0.03/0.24 WORST_CASE(?,O(n^1)) 0.03/0.24 0.03/0.24 Preprocessing Cost Relations 0.03/0.24 ===================================== 0.03/0.24 0.03/0.24 #### Computed strongly connected components 0.03/0.24 0. recursive : [evalDis1bb1in/7,evalDis1bb2in/7,evalDis1bb3in/7,evalDis1bbin/7] 0.03/0.24 1. non_recursive : [evalDis1stop/5] 0.03/0.24 2. non_recursive : [evalDis1returnin/5] 0.03/0.24 3. non_recursive : [exit_location/1] 0.03/0.24 4. non_recursive : [evalDis1bb3in_loop_cont/6] 0.03/0.24 5. non_recursive : [evalDis1entryin/5] 0.03/0.24 6. non_recursive : [evalDis1start/5] 0.03/0.24 0.03/0.24 #### Obtained direct recursion through partial evaluation 0.03/0.24 0. SCC is partially evaluated into evalDis1bb3in/7 0.03/0.24 1. SCC is completely evaluated into other SCCs 0.03/0.24 2. SCC is completely evaluated into other SCCs 0.03/0.24 3. SCC is completely evaluated into other SCCs 0.03/0.24 4. SCC is partially evaluated into evalDis1bb3in_loop_cont/6 0.03/0.24 5. SCC is partially evaluated into evalDis1entryin/5 0.03/0.24 6. SCC is partially evaluated into evalDis1start/5 0.03/0.24 0.03/0.24 Control-Flow Refinement of Cost Relations 0.03/0.24 ===================================== 0.03/0.24 0.03/0.24 ### Specialization of cost equations evalDis1bb3in/7 0.03/0.24 * CE 6 is refined into CE [9] 0.03/0.24 * CE 5 is refined into CE [10] 0.03/0.24 * CE 3 is refined into CE [11] 0.03/0.24 * CE 4 is refined into CE [12] 0.03/0.24 0.03/0.24 0.03/0.24 ### Cost equations --> "Loop" of evalDis1bb3in/7 0.03/0.24 * CEs [11] --> Loop 9 0.03/0.24 * CEs [12] --> Loop 10 0.03/0.24 * CEs [9] --> Loop 11 0.03/0.24 * CEs [10] --> Loop 12 0.03/0.24 0.03/0.24 ### Ranking functions of CR evalDis1bb3in(A,B,C,D,E,F,G) 0.03/0.24 * RF of phase [9]: [C-D] 0.03/0.24 * RF of phase [10]: [A-B] 0.03/0.24 0.03/0.24 #### Partial ranking functions of CR evalDis1bb3in(A,B,C,D,E,F,G) 0.03/0.24 * Partial RF of phase [9]: 0.03/0.24 - RF of loop [9:1]: 0.03/0.24 C-D 0.03/0.24 * Partial RF of phase [10]: 0.03/0.24 - RF of loop [10:1]: 0.03/0.24 A-B 0.03/0.24 0.03/0.24 0.03/0.24 ### Specialization of cost equations evalDis1bb3in_loop_cont/6 0.03/0.24 * CE 8 is refined into CE [13] 0.03/0.24 * CE 7 is refined into CE [14] 0.03/0.24 0.03/0.24 0.03/0.24 ### Cost equations --> "Loop" of evalDis1bb3in_loop_cont/6 0.03/0.24 * CEs [13] --> Loop 13 0.03/0.24 * CEs [14] --> Loop 14 0.03/0.24 0.03/0.24 ### Ranking functions of CR evalDis1bb3in_loop_cont(A,B,C,D,E,F) 0.03/0.24 0.03/0.24 #### Partial ranking functions of CR evalDis1bb3in_loop_cont(A,B,C,D,E,F) 0.03/0.24 0.03/0.24 0.03/0.24 ### Specialization of cost equations evalDis1entryin/5 0.03/0.24 * CE 2 is refined into CE [15,16,17,18,19,20] 0.03/0.24 0.03/0.24 0.03/0.24 ### Cost equations --> "Loop" of evalDis1entryin/5 0.03/0.24 * CEs [15] --> Loop 15 0.03/0.24 * CEs [17,19] --> Loop 16 0.03/0.24 * CEs [16,20] --> Loop 17 0.03/0.24 * CEs [18] --> Loop 18 0.03/0.24 0.03/0.24 ### Ranking functions of CR evalDis1entryin(A,B,C,D,E) 0.03/0.24 0.03/0.24 #### Partial ranking functions of CR evalDis1entryin(A,B,C,D,E) 0.03/0.24 0.03/0.24 0.03/0.24 ### Specialization of cost equations evalDis1start/5 0.03/0.24 * CE 1 is refined into CE [21,22,23,24] 0.03/0.24 0.03/0.24 0.03/0.24 ### Cost equations --> "Loop" of evalDis1start/5 0.03/0.24 * CEs [24] --> Loop 19 0.03/0.24 * CEs [23] --> Loop 20 0.03/0.24 * CEs [22] --> Loop 21 0.03/0.24 * CEs [21] --> Loop 22 0.03/0.24 0.03/0.24 ### Ranking functions of CR evalDis1start(A,B,C,D,E) 0.03/0.24 0.03/0.24 #### Partial ranking functions of CR evalDis1start(A,B,C,D,E) 0.03/0.24 0.03/0.24 0.03/0.24 Computing Bounds 0.03/0.24 ===================================== 0.03/0.24 0.03/0.24 #### Cost of chains of evalDis1bb3in(A,B,C,D,E,F,G): 0.03/0.24 * Chain [[10],12]: 1*it(10)+0 0.03/0.24 Such that:it(10) =< A-B 0.03/0.24 0.03/0.24 with precondition: [E=2,A=F,D=G,A>=B+1,D>=C] 0.03/0.24 0.03/0.24 * Chain [[10],11]: 1*it(10)+0 0.03/0.24 Such that:it(10) =< A-B 0.03/0.24 0.03/0.24 with precondition: [E=3,A>=B+1,D>=C] 0.03/0.24 0.03/0.24 * Chain [[9],[10],12]: 1*it(9)+1*it(10)+0 0.03/0.24 Such that:it(10) =< A-B 0.03/0.24 it(9) =< C-D 0.03/0.24 0.03/0.24 with precondition: [E=2,A=F,C=G,A>=B+1,C>=D+1] 0.03/0.24 0.03/0.24 * Chain [[9],[10],11]: 1*it(9)+1*it(10)+0 0.03/0.24 Such that:it(10) =< A-B 0.03/0.24 it(9) =< C-D 0.03/0.24 0.03/0.24 with precondition: [E=3,A>=B+1,C>=D+1] 0.03/0.24 0.03/0.24 * Chain [[9],11]: 1*it(9)+0 0.03/0.24 Such that:it(9) =< C-D 0.03/0.24 0.03/0.24 with precondition: [E=3,A>=B+1,C>=D+1] 0.03/0.24 0.03/0.24 * Chain [12]: 0 0.03/0.24 with precondition: [E=2,G=D,B=F,B>=A] 0.03/0.24 0.03/0.24 * Chain [11]: 0 0.03/0.24 with precondition: [E=3] 0.03/0.24 0.03/0.24 0.03/0.24 #### Cost of chains of evalDis1bb3in_loop_cont(A,B,C,D,E,F): 0.03/0.24 * Chain [14]: 0 0.03/0.24 with precondition: [A=2] 0.03/0.24 0.03/0.24 * Chain [13]: 0 0.03/0.24 with precondition: [A=3] 0.03/0.24 0.03/0.24 0.03/0.24 #### Cost of chains of evalDis1entryin(A,B,C,D,E): 0.03/0.24 * Chain [18]: 0 0.03/0.24 with precondition: [] 0.03/0.24 0.03/0.24 * Chain [17]: 2*s(4)+3*s(5)+0 0.03/0.24 Such that:aux(2) =< -A+B 0.03/0.24 aux(3) =< -C+D 0.03/0.24 s(4) =< aux(2) 0.03/0.24 s(5) =< aux(3) 0.03/0.24 0.03/0.24 with precondition: [B>=A+1,D>=C+1] 0.03/0.24 0.03/0.24 * Chain [16]: 2*s(9)+0 0.03/0.24 Such that:aux(4) =< -A+B 0.03/0.24 s(9) =< aux(4) 0.03/0.24 0.03/0.24 with precondition: [B>=A+1,C>=D] 0.03/0.24 0.03/0.24 * Chain [15]: 0 0.03/0.24 with precondition: [A>=B] 0.03/0.24 0.03/0.24 0.03/0.24 #### Cost of chains of evalDis1start(A,B,C,D,E): 0.03/0.24 * Chain [22]: 0 0.03/0.24 with precondition: [] 0.03/0.24 0.03/0.24 * Chain [21]: 2*s(13)+3*s(14)+0 0.03/0.24 Such that:s(11) =< -A+B 0.03/0.24 s(12) =< -C+D 0.03/0.24 s(13) =< s(11) 0.03/0.24 s(14) =< s(12) 0.03/0.24 0.03/0.24 with precondition: [B>=A+1,D>=C+1] 0.03/0.24 0.03/0.24 * Chain [20]: 2*s(16)+0 0.03/0.24 Such that:s(15) =< -A+B 0.03/0.24 s(16) =< s(15) 0.03/0.24 0.03/0.24 with precondition: [B>=A+1,C>=D] 0.03/0.24 0.03/0.24 * Chain [19]: 0 0.03/0.24 with precondition: [A>=B] 0.03/0.24 0.03/0.24 0.03/0.24 Closed-form bounds of evalDis1start(A,B,C,D,E): 0.03/0.24 ------------------------------------- 0.03/0.24 * Chain [22] with precondition: [] 0.03/0.24 - Upper bound: 0 0.03/0.24 - Complexity: constant 0.03/0.24 * Chain [21] with precondition: [B>=A+1,D>=C+1] 0.03/0.24 - Upper bound: -2*A+2*B-3*C+3*D 0.03/0.24 - Complexity: n 0.03/0.24 * Chain [20] with precondition: [B>=A+1,C>=D] 0.03/0.24 - Upper bound: -2*A+2*B 0.03/0.24 - Complexity: n 0.03/0.24 * Chain [19] with precondition: [A>=B] 0.03/0.24 - Upper bound: 0 0.03/0.24 - Complexity: constant 0.03/0.24 0.03/0.24 ### Maximum cost of evalDis1start(A,B,C,D,E): nat(-C+D)*3+nat(-A+B)*2 0.03/0.24 Asymptotic class: n 0.03/0.24 * Total analysis performed in 180 ms. 0.03/0.24 0.03/0.35 EOF