0.05/0.24 WORST_CASE(?,O(n^1)) 0.05/0.24 0.05/0.24 Preprocessing Cost Relations 0.05/0.24 ===================================== 0.05/0.24 0.05/0.24 #### Computed strongly connected components 0.05/0.24 0. recursive : [eval_sipma91_bb1_in/5,eval_sipma91_bb2_in/5] 0.05/0.24 1. recursive : [eval_sipma91_bb3_in/3,eval_sipma91_bb4_in/3,eval_sipma91_bb5_in/5,eval_sipma91_bb6_in/5,eval_sipma91_bb7_in/7] 0.05/0.24 2. non_recursive : [eval_sipma91_stop/1] 0.05/0.24 3. non_recursive : [eval_sipma91_bb8_in/1] 0.05/0.24 4. non_recursive : [eval_sipma91_bb3_in_loop_cont/2] 0.05/0.24 5. non_recursive : [eval_sipma91_bb1_in_loop_cont/4] 0.05/0.24 6. non_recursive : [eval_sipma91_bb0_in/2] 0.05/0.24 7. non_recursive : [eval_sipma91_start/2] 0.05/0.24 0.05/0.24 #### Obtained direct recursion through partial evaluation 0.05/0.24 0. SCC is partially evaluated into eval_sipma91_bb1_in/5 0.05/0.24 1. SCC is partially evaluated into eval_sipma91_bb3_in/3 0.05/0.24 2. SCC is completely evaluated into other SCCs 0.05/0.24 3. SCC is completely evaluated into other SCCs 0.05/0.24 4. SCC is completely evaluated into other SCCs 0.05/0.24 5. SCC is partially evaluated into eval_sipma91_bb1_in_loop_cont/4 0.05/0.24 6. SCC is partially evaluated into eval_sipma91_bb0_in/2 0.05/0.24 7. SCC is partially evaluated into eval_sipma91_start/2 0.05/0.24 0.05/0.24 Control-Flow Refinement of Cost Relations 0.05/0.24 ===================================== 0.05/0.24 0.05/0.24 ### Specialization of cost equations eval_sipma91_bb1_in/5 0.05/0.24 * CE 5 is refined into CE [11] 0.05/0.24 * CE 4 is refined into CE [12] 0.05/0.24 0.05/0.24 0.05/0.24 ### Cost equations --> "Loop" of eval_sipma91_bb1_in/5 0.05/0.24 * CEs [12] --> Loop 11 0.05/0.24 * CEs [11] --> Loop 12 0.05/0.24 0.05/0.24 ### Ranking functions of CR eval_sipma91_bb1_in(V_y2_0,V_y1_0,B,C,D) 0.05/0.24 * RF of phase [11]: [-V_y1_0/11+101/11] 0.05/0.24 0.05/0.24 #### Partial ranking functions of CR eval_sipma91_bb1_in(V_y2_0,V_y1_0,B,C,D) 0.05/0.24 * Partial RF of phase [11]: 0.05/0.24 - RF of loop [11:1]: 0.05/0.24 -V_y1_0/11+101/11 0.05/0.24 0.05/0.24 0.05/0.24 ### Specialization of cost equations eval_sipma91_bb3_in/3 0.05/0.24 * CE 10 is refined into CE [13] 0.05/0.24 * CE 8 is refined into CE [14] 0.05/0.24 * CE 9 is refined into CE [15] 0.05/0.24 * CE 7 is refined into CE [16] 0.05/0.24 0.05/0.24 0.05/0.24 ### Cost equations --> "Loop" of eval_sipma91_bb3_in/3 0.05/0.24 * CEs [14] --> Loop 13 0.05/0.24 * CEs [15] --> Loop 14 0.05/0.24 * CEs [16] --> Loop 15 0.05/0.24 * CEs [13] --> Loop 16 0.05/0.24 0.05/0.24 ### Ranking functions of CR eval_sipma91_bb3_in(V_y2_1,V_y1_1,B) 0.05/0.24 0.05/0.24 #### Partial ranking functions of CR eval_sipma91_bb3_in(V_y2_1,V_y1_1,B) 0.05/0.24 * Partial RF of phase [13,14]: 0.05/0.24 - RF of loop [13:1]: 0.05/0.24 V_y1_1/9-110/9 depends on loops [14:1] 0.05/0.24 V_y2_1-2 0.05/0.24 - RF of loop [14:1]: 0.05/0.24 -V_y1_1+111 depends on loops [13:1] 0.05/0.24 0.05/0.24 0.05/0.24 ### Specialization of cost equations eval_sipma91_bb1_in_loop_cont/4 0.05/0.24 * CE 6 is refined into CE [17,18,19] 0.05/0.24 0.05/0.24 0.05/0.24 ### Cost equations --> "Loop" of eval_sipma91_bb1_in_loop_cont/4 0.05/0.24 * CEs [19] --> Loop 17 0.05/0.24 * CEs [18] --> Loop 18 0.05/0.24 * CEs [17] --> Loop 19 0.05/0.24 0.05/0.24 ### Ranking functions of CR eval_sipma91_bb1_in_loop_cont(A,B,C,D) 0.05/0.24 0.05/0.24 #### Partial ranking functions of CR eval_sipma91_bb1_in_loop_cont(A,B,C,D) 0.05/0.24 0.05/0.24 0.05/0.24 ### Specialization of cost equations eval_sipma91_bb0_in/2 0.05/0.24 * CE 2 is refined into CE [20] 0.05/0.24 * CE 3 is refined into CE [21,22] 0.05/0.24 0.05/0.24 0.05/0.24 ### Cost equations --> "Loop" of eval_sipma91_bb0_in/2 0.05/0.24 * CEs [20] --> Loop 20 0.05/0.24 * CEs [22] --> Loop 21 0.05/0.24 * CEs [21] --> Loop 22 0.05/0.24 0.05/0.24 ### Ranking functions of CR eval_sipma91_bb0_in(V_x,B) 0.05/0.24 0.05/0.24 #### Partial ranking functions of CR eval_sipma91_bb0_in(V_x,B) 0.05/0.24 0.05/0.24 0.05/0.24 ### Specialization of cost equations eval_sipma91_start/2 0.05/0.24 * CE 1 is refined into CE [23,24,25] 0.05/0.24 0.05/0.24 0.05/0.24 ### Cost equations --> "Loop" of eval_sipma91_start/2 0.05/0.24 * CEs [25] --> Loop 23 0.05/0.24 * CEs [24] --> Loop 24 0.05/0.24 * CEs [23] --> Loop 25 0.05/0.24 0.05/0.24 ### Ranking functions of CR eval_sipma91_start(V_x,B) 0.05/0.24 0.05/0.24 #### Partial ranking functions of CR eval_sipma91_start(V_x,B) 0.05/0.24 0.05/0.24 0.05/0.24 Computing Bounds 0.05/0.24 ===================================== 0.05/0.24 0.05/0.24 #### Cost of chains of eval_sipma91_bb1_in(V_y2_0,V_y1_0,B,C,D): 0.05/0.24 * Chain [[11],12]: 1*it(11)+0 0.05/0.24 Such that:it(11) =< -V_y1_0/11+101/11 0.05/0.24 0.05/0.24 with precondition: [B=3,D+11*V_y2_0=11*C+V_y1_0,V_y2_0>=1,C>=V_y2_0+1,V_y1_0+11*C>=11*V_y2_0+101,11*V_y2_0+111>=11*C+V_y1_0] 0.05/0.24 0.05/0.24 0.05/0.24 #### Cost of chains of eval_sipma91_bb3_in(V_y2_1,V_y1_1,B): 0.05/0.24 * Chain [[13,14],15,16]: 1*it(13)+1*it(14)+1 0.05/0.24 Such that:it(13) =< V_y2_1 0.05/0.24 aux(3) =< -V_y1_1+111 0.05/0.24 it(14) =< it(13)*9+aux(3) 0.05/0.24 0.05/0.24 with precondition: [B=2,V_y2_1>=2] 0.05/0.24 0.05/0.24 * Chain [16]: 0 0.05/0.24 with precondition: [B=2,1>=V_y2_1] 0.05/0.24 0.05/0.24 * Chain [15,16]: 1 0.05/0.24 with precondition: [V_y2_1=2,B=2,V_y1_1>=111] 0.05/0.24 0.05/0.24 0.05/0.24 #### Cost of chains of eval_sipma91_bb1_in_loop_cont(A,B,C,D): 0.05/0.24 * Chain [19]: 1 0.05/0.24 with precondition: [A=3,B=2,C>=111] 0.05/0.24 0.05/0.24 * Chain [18]: 0 0.05/0.24 with precondition: [A=3,1>=B] 0.05/0.24 0.05/0.24 * Chain [17]: 1*s(1)+1*s(3)+1 0.05/0.24 Such that:s(1) =< B 0.05/0.24 s(2) =< -C+111 0.05/0.24 s(3) =< s(1)*9+s(2) 0.05/0.24 0.05/0.24 with precondition: [A=3,B>=2] 0.05/0.24 0.05/0.24 0.05/0.24 #### Cost of chains of eval_sipma91_bb0_in(V_x,B): 0.05/0.24 * Chain [22]: 1*s(4)+1 0.05/0.24 Such that:s(4) =< 1/11 0.05/0.24 0.05/0.24 with precondition: [V_x=100] 0.05/0.24 0.05/0.24 * Chain [21]: 1*s(5)+1*s(6)+1*s(8)+1 0.05/0.24 Such that:s(7) =< 10 0.05/0.24 s(5) =< -V_x/11+101/11 0.05/0.24 s(6) =< -V_x/11+122/11 0.05/0.24 aux(5) =< -V_x+122 0.05/0.24 s(6) =< aux(5) 0.05/0.24 s(7) =< aux(5) 0.05/0.24 s(8) =< s(6)*9+s(7) 0.05/0.24 0.05/0.24 with precondition: [100>=V_x] 0.05/0.24 0.05/0.24 * Chain [20]: 0 0.05/0.24 with precondition: [V_x>=101] 0.05/0.24 0.05/0.24 0.05/0.24 #### Cost of chains of eval_sipma91_start(V_x,B): 0.05/0.24 * Chain [25]: 1*s(9)+1 0.05/0.24 Such that:s(9) =< 1/11 0.05/0.24 0.05/0.24 with precondition: [V_x=100] 0.05/0.24 0.05/0.24 * Chain [24]: 1*s(11)+1*s(12)+1*s(14)+1 0.05/0.24 Such that:s(10) =< 10 0.05/0.24 s(13) =< -V_x+122 0.05/0.24 s(11) =< -V_x/11+101/11 0.05/0.24 s(12) =< -V_x/11+122/11 0.05/0.24 s(12) =< s(13) 0.05/0.24 s(10) =< s(13) 0.05/0.24 s(14) =< s(12)*9+s(10) 0.05/0.24 0.05/0.24 with precondition: [100>=V_x] 0.05/0.24 0.05/0.24 * Chain [23]: 0 0.05/0.24 with precondition: [V_x>=101] 0.05/0.24 0.05/0.24 0.05/0.24 Closed-form bounds of eval_sipma91_start(V_x,B): 0.05/0.24 ------------------------------------- 0.05/0.24 * Chain [25] with precondition: [V_x=100] 0.05/0.24 - Upper bound: 12/11 0.05/0.24 - Complexity: constant 0.05/0.24 * Chain [24] with precondition: [100>=V_x] 0.05/0.24 - Upper bound: -V_x+1442/11 0.05/0.24 - Complexity: n 0.05/0.24 * Chain [23] with precondition: [V_x>=101] 0.05/0.24 - Upper bound: 0 0.05/0.24 - Complexity: constant 0.05/0.24 0.05/0.24 ### Maximum cost of eval_sipma91_start(V_x,B): max([12/11,nat(-V_x/11+101/11)+11+nat(-V_x/11+122/11)*10]) 0.05/0.24 Asymptotic class: n 0.05/0.24 * Total analysis performed in 160 ms. 0.05/0.24 0.05/0.34 EOF