19 * CE 1 is refined into CE [25,26,27,28] 0.04/0.19 0.04/0.19 0.04/0.19 ### Cost equations --> "Loop" of eval_t07_start/3 0.04/0.19 * CEs [28] --> Loop 25 0.04/0.19 * CEs [27] --> Loop 26 0.04/0.19 * CEs [26] --> Loop 27 0.04/0.19 * CEs [25] --> Loop 28 0.04/0.19 0.04/0.19 ### Ranking functions of CR eval_t07_start(V_x,V_y,B) 0.04/0.19 0.04/0.19 #### Partial ranking functions of CR eval_t07_start(V_x,V_y,B) 0.04/0.19 0.04/0.19 0.04/0.19 Computing Bounds 0.04/0.19 ===================================== 0.04/0.19 0.04/0.19 #### Cost of chains of eval_t07_bb1_in(V__01,V__0,B,C): 0.04/0.19 * Chain [[11],12]: 1*it(11)+0 0.04/0.19 Such that:it(11) =< -V__01/2+C/2 0.04/0.19 0.04/0.19 with precondition: [B=4,V__01+2*V__0=C,V__0>=1] 0.04/0.19 0.04/0.19 * Chain [12]: 0 0.04/0.19 with precondition: [B=4,C=V__01,0>=V__0] 0.04/0.19 0.04/0.19 0.04/0.19 #### Cost of chains of eval_t07_bb3_in(V__1,B,C): 0.04/0.19 * Chain [[13],14]: 1*it(13)+0 0.04/0.19 Such that:it(13) =< V__1 0.04/0.19 0.04/0.19 with precondition: [B=3,C=0,V__1>=1] 0.04/0.19 0.04/0.19 * Chain [14]: 0 0.04/0.19 with precondition: [B=3,V__1=C,0>=V__1] 0.04/0.19 0.04/0.19 0.04/0.19 #### Cost of chains of eval_t07_bb5_in(V__2,B): 0.04/0.19 * Chain [[15],16]: 1*it(15)+0 0.04/0.19 Such that:it(15) =< V__2 0.04/0.19 0.04/0.19 with precondition: [B=2,V__2>=1] 0.04/0.19 0.04/0.19 * Chain [16]: 0 0.04/0.19 with precondition: [B=2,0>=V__2] 0.04/0.19 0.04/0.19 0.04/0.19 #### Cost of chains of eval_t07_bb3_in_loop_cont(A,B,C): 0.04/0.19 * Chain [18]: 0 0.04/0.19 with precondition: [A=3,0>=B] 0.04/0.19 0.04/0.19 * Chain [17]: 1*s(1)+0 0.04/0.19 Such that:s(1) =< B 0.04/0.19 0.04/0.19 with precondition: [A=3,B>=1] 0.04/0.19 0.04/0.19 0.04/0.19 #### Cost of chains of eval_t07_bb1_in_loop_cont(A,B,C): 0.04/0.19 * Chain [20]: 0 0.04/0.19 with precondition: [A=4,0>=B] 0.04/0.19 0.04/0.19 * Chain [19]: 1*s(2)+0 0.04/0.19 Such that:s(2) =< B 0.04/0.19 0.04/0.19 with precondition: [A=4,B>=1] 0.04/0.19 0.04/0.19 0.04/0.19 #### Cost of chains of eval_t07_bb0_in(V_x,V_y,B): 0.04/0.19 * Chain [24]: 0 0.04/0.19 with precondition: [0>=V_x,0>=V_y] 0.04/0.19 0.04/0.19 * Chain [23]: 1*s(3)+0 0.04/0.19 Such that:s(3) =< V_y 0.04/0.19 0.04/0.19 with precondition: [0>=V_x,V_y>=1] 0.04/0.19 0.04/0.19 * Chain [22]: 1*s(4)+0 0.04/0.19 Such that:s(4) =< V_x 0.04/0.19 0.04/0.19 with precondition: [V_x>=1,0>=2*V_x+V_y] 0.04/0.19 0.04/0.19 * Chain [21]: 1*s(5)+1*s(6)+0 0.04/0.19 Such that:s(5) =< V_x 0.04/0.19 s(6) =< 2*V_x+V_y 0.04/0.19 0.04/0.19 with precondition: [V_x>=1,V_y+2*V_x>=1] 0.04/0.19 0.04/0.19 0.04/0.19 #### Cost of chains of eval_t07_start(V_x,V_y,B): 0.04/0.19 * Chain [28]: 0 0.04/0.19 with precondition: [0>=V_x,0>=V_y] 0.04/0.19 0.04/0.19 * Chain [27]: 1*s(7)+0 0.04/0.19 Such that:s(7) =< V_y 0.04/0.19 0.04/0.19 with precondition: [0>=V_x,V_y>=1] 0.04/0.19 0.04/0.19 * Chain [26]: 1*s(8)+0 0.04/0.19 Such that:s(8) =< V_x 0.04/0.19 0.04/0.19 with precondition: [V_x>=1,0>=2*V_x+V_y] 0.04/0.19 0.04/0.19 * Chain [25]: 1*s(9)+1*s(10)+0 0.04/0.19 Such that:s(9) =< V_x 0.04/0.19 s(10) =< 2*V_x+V_y 0.04/0.19 0.04/0.19 with precondition: [V_x>=1,V_y+2*V_x>=1] 0.04/0.19 0.04/0.19 0.04/0.19 Closed-form bounds of eval_t07_start(V_x,V_y,B): 0.04/0.19 ------------------------------------- 0.04/0.19 * Chain [28] with precondition: [0>=V_x,0>=V_y] 0.04/0.19 - Upper bound: 0 0.04/0.19 - Complexity: constant 0.04/0.19 * Chain [27] with precondition: [0>=V_x,V_y>=1] 0.04/0.19 - Upper bound: V_y 0.04/0.19 - Complexity: n 0.04/0.19 * Chain [26] with precondition: [V_x>=1,0>=2*V_x+V_y] 0.04/0.19 - Upper bound: V_x 0.04/0.19 - Complexity: n 0.04/0.19 * Chain [25] with precondition: [V_x>=1,V_y+2*V_x>=1] 0.04/0.19 - Upper bound: 3*V_x+V_y 0.04/0.19 - Complexity: n 0.04/0.19 0.04/0.19 ### Maximum cost of eval_t07_start(V_x,V_y,B): max([nat(V_y),nat(2*V_x+V_y)+nat(V_x)]) 0.04/0.19 Asymptotic class: n 0.04/0.19 * Total analysis performed in 120 ms. 0.04/0.19 0.04/0.29 EOF