0.03/0.26 WORST_CASE(?,O(n^2)) 0.03/0.26 0.03/0.26 Preprocessing Cost Relations 0.03/0.26 ===================================== 0.03/0.26 0.03/0.26 #### Computed strongly connected components 0.03/0.26 0. recursive : [evalrealselectbb1in/4,evalrealselectbb4in/4] 0.03/0.26 1. recursive : [evalrealselectbb4in_loop_cont/7,evalrealselectbb5in/6,evalrealselectbb6in/6,evalrealselectbbin/6] 0.03/0.26 2. non_recursive : [evalrealselectstop/4] 0.03/0.26 3. non_recursive : [evalrealselectreturnin/4] 0.03/0.26 4. non_recursive : [exit_location/1] 0.03/0.26 5. non_recursive : [evalrealselectbb6in_loop_cont/5] 0.03/0.26 6. non_recursive : [evalrealselectentryin/4] 0.03/0.26 7. non_recursive : [evalrealselectstart/4] 0.03/0.26 0.03/0.26 #### Obtained direct recursion through partial evaluation 0.03/0.26 0. SCC is partially evaluated into evalrealselectbb4in/4 0.03/0.26 1. SCC is partially evaluated into evalrealselectbb6in/6 0.03/0.26 2. SCC is completely evaluated into other SCCs 0.03/0.26 3. SCC is completely evaluated into other SCCs 0.03/0.26 4. SCC is completely evaluated into other SCCs 0.03/0.26 5. SCC is partially evaluated into evalrealselectbb6in_loop_cont/5 0.03/0.26 6. SCC is partially evaluated into evalrealselectentryin/4 0.03/0.26 7. SCC is partially evaluated into evalrealselectstart/4 0.03/0.26 0.03/0.26 Control-Flow Refinement of Cost Relations 0.03/0.26 ===================================== 0.03/0.26 0.03/0.26 ### Specialization of cost equations evalrealselectbb4in/4 0.03/0.26 * CE 11 is refined into CE [12] 0.03/0.26 * CE 10 is refined into CE [13] 0.03/0.26 * CE 9 is refined into CE [14] 0.03/0.26 0.03/0.26 0.03/0.26 ### Cost equations --> "Loop" of evalrealselectbb4in/4 0.03/0.26 * CEs [14] --> Loop 12 0.03/0.26 * CEs [12] --> Loop 13 0.03/0.26 * CEs [13] --> Loop 14 0.03/0.26 0.03/0.26 ### Ranking functions of CR evalrealselectbb4in(B,C,F,G) 0.03/0.26 * RF of phase [12]: [B-C] 0.03/0.26 0.03/0.26 #### Partial ranking functions of CR evalrealselectbb4in(B,C,F,G) 0.03/0.26 * Partial RF of phase [12]: 0.03/0.26 - RF of loop [12:1]: 0.03/0.26 B-C 0.03/0.26 0.03/0.26 0.03/0.26 ### Specialization of cost equations evalrealselectbb6in/6 0.03/0.26 * CE 5 is refined into CE [15] 0.03/0.26 * CE 3 is refined into CE [16,17] 0.03/0.26 * CE 6 is refined into CE [18] 0.03/0.26 * CE 4 is refined into CE [19] 0.03/0.26 0.03/0.26 0.03/0.26 ### Cost equations --> "Loop" of evalrealselectbb6in/6 0.03/0.26 * CEs [19] --> Loop 15 0.03/0.26 * CEs [15] --> Loop 16 0.03/0.26 * CEs [16,17] --> Loop 17 0.03/0.26 * CEs [18] --> Loop 18 0.03/0.26 0.03/0.26 ### Ranking functions of CR evalrealselectbb6in(A,B,C,F,G,H) 0.03/0.26 * RF of phase [15]: [-A+B-1] 0.03/0.26 0.03/0.26 #### Partial ranking functions of CR evalrealselectbb6in(A,B,C,F,G,H) 0.03/0.26 * Partial RF of phase [15]: 0.03/0.26 - RF of loop [15:1]: 0.03/0.26 -A+B-1 0.03/0.26 0.03/0.26 0.03/0.26 ### Specialization of cost equations evalrealselectbb6in_loop_cont/5 0.03/0.26 * CE 7 is refined into CE [20] 0.03/0.26 * CE 8 is refined into CE [21] 0.03/0.26 0.03/0.26 0.03/0.26 ### Cost equations --> "Loop" of evalrealselectbb6in_loop_cont/5 0.03/0.26 * CEs [20] --> Loop 19 0.03/0.26 * CEs [21] --> Loop 20 0.03/0.26 0.03/0.26 ### Ranking functions of CR evalrealselectbb6in_loop_cont(A,B,C,D,E) 0.03/0.26 0.03/0.26 #### Partial ranking functions of CR evalrealselectbb6in_loop_cont(A,B,C,D,E) 0.03/0.26 0.03/0.26 0.03/0.26 ### Specialization of cost equations evalrealselectentryin/4 0.03/0.26 * CE 2 is refined into CE [22,23,24,25,26] 0.03/0.26 0.03/0.26 0.03/0.26 ### Cost equations --> "Loop" of evalrealselectentryin/4 0.03/0.26 * CEs [24] --> Loop 21 0.03/0.26 * CEs [23,26] --> Loop 22 0.03/0.26 * CEs [25] --> Loop 23 0.03/0.26 * CEs [22] --> Loop 24 0.03/0.26 0.03/0.26 ### Ranking functions of CR evalrealselectentryin(A,B,C,F) 0.03/0.26 0.03/0.26 #### Partial ranking functions of CR evalrealselectentryin(A,B,C,F) 0.03/0.26 0.03/0.26 0.03/0.26 ### Specialization of cost equations evalrealselectstart/4 0.03/0.26 * CE 1 is refined into CE [27,28,29,30] 0.03/0.26 0.03/0.26 0.03/0.26 ### Cost equations --> "Loop" of evalrealselectstart/4 0.03/0.26 * CEs [30] --> Loop 25 0.03/0.26 * CEs [29] --> Loop 26 0.03/0.26 * CEs [28] --> Loop 27 0.03/0.26 * CEs [27] --> Loop 28 0.03/0.26 0.03/0.26 ### Ranking functions of CR evalrealselectstart(A,B,C,F) 0.03/0.26 0.03/0.26 #### Partial ranking functions of CR evalrealselectstart(A,B,C,F) 0.03/0.26 0.03/0.26 0.03/0.26 Computing Bounds 0.03/0.26 ===================================== 0.03/0.26 0.03/0.26 #### Cost of chains of evalrealselectbb4in(B,C,F,G): 0.03/0.26 * Chain [[12],14]: 1*it(12)+0 0.03/0.26 Such that:it(12) =< -C+G 0.03/0.26 0.03/0.26 with precondition: [F=2,B=G,C>=1,B>=C+1] 0.03/0.26 0.03/0.26 * Chain [[12],13]: 1*it(12)+0 0.03/0.26 Such that:it(12) =< B-C 0.03/0.26 0.03/0.26 with precondition: [F=3,C>=1,B>=C+1] 0.03/0.26 0.03/0.26 * Chain [13]: 0 0.03/0.26 with precondition: [F=3,B>=2,C>=1,B>=C] 0.03/0.26 0.03/0.26 0.03/0.26 #### Cost of chains of evalrealselectbb6in(A,B,C,F,G,H): 0.03/0.26 * Chain [[15],18]: 1*it(15)+1*s(3)+0 0.03/0.26 Such that:aux(1) =< B 0.03/0.26 aux(3) =< -A+B 0.03/0.26 it(15) =< aux(3) 0.03/0.26 aux(1) =< aux(3) 0.03/0.26 s(3) =< it(15)*aux(1) 0.03/0.26 0.03/0.26 with precondition: [F=3,A>=0,B>=A+2] 0.03/0.26 0.03/0.26 * Chain [[15],17]: 2*it(15)+1*s(3)+0 0.03/0.26 Such that:aux(1) =< B 0.03/0.26 aux(4) =< -A+B 0.03/0.26 it(15) =< aux(4) 0.03/0.26 aux(1) =< aux(4) 0.03/0.26 s(3) =< it(15)*aux(1) 0.03/0.26 0.03/0.26 with precondition: [F=3,A>=0,B>=A+3] 0.03/0.26 0.03/0.26 * Chain [[15],16]: 1*it(15)+1*s(3)+0 0.03/0.26 Such that:it(15) =< -A+G 0.03/0.26 aux(2) =< -A+G+1 0.03/0.26 aux(1) =< G+1 0.03/0.26 aux(1) =< aux(2) 0.03/0.26 it(15) =< aux(2) 0.03/0.26 s(3) =< it(15)*aux(1) 0.03/0.26 0.03/0.26 with precondition: [F=4,B=G+1,B=H,A>=0,B>=A+2] 0.03/0.26 0.03/0.26 * Chain [18]: 0 0.03/0.26 with precondition: [F=3,A>=0] 0.03/0.26 0.03/0.26 * Chain [17]: 1*s(4)+0 0.03/0.26 Such that:s(4) =< -A+B 0.03/0.26 0.03/0.26 with precondition: [F=3,A>=0,B>=A+2] 0.03/0.26 0.03/0.26 * Chain [16]: 0 0.03/0.26 with precondition: [F=4,H=C,A=G,A>=0,A+1>=B] 0.03/0.26 0.03/0.26 0.03/0.26 #### Cost of chains of evalrealselectbb6in_loop_cont(A,B,C,D,E): 0.03/0.26 * Chain [20]: 0 0.03/0.26 with precondition: [A=3] 0.03/0.26 0.03/0.26 * Chain [19]: 0 0.03/0.26 with precondition: [A=4] 0.03/0.26 0.03/0.26 0.03/0.26 #### Cost of chains of evalrealselectentryin(A,B,C,F): 0.03/0.26 * Chain [24]: 0 0.03/0.26 with precondition: [] 0.03/0.26 0.03/0.26 * Chain [23]: 0 0.03/0.26 with precondition: [1>=B] 0.03/0.26 0.03/0.26 * Chain [22]: 3*s(12)+2*s(13)+0 0.03/0.26 Such that:aux(8) =< B 0.03/0.26 s(12) =< aux(8) 0.03/0.26 s(13) =< s(12)*aux(8) 0.03/0.26 0.03/0.26 with precondition: [B>=2] 0.03/0.26 0.03/0.26 * Chain [21]: 2*s(20)+1*s(21)+0 0.03/0.26 Such that:aux(9) =< B 0.03/0.26 s(20) =< aux(9) 0.03/0.26 s(21) =< s(20)*aux(9) 0.03/0.26 0.03/0.26 with precondition: [B>=3] 0.03/0.26 0.03/0.26 0.03/0.26 #### Cost of chains of evalrealselectstart(A,B,C,F): 0.03/0.26 * Chain [28]: 0 0.03/0.26 with precondition: [] 0.03/0.26 0.03/0.26 * Chain [27]: 0 0.03/0.26 with precondition: [1>=B] 0.03/0.26 0.03/0.26 * Chain [26]: 3*s(23)+2*s(24)+0 0.03/0.26 Such that:s(22) =< B 0.03/0.26 s(23) =< s(22) 0.03/0.26 s(24) =< s(23)*s(22) 0.03/0.26 0.03/0.26 with precondition: [B>=2] 0.03/0.26 0.03/0.26 * Chain [25]: 2*s(26)+1*s(27)+0 0.03/0.26 Such that:s(25) =< B 0.03/0.26 s(26) =< s(25) 0.03/0.26 s(27) =< s(26)*s(25) 0.03/0.26 0.03/0.26 with precondition: [B>=3] 0.03/0.26 0.03/0.26 0.03/0.26 Closed-form bounds of evalrealselectstart(A,B,C,F): 0.03/0.26 ------------------------------------- 0.03/0.26 * Chain [28] with precondition: [] 0.03/0.26 - Upper bound: 0 0.03/0.26 - Complexity: constant 0.03/0.26 * Chain [27] with precondition: [1>=B] 0.03/0.26 - Upper bound: 0 0.03/0.26 - Complexity: constant 0.03/0.26 * Chain [26] with precondition: [B>=2] 0.03/0.26 - Upper bound: 2*B*B+3*B 0.03/0.26 - Complexity: n^2 0.03/0.26 * Chain [25] with precondition: [B>=3] 0.03/0.26 - Upper bound: 2*B+B*B 0.03/0.26 - Complexity: n^2 0.03/0.26 0.03/0.26 ### Maximum cost of evalrealselectstart(A,B,C,F): nat(B)*nat(B)+nat(B)*2+(nat(B)*nat(B)+nat(B)) 0.03/0.26 Asymptotic class: n^2 0.03/0.26 * Total analysis performed in 193 ms. 0.03/0.26 0.03/0.36 EOF